Details Example for PROC VARMAX
/*--------------------------------------------------------------
SAS Sample Library
Name: vardt.sas
Description: Example program from SAS/ETS User's Guide,
The VARMAX Procedure
Title: Details Example for PROC VARMAX
Product: SAS/ETS Software
Keys: Vector AutoRegressive Moving-Average
processes with eXogenous regressors
PROC: VARMAX
Notes:
--------------------------------------------------------------*/
proc iml;
sig = {1.0 0.5, 0.5 1.25};
phi = {1.2 -0.5, 0.6 0.3};
/* simulate the vector time series */
call varmasim(y,phi) sigma = sig n = 100 seed = 34657;
cn = {'y1' 'y2'};
create simul1 from y[colname=cn];
append from y;
quit;
data simul1;
set simul1;
date = intnx( 'year', '01jan1900'd, _n_-1 );
format date year4.;
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint print=(dynamic);
run;
data grunfeld;
input year y1 y2 y3 x1 x2 x3;
label y1='Gross Investment GE'
y2='Capital Stock Lagged GE'
y3='Value of Outstanding Shares GE Lagged'
x1='Gross Investment W'
x2='Capital Stock Lagged W'
x3='Value of Outstanding Shares Lagged W';
datalines;
1935 33.1 1170.6 97.8 12.93 191.5 1.8
1936 45.0 2015.8 104.4 25.90 516.0 .8
1937 77.2 2803.3 118.0 35.05 729.0 7.4
1938 44.6 2039.7 156.2 22.89 560.4 18.1
1939 48.1 2256.2 172.6 18.84 519.9 23.5
1940 74.4 2132.2 186.6 28.57 628.5 26.5
1941 113.0 1834.1 220.9 48.51 537.1 36.2
1942 91.9 1588.0 287.8 43.34 561.2 60.8
1943 61.3 1749.4 319.9 37.02 617.2 84.4
1944 56.8 1687.2 321.3 37.81 626.7 91.2
1945 93.6 2007.7 319.6 39.27 737.2 92.4
1946 159.9 2208.3 346.0 53.46 760.5 86.0
1947 147.2 1656.7 456.4 55.56 581.4 111.1
1948 146.3 1604.4 543.4 49.56 662.3 130.6
1949 98.3 1431.8 618.3 32.04 583.8 141.8
1950 93.5 1610.5 647.4 32.24 635.2 136.7
1951 135.2 1819.4 671.3 54.38 723.8 129.7
1952 157.3 2079.7 726.1 71.78 864.1 145.5
1953 179.5 2371.6 800.3 90.08 1193.5 174.8
1954 189.6 2759.9 888.9 68.60 1188.9 213.5
;
proc varmax data=grunfeld plot=impulse;
model y1-y3 = x1 x2 / p=1 lagmax=5
printform=univariate
print=(impulsx=(all) estimates);
run;
proc varmax data=simul1 plot=impulse;
model y1 y2 / p=1 noint lagmax=5
print=(impulse=(all))
printform=univariate;
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint lagmax=5
printform=both
print=(decompose(5) impulse=(all) covpe(5));
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint print=(decompose(15))
printform=univariate;
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint lagmax=3 print=(corry)
printform=univariate;
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint lagmax=3
printform=univariate
print=(corry parcoef pcorr
pcancorr roots);
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint lagmax=3
print=(pcorr)
printform=univariate;
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint lagmax=3 print=(pcancorr);
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint minic=(p=3 q=3);
run;
proc varmax data=simul1;
model y1 y2 / p=1 noint print=(roots);
run;
proc varmax data=grunfeld;
model y1 = x1, y2 = x2, y3 / p=1 print=(estimates);
run;
data One;
format date date9.;
do obs = 1 to 100;
date=intnx('quarter','01Jan1990'd,obs-1);
y1 = normal(1); y2 = normal(1); x = normal(1);
output;
end;
run;
proc varmax data=One;
model y1 y2 = x / nseason=4 xlag=2 p=1 trend=quad;
run;
data Two;
set one;
y1lag1 = lag(y1); y2lag1 = lag(y2);
xlag1 = lag(x); xlag2 = lag2(x);
if (obs>2) then do;
ltrend = obs - 2;
qtrend = ltrend * ltrend;
const = 1;
if (mod(ltrend-2,4)=0) then sd1 = 1;
else sd1 = 0;
if (mod(ltrend-3,4)=0) then sd2 = 1;
else sd2 = 0;
if (mod(ltrend-4,4)=0) then sd3 = 1;
else sd3 = 0;
end;
run;
proc reg data=Two(firstobs=3);
model y1 = const sd1 sd2 sd3 ltrend qtrend
x xlag1 xlag2 y1lag1 y2lag1 / noint;
model y2 = const sd1 sd2 sd3 ltrend qtrend
x xlag1 xlag2 y1lag1 y2lag1 / noint;
run;
proc print data=Two(obs=11);
var date const sd1 sd2 sd3 ltrend qtrend;
run;
proc iml;
sig = {1.0 0.5, 0.5 1.25};
phi = {1.2 -0.5, 0.6 0.3};
theta = {0.5 -0.2, 0.1 0.3};
/* to simulate the vector time series */
call varmasim(y,phi,theta) sigma=sig n=100 seed=34657;
cn = {'y1' 'y2'};
create simul3 from y[colname=cn];
append from y;
run;
proc varmax data=simul3;
nloptions tech=qn;
model y1 y2 / p=1 q=1 noint print=(estimates);
run;
proc iml;
sig = 100*i(2);
phi = {-0.2 0.1, 0.5 0.2, 0.8 0.7, -0.4 0.6};
call varmasim(y,phi) sigma=sig n=100 initial=0
seed=45876;
cn = {'y1' 'y2'};
create simul2 from y[colname=cn];
append from y;
quit;
data simul2;
set simul2;
date = intnx( 'year', '01jan1900'd, _n_-1 );
format date year4. ;
run;
proc varmax data=simul2;
model y1 y2 / p=2 cointtest=(sw);
run;
proc varmax data=simul2;
model y1 y2 / p=2 cointtest=(johansen=(normalize=y1));
run;
proc varmax data=simul2;
model y1 y2 / p=2 print=(estimates);
cointeg rank=1 normalize=y1 ectrend;
run;
proc varmax data=simul2;
model y1 y2 / p=2 print=(estimates);
cointeg rank=1 normalize=y1;
run;
proc varmax data=simul2;
model y1 y2 / p=2;
cointeg rank=1 h=(1,-2) normalize=y1;
run;
proc varmax data=simul2;
model y1 y2 / p=2;
cointeg rank=1 exogeneity normalize=y1;
run;
proc iml;
alpha = { 1, 1}; * alphaOrthogonal = { 1, -1};
beta = { 1, -0.5}; * betaOrthogonal = { 1, 2};
* alphaOrthogonal' * phiStar * betaOrthogonal = 0;
phiStar = { 1 0, 0 0.5};
A1 = 2 * I(2) + alpha * beta` - phiStar;
A2 = phiStar - I(2);
phi = A1 // A2;
sig = I(2);
/* to simulate the vector time series */
call varmasim(y,phi) sigma=sig n=200 seed=2;
cn = {'y1' 'y2'};
create simul4 from y[colname=cn];
append from y;
close;
quit;
proc varmax data=simul4;
model y1 y2 /noint p=2 cointtest=(johansen=(iorder=2));
run;
data garch;
retain seed 16587;
esq1 = 0; esq2 = 0;
ly1 = 0; ly2 = 0;
do i = 1 to 1000;
ht = 6.25 + 0.5*esq1;
call rannor(seed,ehat);
e1 = sqrt(ht)*ehat;
ht = 1.25 + 0.7*esq2;
call rannor(seed,ehat);
e2 = sqrt(ht)*ehat;
y1 = 2 + 1.2*ly1 - 0.5*ly2 + e1;
y2 = 4 + 0.6*ly1 + 0.3*ly2 + e2;
if i>500 then output;
esq1 = e1*e1; esq2 = e2*e2;
ly1 = y1; ly2 = y2;
end;
keep y1 y2;
run;
proc varmax data=garch;
model y1 y2 / p=1
print=(roots estimates diagnose);
garch q=1;
nloptions tech=qn;
run;
data VARFIMA1D1;
time = _N_;
input y1 y2;
datalines;
1.495250048 2.694910375
4.503081454 1.42319642
6.915384631 2.360965963
6.877565437 1.10123227
3.35165676 -0.628103004
1.097675845 -0.39020643
-1.662975625 2.323144163
-4.174778734 0.187445009
-3.87492887 0.901060314
-3.670495506 0.258036933
-4.086794756 -0.052344546
-3.312092427 2.238445627
-2.55722417 2.305827824
-1.494388884 0.97630964
-3.320508791 -0.311914751
-5.141007608 0.250869668
-7.714073832 2.853245569
-8.393932831 2.556290289
-9.012876486 0.637755281
-6.975249018 -0.073649393
-5.01979586 2.842448561
0.150350338 6.27972031
0.627408747 5.915786444
-0.450849639 3.406840767
-3.16798044 3.611555664
-5.332107147 2.568168142
-5.654875114 0.082762888
-3.915662832 3.458256209
-1.834319706 1.702862177
1.351844711 0.976837127
-1.0456764 -0.571033364
-1.351342109 -1.472316382
-0.530356083 -0.432406672
-3.317707864 -0.126330969
-3.618388578 -0.89715997
-1.709143909 0.48328072
1.231456814 1.716857243
6.267868064 -1.080694975
7.092051069 2.154666137
7.086824932 2.386927028
8.109313153 -1.619138987
7.64722742 -1.391139967
6.540758359 -1.013773277
9.689321516 1.870234479
9.646701177 0.459082662
8.51168746 0.777717697
7.436913844 -0.519965884
7.410491333 -1.51469051
6.472433058 0.478092055
6.17527226 0.798079368
5.626937234 0.094915172
5.598662995 2.051144157
10.06896715 0.801583197
10.71383357 4.65722961
14.50664716 1.709090713
14.58085035 1.934682743
14.87295031 1.90425192
13.93351437 0.80088361
15.60189108 2.923200064
14.47432724 1.031869377
14.57121817 -1.173995627
14.01268119 -4.624380842
14.68591628 -1.66369111
13.06322957 -0.55756699
11.30882871 -1.48243177
8.912162248 -2.283075727
10.46526896 -0.628817673
11.65839228 0.985175941
8.842468076 -0.406080938
5.526317492 -2.606514902
3.89238815 -0.705416497
4.489003261 -2.637428062
8.336323206 0.03892397
12.21021423 1.086554672
12.65734827 -2.481584122
12.33363989 -3.491834368
12.04171105 -2.515692469
10.65285163 -0.055151979
8.49717706 -1.055547028
9.073845347 -1.375366973
7.059008569 -0.573308478
6.580257607 -2.454079378
6.982951142 -3.180017648
4.977667229 -1.487506438
2.716095301 0.047715236
0.858970856 -0.019151444
3.065415481 2.990390354
5.846265704 7.577038357
8.044759192 5.229306559
9.975059141 4.342524723
14.56678203 5.636229178
19.1707725 5.160858171
21.47019651 1.929437681
22.26867996 -0.897855813
23.40232302 -2.417358683
25.22801859 0.629009877
28.80460322 2.551835713
29.24214399 1.12539654
27.62237102 -0.897311389
27.05172119 -2.338192503
27.68370353 -2.183612435
28.68056622 -0.577286949
29.69891459 -1.981265512
24.87315792 -2.116793789
21.39333094 -2.414831643
17.8756053 0.018409736
19.00540259 1.920106089
19.95174837 1.976348653
18.25523291 -1.984249333
17.12825874 -3.486124012
15.52942725 -3.018605271
14.2625783 -2.341908972
15.16998026 -1.86682429
18.61250253 1.309355326
22.84789865 -0.805549737
23.59289311 -0.113446006
23.94876798 -1.94929691
24.93162846 -1.104567658
24.17726604 -2.664930528
23.71279167 -3.988878176
24.4917644 -4.441980542
23.73886885 -3.642420273
17.58379694 -3.264951618
15.69134185 -5.591695459
14.58736996 -3.63786091
16.54400512 -3.942510581
18.93466336 -1.385821438
19.43674176 -1.252246188
22.17930861 -1.915265052
24.69009608 -1.128886005
24.76250545 -2.641656108
22.81459338 -1.467653498
19.5153169 -2.861602354
18.20736486 -3.549895486
17.65307937 -2.584209159
17.36640564 -0.447558627
17.85448646 1.316421695
18.07625367 0.022214176
21.68058831 0.616178683
20.84810958 2.645673719
21.9556471 -1.355271928
20.59367952 -0.210650191
22.58470732 -1.706389151
19.84313771 0.694286043
17.55226086 -1.638753075
13.05457858 -3.253082751
10.46837913 -3.91372586
4.919659228 0.218273336
5.386754251 1.032840314
1.535744603 3.641692723
4.971773241 2.103264943
5.929186825 -0.934619725
6.338080761 -5.807032054
7.344750658 -4.472211389
13.60250495 0.611499701
19.31089003 0.004970438
16.18867165 -0.958700717
10.84431284 -2.305084091
11.88292752 -2.380096919
14.34622451 -4.184406978
16.80720691 -2.225638647
16.21531923 1.284185593
17.82722844 -0.434302291
19.28503579 -0.806880695
20.35065388 -0.510806562
20.2734241 1.678893003
16.57210654 -1.884638395
15.60551716 -3.178795742
12.96964377 -2.557497575
13.1726833 -3.072542924
13.70831739 -0.878258892
13.78757758 -0.140015146
15.06229758 -0.977369928
12.10148344 -1.15806989
12.66335939 -2.224454743
13.33285249 -2.020013838
12.84573892 -1.178630037
12.31881891 -0.104791402
11.33220114 -2.440407835
9.992023613 -1.409276551
11.34334785 -0.324832047
15.4396763 -0.686530499
14.23023367 -1.007736271
13.93325116 -2.783397063
14.39558543 -0.826935578
15.76805489 0.906902353
16.4062879 -1.581942987
15.21020459 -3.062459036
11.94452638 -2.69239175
7.927577168 -0.308544939
7.933749572 0.77338591
7.751470243 1.169395776
8.401304401 -1.585200131
8.529219667 0.426755312
7.727746697 2.709212739
9.723850088 -0.825989196
9.461318879 -3.062506224
8.480315287 -1.568350201
7.831486522 0.69294977
7.025100377 -0.26120186
9.016737774 1.264274739
15.61096156 1.189591524
20.6663381 -0.18603443
22.58722279 -0.638643162
23.09550825 -1.222363289
20.11947584 -3.428160877
16.48963492 -2.378011151
14.43591322 -4.773872346
13.30445426 -3.798906377
9.589624108 -2.377067264
3.849348108 -3.14418591
1.748347617 -1.398389807
-0.234932363 1.859630418
0.895754662 0.812722675
-1.410897692 1.225978962
-3.676517863 -0.605358201
-4.193352528 -0.543783475
-2.394065743 -0.644320265
-2.790283378 0.657571954
-2.393455151 -3.645321172
0.664609626 2.622216946
4.946845589 2.025540747
12.61207055 0.140201024
14.65200719 2.032210389
14.98285412 1.239293342
12.31106943 1.820879839
12.27089299 0.032459113
9.836502248 -0.097273876
7.837010372 -0.722407838
5.973443059 -0.8823979
6.19003885 4.700424631
7.440055544 4.693131662
9.074005842 2.772110768
9.077472291 3.594091787
9.95953654 5.143175188
11.45023746 3.616804861
11.02480187 1.84216577
7.846990058 0.753771103
8.937907505 0.928295883
7.496819237 3.357206533
8.516523598 2.406840074
8.908909213 1.032292074
6.504009795 0.103039255
3.739832113 0.619752471
0.18966956 -1.217552839
-3.680496697 -0.903091817
-2.715621124 -0.711598051
-3.806173288 2.47932229
-2.489114515 3.509116814
-1.919341527 2.979922884
-3.517832665 2.844941176
-6.839284845 0.838787962
-6.651799219 3.986812666
-2.825205661 4.2632969
-1.851855386 3.774944591
-1.032014058 -2.440648213
0.044074004 -3.432702684
0.782165709 -1.395122562
1.305495751 -0.554420524
2.196589057 0.274602984
1.367558312 1.266110753
2.165291885 0.669380735
4.568496208 -0.292605231
4.137820577 1.869446292
2.291175182 1.723841797
3.664771642 -1.979575365
5.26788643 0.298209889
7.651000066 1.413136048
6.571418127 0.781397767
5.275529387 -1.242933652
2.130772011 -2.200871896
3.696200204 -0.228685991
2.898514438 2.022798312
3.527105467 -0.434074676
4.166428211 2.071214816
7.642074439 0.697574297
10.87132677 0.575857799
12.13659318 -0.567726613
12.10965996 1.476217109
11.18858575 -2.108374076
10.40802433 -4.064450301
11.50719727 -0.650660815
12.6860634 0.86809648
14.46918931 -1.380312688
18.33751641 -1.698251071
20.65669609 -0.371849252
19.87655643 -0.768018885
19.77448371 -4.117580234
17.43302749 -2.630388181
14.14128657 -4.025286972
13.10187246 -1.655224509
13.08961657 1.64691824
13.56444854 2.856326251
15.72516897 2.088990045
15.58968231 2.099092973
14.50817502 -0.748148611
14.06691319 2.753107803
13.05451431 3.786153897
13.81913826 3.815639624
15.67681959 0.945932414
13.89522073 -0.621560046
13.23377879 -2.416646771
10.52187909 -3.64979967
11.79376006 -3.104709774
10.89259951 1.120034162
8.157235262 0.568615301
6.440408516 -0.972244342
8.244300606 -1.71669743
8.758790249 -1.321449784
7.756096013 -0.265811112
7.06298995 -1.572038404
7.471025411 -1.638182114
6.876383658 0.749911432
6.810667407 -1.30691823
7.799653966 1.623591234
10.5670077 1.020932631
8.425947614 -0.008187215
4.96601321 -2.217158881
3.625194759 -6.12177123
3.692454313 -0.88716782
2.893774696 -2.454218715
2.817474648 -0.916272458
4.264504967 -2.554407251
3.607210028 -0.645837905
3.098923226 -1.17088281
1.808513407 -0.856357287
2.618847879 1.682214806
5.521792871 2.04204493
4.832703205 -0.535634047
7.060138193 -2.122968514
7.521794197 2.741900586
11.27765583 -0.324312219
14.37193914 1.062003376
17.11255507 1.193403562
17.92816341 -3.082459465
16.08336562 -2.421647751
14.56020199 -1.460900677
12.36357927 -2.917762747
10.70048854 -1.936186573
14.35411611 1.669666488
17.72782451 2.254511148
20.80132944 -0.966097669
21.0660659 -3.609053562
19.96755756 -7.143014164
17.00262916 -4.92787822
17.93053388 -3.70158082
18.5444933 -1.914528276
16.2988558 -2.300084247
13.16718404 -3.681124077
8.671329757 -2.48211882
6.871614211 0.362796656
6.132654664 0.501078068
8.020853861 1.075306461
8.557039785 0.364111831
9.346643793 0.501501974
10.96790162 -1.308642743
8.850505864 0.50736371
6.659797688 0.420559731
1.659997767 -1.607891665
2.362666817 -4.115837084
5.413836627 0.136887887
4.671572939 0.966636827
6.681517928 -2.550454182
3.802322143 -1.036428193
6.786021346 -2.465888913
8.395862364 -0.775812087
7.747482923 -1.288682008
8.938001871 -0.015742901
7.038076107 -0.738086837
3.140020478 -2.33381351
1.474911559 0.098824039
2.793482433 0.752776291
-0.02142088 -2.007379742
1.084059722 -3.20160335
4.348377969 -2.20861533
5.547858441 -1.957287185
3.607269017 -2.105144467
5.163461848 -3.342446263
5.541872409 -3.538230394
4.596928687 -2.036437837
5.709874474 -1.27780016
4.85340458 0.558147955
8.582961898 -2.963614241
11.85946303 0.28592856
13.9871061 -0.157246021
17.47870844 -1.976231966
21.37819226 -1.551032233
20.48488372 -3.61572329
19.67747936 -3.012395361
19.3330637 -0.722386825
20.34858735 -1.939346728
19.11687348 -2.987395555
20.17905858 -1.820680289
17.84462631 -1.341102998
17.77306979 -4.135649348
15.87470339 -3.36642104
16.25472187 -2.359564558
14.85008194 -3.751594717
15.15171297 -3.25311479
16.17791156 -3.281915368
18.22574793 -4.350273094
18.8421479 -5.868983072
19.66803521 -4.233027773
19.88863331 -2.436858338
22.28177426 -3.486033101
22.42444587 -0.697760003
24.46462486 -2.016333902
24.49605445 -2.612448698
20.27062087 -3.463637694
20.95913438 -4.83521981
20.94104668 -1.587483886
21.34421871 -3.893084483
20.02415345 -4.562769065
15.48110443 -5.512774841
12.17384665 -4.980921569
10.86981861 -1.834184634
9.59068077 0.346592888
10.73539798 -1.532414206
12.91788374 -0.751174322
16.90219528 2.279550091
19.5020885 3.382484447
19.47896421 -0.164751327
19.9983235 -2.296732029
18.64019508 -1.327776942
19.28868161 -3.263367596
18.90736314 -3.894984432
18.30734777 -4.518898382
17.36281185 -4.294796305
15.65857058 -1.117966741
16.35330215 2.571605958
18.94795046 3.216131057
18.72984444 -3.288223589
15.37895202 -4.615527926
11.42972667 -4.052493568
11.74753436 -3.689589646
9.463143158 -3.736054321
7.435467044 -0.498137271
8.030832332 0.430156151
8.666777239 1.033167759
9.363481788 -0.736835156
7.130649172 -1.723667033
11.32316743 0.716293447
13.96419727 1.617857999
15.77517809 0.251109792
17.98858109 0.344616052
22.39571222 -0.927488894
24.30239586 -0.912973429
25.22958924 -4.853166792
23.88834746 -3.869990731
20.75623577 -4.78938914
21.00329066 -0.305959365
18.74196893 1.098751018
16.71048378 -2.039981572
13.66029874 -2.246014679
9.659629954 -0.164688984
4.171047504 0.283310371
0.115328284 -2.033070931
-5.917189745 -4.068664914
-7.952884635 -0.639882711
-11.26799999 -1.059982091
-11.2755813 -1.604694716
-11.14945221 2.083231139
-6.091345038 1.444416041
-2.913993269 3.689643465
3.625235815 2.35211933
6.836504407 2.383636244
8.309400686 -0.005260084
10.71358939 0.048135923
9.11040065 -0.646780167
8.017825324 -3.397086458
9.213666278 -0.058982458
11.07581718 0.546038618
12.32754079 -0.092602236
10.77451252 -2.328625257
6.96245584 -1.389467448
6.888242471 -0.993124146
7.343166994 -0.291226447
5.026148781 0.868774899
4.281401003 -0.06825835
2.399364477 -0.856982174
3.130991515 1.23376959
4.160435876 2.131263091
5.51508252 -1.79890216
6.801000194 0.288520953
10.38257691 2.024601596
14.39398151 1.346006125
14.00960184 -1.748680528
11.43633078 -3.74056775
9.885841934 -3.314024734
6.482776748 -1.99071428
7.526943366 -0.117031646
9.650586957 1.072936684
12.43910398 1.204603031
12.93466202 0.660096292
11.46160944 -0.098933245
9.137960662 -3.337913824
6.125181183 -0.746824989
0.996104773 0.317771269
1.880953517 -0.586439568
2.936487829 2.479847711
5.686698936 2.053394328
8.28848285 -0.257617755
9.699085543 0.470640358
11.68409641 1.050022085
12.53499345 1.200114786
15.57751105 -0.186961176
14.61840601 -0.223896207
13.59760603 0.204823824
11.23905587 0.464548144
7.970693468 -0.418548845
6.72327933 0.869579434
5.651377132 1.4060271
6.471718129 1.000744128
8.684501552 0.707459976
7.515699311 0.406393007
8.446083546 -1.741073349
11.39289667 0.127109012
13.49734314 -0.230311104
12.88962334 0.042176403
16.68875583 -0.429997296
13.94917735 1.078745661
11.62100049 -1.557610733
8.95968501 -2.6821345
7.10283174 -3.652659424
5.429401267 -1.858628735
3.60121033 1.848590844
3.090419918 2.128537442
5.158437213 4.140541938
7.848439481 4.249421378
7.243822551 5.085652691
8.72687762 1.656391022
8.87505683 0.036910613
4.874277356 -2.673806419
1.212635384 -0.906589107
2.055802665 -0.221896902
5.598556227 2.313749979
8.031984697 2.615843016
7.748234518 2.461562268
9.378816806 0.011784023
9.686248293 -0.876359699
9.097715796 -3.659455416
9.702994529 -3.179594566
10.66237272 -6.029162436
8.404492207 -4.309650645
7.637447609 -3.445109577
7.046919837 -2.661021742
8.592753063 -0.21110562
7.459236282 -4.435159068
8.016697173 -3.664852367
6.774065828 -2.187385441
8.195921966 -4.184525418
9.183784835 -1.264954751
11.30944292 1.774277776
13.87925504 2.253954579
17.94644559 -0.42062994
17.25989877 -4.09910104
12.68387133 -1.763097269
11.27670755 -1.369383829
10.73921973 -2.115450317
8.267144846 -3.023149709
7.24117601 -3.964380673
5.328402987 -1.715840443
3.587157839 -0.098750351
3.776144325 1.386737188
2.776791927 2.830965002
0.361834677 3.611852468
-1.840950835 -0.397567079
-3.965736269 -2.716247821
-2.197386529 -1.662059442
-1.727640315 0.332408116
-0.870976792 -0.152976762
-0.478042681 0.444914706
2.774708572 -0.228639944
5.783293221 -1.929065543
6.406345342 -3.008996597
7.900280842 -2.312918864
12.09071374 -1.550300086
15.62634065 -0.164540923
17.49428132 -3.125977507
20.42450647 -2.434101967
23.99565675 -0.770494592
22.13006361 0.632745667
18.92074223 -1.837500525
17.15581193 -2.02977869
13.05863599 -3.158545046
7.605608116 -3.212607915
5.471909619 -2.405025367
4.65154688 -0.413304751
5.828883745 -1.02989615
4.084443524 -1.969051289
2.976499523 -3.119533448
-1.114691006 -4.161862439
-3.697654309 -4.954304459
-6.332534876 -5.080941332
-5.441429442 -3.581301767
-7.022936665 -2.234661978
-9.780023511 -3.054249565
-11.71121571 -4.585824238
-11.91393273 -4.147943606
-9.039544515 -1.742882945
-5.357984001 -1.510322323
-2.506975148 1.041499363
1.960092474 -1.620672382
0.891249864 -3.269353013
0.887284093 -4.489808324
1.889235136 -4.81239625
3.52553984 -2.342092146
2.61190051 -1.138626654
-0.052556319 -4.215224123
-1.12822677 -2.522880727
-3.301161608 -1.33045062
-1.535808826 -0.95038888
-3.857455683 -2.257599359
-2.912663932 -1.743938604
0.591877375 1.007186022
2.002563965 -0.624528646
3.416350307 -1.787180166
4.721491844 -2.0639475
7.283610971 -1.58469455
7.627386896 -2.740750107
4.841197112 -4.154433802
2.798504166 -2.042724376
2.752102973 -0.95140773
5.732966962 -0.631866673
4.276912271 -1.444601476
6.2504159 2.010158072
6.82136918 -0.791324641
6.178140366 -1.629192636
4.839982006 -1.407368521
2.974173464 -0.150419836
3.526700953 -1.833321433
7.544299952 -1.705373806
9.526481947 -4.978451121
11.72412097 -2.023980457
11.40949926 -2.538354866
10.77750279 -2.227577903
11.32722343 0.626623941
14.16811636 -3.13805429
17.14010417 -5.687082196
17.99871687 -6.717893789
15.32246537 -7.994606302
12.85446608 -4.593351751
12.92614009 -0.240299198
15.3669826 -0.654348221
16.96605798 -1.591024867
16.39856324 1.381466767
17.52917094 -1.16238207
13.03700322 -4.471668861
11.31326205 -3.113659243
14.52937733 -1.38467376
16.70753678 -1.063288776
15.43599915 -1.087839059
14.60844361 -1.672753922
12.03304311 -3.444022495
11.92427954 -4.300313095
12.77205138 -1.882372535
14.46822241 -1.118527953
16.51998278 -2.170585335
15.41538421 -0.8769443
11.91851756 -0.873019833
7.836153735 -1.402351394
4.839424317 -3.739610197
4.238763536 -2.265427326
6.675477726 -2.024334759
9.998087354 0.442532714
7.541394235 0.022533377
7.919987394 -1.474055493
6.490787442 -2.950305422
6.150971147 -0.193237159
5.376172804 0.993754027
3.595648138 2.330688299
3.16947144 -2.291773885
2.437221387 -2.240435424
3.429902488 -2.255558813
3.824306904 0.556687707
8.243768761 4.316987581
11.51954698 5.091226046
13.72138862 -2.332793571
14.09892912 -3.376533386
15.03052626 -2.312638526
14.90092959 0.048229179
15.25293487 1.778925827
16.17597691 0.159506355
17.74737665 -1.296708545
18.11300849 -3.699316921
14.17632348 -2.958216624
8.594535335 -3.699590588
5.486837713 -2.258392994
2.232656297 -0.117924675
0.303468527 -2.381281849
-2.445401087 -1.294978421
-0.295429775 -0.063393443
1.677743051 1.838557254
4.220876734 2.026388005
7.033740818 -1.17576363
6.213962966 0.3083266
5.605640373 -0.431020105
6.133379827 0.92911722
7.923799898 1.635033965
7.178384273 3.610949932
7.690351094 0.091567783
8.984031131 0.873833196
12.78084198 6.562913981
16.68308794 5.006826813
17.14069338 2.088930661
17.79674503 -0.607080316
18.93925723 -2.12878561
18.75532896 -1.264982331
15.49910816 -2.205536128
13.09423723 -4.388034146
13.0999383 -1.787495136
15.22682483 2.167087525
17.48737049 3.812591312
19.62071397 4.015439654
18.79779043 -0.366854282
19.7754188 -2.773092412
19.0044228 -0.870715883
19.13773735 -1.407841087
18.7067679 0.329989104
17.6803058 0.687136098
19.84034631 0.037577827
20.4466521 -0.442198172
18.03519522 -3.813900587
12.83987662 -5.622627645
6.655681753 -3.421787971
2.831184175 -1.956909056
2.329257217 0.76127489
0.062753686 -1.46681712
-2.846822898 -2.057065269
-9.469366551 0.60041389
-9.854959141 -0.353331379
-13.06279405 0.519942196
-12.8750294 2.53372325
-12.49284697 5.519670938
-13.22778582 4.689398081
-10.26936198 3.375175631
-6.433457867 3.37350774
-3.580988089 1.587150011
-3.182749429 -1.056567233
-4.533396779 -1.17750795
-4.115048529 0.601320656
-0.856891115 -0.653203084
0.387950443 2.065118432
1.432965435 -0.278934449
2.310355031 -0.980143379
3.033356472 0.743462406
0.741008043 2.193650734
-2.187105322 -0.758204034
-2.654260101 -2.233254574
1.861635613 -1.156788286
5.060434981 -1.047864881
4.152976872 -1.786579451
1.786918255 -3.471156084
-1.265231998 -2.536213418
-4.365370625 0.542159642
-2.150901244 2.830999598
0.14346119 6.845421213
1.770987821 5.143169377
2.202398683 3.29874558
0.896084056 3.100078093
-0.766337558 4.130287931
-0.073228273 2.106587611
-2.056588321 -0.58243402
-2.633429064 1.632784207
-2.128895191 3.826454747
-2.075890973 1.108199887
-5.005253333 1.581195926
-3.242508628 1.805036028
-0.10818662 2.080119557
1.935658968 0.907235865
5.085368613 1.148670305
5.304358213 1.308073448
6.458191255 -1.641148975
5.881585611 -1.341186046
6.230720531 1.583231207
4.252678842 -0.668874533
1.194124582 0.196690814
2.066115756 2.10174783
3.424812385 0.173506086
4.48912302 -2.214251478
4.113975966 0.585963678
7.656765315 2.111606935
11.26059891 3.320207867
9.601374226 -1.091179755
6.014515723 -2.428489009
5.580207548 -1.406908421
1.813272135 -3.149532661
-0.003467803 -0.076792549
-1.593259975 -0.086189123
-0.381210654 1.849270293
1.192497611 2.805227452
-0.603985307 2.746950087
-2.154753998 4.370513883
-0.276862218 3.943251924
-3.232507939 2.970527814
-3.492758659 1.698862248
-3.247500272 0.627797294
0.510858536 -0.373339783
3.602003713 1.476061497
6.899184965 1.9903142
10.56020071 -0.16089761
11.98934261 -2.259327128
10.01107197 -3.083227912
7.169559023 -5.886182241
1.985751523 -5.715511881
-2.888108948 -0.99297945
-3.48989547 2.639558203
-3.042213097 2.672942866
-0.635213282 0.212186859
0.92175841 -1.284641574
-0.635203119 -1.190712999
1.383001002 -3.768316376
1.469399721 -2.806010465
2.426276968 -2.536666764
5.749702092 -4.519389587
5.983803337 -2.935908067
8.738445514 0.638608842
10.76127942 1.3023627
9.973472758 -0.592516973
8.047059323 -2.243500971
8.432064495 -1.236678337
5.542692553 -1.099713417
2.710366387 -1.54258036
-0.281998905 -2.18337293
-0.973149207 -1.506570921
-1.613312595 0.899317878
-2.233956399 -0.864999586
-2.129297708 -2.63789963
-3.492272541 1.273640799
-2.697756985 2.078825892
-2.699382012 1.097795784
-0.149923509 1.570516952
1.511995985 3.24939667
0.576729231 3.77742719
-1.274463205 2.793847262
1.737740614 0.801154276
2.719660334 2.828813031
3.394248822 0.729601746
3.927847129 1.971643999
2.059475417 3.072743952
3.18701859 1.592486441
1.407261035 1.456596054
-0.640346083 0.900434082
-1.504790544 2.14496888
0.390860895 3.673842981
-1.032244792 4.540976732
-1.664130578 5.001597453
-0.257113305 8.63313482
0.419814253 4.370220851
-3.708402157 2.117335697
-8.28825737 0.655583212
-9.948540768 1.676165031
-10.60168244 4.237169505
-11.88251829 4.738390854
-11.26632756 4.218401993
-8.789640316 4.462317616
-5.844869937 4.426937083
-2.91729566 2.68646027
-1.353173367 3.703005005
0.678058368 0.881096061
5.824282438 0.836031236
10.12612159 3.340228366
15.23461292 0.716580876
16.67092439 0.538217228
15.7950477 -4.509450905
12.02653193 -5.379413449
10.20657416 -2.801288888
8.948947263 -2.845698525
4.275889314 -1.387016054
1.362416689 0.507628975
-0.154323899 -1.470771385
-2.704252177 -1.082228215
-1.928260581 2.494388775
0.022853772 1.335509464
-0.798268812 2.7799609
1.235627807 0.252335194
1.7618732 2.027433856
3.99896413 5.10644026
6.316658028 5.308777521
9.878882569 5.450729737
10.51012571 3.668460741
10.42676583 3.115766473
10.93175461 2.112484809
12.36330251 4.988362101
13.99118527 4.377644478
15.752909 3.213197818
13.90365323 0.888092382
13.46817992 -0.243236495
12.77982994 -2.260777838
13.82295652 -3.144595066
13.78395432 -2.823221225
11.78595024 -0.585182881
9.223045829 -0.427498858
7.30643288 -0.95249501
4.79213135 -4.401968552
4.476276745 -4.768854481
1.846666779 -1.745538636
2.24614036 -2.073398288
4.724448178 0.054749877
3.767060782 -1.916673693
0.040523616 -0.401075205
0.107472917 2.779733255
0.514751079 3.185316642
4.32777318 1.201999984
7.370376636 1.611035322
6.882796225 0.209104189
3.996227959 0.235300792
4.529400381 2.77733804
6.761238684 1.221551014
6.682349998 0.205626571
4.956661895 -0.013124825
5.72697049 -2.385105794
7.688371272 0.65007283
7.643482225 -0.045768037
10.83130377 0.877418053
13.32191093 -0.70636686
14.34419719 -0.779706185
16.06832222 -1.674178477
14.48064242 -1.728398266
10.26476633 -2.602301288
8.181080489 -0.98694428
10.61889356 -0.573597918
11.44800756 0.627300694
13.59636608 -1.529684035
13.78565307 -3.557398992
12.4053198 -4.277269758
9.627808197 -6.266515417
6.966445691 -3.661380123
7.058052755 -1.100649254
9.692839973 -2.856359875
11.63165217 -3.149654448
11.84231424 -2.387164532
14.86926343 0.539335976
16.74868361 2.161693243
15.00198815 -0.4390896
14.07769196 -3.759670611
13.22951227 -1.922680213
12.93906428 -0.498429414
14.57326739 -1.67976627
15.60371808 -0.610094312
17.26705512 0.955199352
19.59479344 -1.539994699
20.68095508 -2.393199315
21.86960518 -2.718838846
17.79664645 -5.214580424
14.24305456 -2.475150462
13.00498862 -4.500337211
8.37961671 -2.384460028
7.215456433 -1.146648129
8.316943063 -2.173534526
7.9094117 -0.589712252
7.025045532 -0.226362244
6.44622974 -2.579801696
6.201462057 -2.621449239
5.737963063 -0.925102314
5.627385628 -1.721363321
5.515330913 0.545324455
7.710976816 -1.517414717
5.77876089 -2.77995461
6.939837593 -2.787087359
8.01061706 -0.194495209
5.762066328 -4.012200572
1.447463649 -3.989579042
-0.596180216 -3.552986166
-1.109931736 1.392612029
2.799382735 4.759523292
3.308204538 1.500465422
0.224979668 -3.594675311
-1.124729089 -1.756629226
-0.030515277 -2.126440296
-1.130707766 -2.103243175
-0.355823989 -3.906591258
-1.479036639 -2.450610497
-3.715520639 3.184939181
-1.724876885 1.251159073
2.686800383 1.683652377
4.066704022 2.659896637
6.038066973 1.628319998
4.752264443 -1.53865781
2.643953941 -3.667211048
2.3391709 -4.83417199
0.716620505 -6.367056457
-3.513199162 -3.825832014
-4.178105551 0.505086237
0.220444136 4.197272568
2.832581091 5.820820846
5.963363824 6.833025637
8.465607164 2.837479556
9.620205294 1.288479844
6.962593342 3.870760095
6.961949704 4.428163276
8.789720926 3.381250504
8.497091239 1.840081404
5.541665604 -3.295745875
3.031868653 -1.732476419
2.025950224 -2.322025283
-0.548748916 0.885398717
3.181246873 -0.497887095
6.413024431 0.398485988
9.555416769 -1.467831034
11.14088565 -1.224327244
9.674625288 -1.709166193
11.68468037 -3.303855377
9.47958516 0.235036688
9.50877258 -0.203676617
8.581016065 1.423331187
7.710262984 -1.797121822
4.252611125 -1.051622201
2.28514676 -0.323755049
2.365679285 -0.563747196
1.677451884 -0.536712634
2.783290296 2.067635183
5.866419603 4.146304898
8.34379033 3.725185262
10.77056347 2.795902188
8.539499434 0.648258272
7.805971708 -0.956414873
6.387591258 -0.670674498
3.889883281 0.434752702
5.738313974 -2.125121715
6.828925368 1.995442624
9.938159606 4.310279933
14.57084486 5.077769386
14.70382133 2.383510426
14.04598528 0.724677497
11.512373 -2.6581454
6.540208413 -4.402981783
0.752666403 -2.1801272
-1.403331159 0.286009226
-2.36620256 3.532786693
0.071999906 3.500933788
2.692002486 1.396897769
3.979691168 1.73538544
3.467765994 1.629050396
3.006249578 -0.018389639
0.832846628 0.700079557
1.785036544 0.834232083
1.939019061 1.81873474
1.769673324 3.735907413
2.06080554 2.094545631
4.020695835 0.002546798
5.155548147 -1.799255186
4.638725686 -3.051556831
5.378565731 -0.311731043
3.437942985 -0.750547511
0.162041731 -1.716576227
-3.345154355 -2.125664523
-5.554971817 0.494169754
-2.256987276 3.112467546
-0.788027359 3.195714546
-1.961073035 3.01878214
-3.746910436 1.86645159
-6.655367154 -0.36836641
-8.305279324 1.362279505
-8.931464788 3.241606639
-9.45577054 1.930844177
-8.809558163 1.846853403
-10.91220178 1.626350547
-11.01961835 -0.289585033
-10.01554024 -0.03525745
-9.337433879 2.394321979
-10.97814779 0.765292782
-12.94405646 0.210671274
-12.42861128 1.613512848
-9.881077931 2.963586068
-10.12945274 1.665110288
-10.84228578 0.730871858
-8.671538844 0.435782286
-6.162600057 2.894143736
-6.246294128 3.159981226
-6.196017831 0.473789466
-9.109254101 -2.082685714
-8.838254283 -1.71908089
-7.793946584 -0.203787156
-7.416073338 0.420461985
-5.604003169 0.473971988
-3.931484841 -1.120823306
-4.219122017 -1.831647024
-7.0023729 -0.351499519
-9.273794953 0.430931825
-12.81065183 -0.676610982
-12.16276357 -3.024128747
-12.65194387 1.532601541
-12.59422268 2.672916841
-9.557980374 1.285525325
-8.647153064 -1.019382008
-6.605316344 -1.347103623
-6.667151583 -0.067197553
-4.675001385 1.867802502
-2.447560912 2.990443693
-0.610985432 3.786847746
1.805752702 3.309990732
-1.016706411 1.010687104
-4.644833665 -1.759243494
-7.908448263 -3.236311786
-11.91562906 -4.096216703
-13.41520977 -0.886818024
-14.312034 -1.737097237
-14.3794062 -0.462912511
-11.03621607 2.183116375
-7.584621916 2.05069263
-2.97545203 -1.231382788
-0.191276113 -1.879170935
-1.524483638 -0.774121353
-1.768865314 -2.879711345
-1.293515828 -3.839656783
-2.623073822 -2.410991266
-2.694788881 -2.848117095
-1.324749653 -2.485673219
-2.242823675 -3.661067384
-4.464925718 -2.338409468
-7.04349338 -1.644942858
-10.23918889 -2.43969734
-12.00910874 -0.114237954
-10.70071346 0.754767817
-9.933322614 0.530537117
-9.742224442 -0.904211837
-9.659770436 -2.521708652
-11.62981329 0.84494264
-15.55369929 0.227949062
-15.98036377 3.70299087
-13.70870938 4.832034259
-11.62599655 2.476210306
-10.57370829 0.737837736
-11.49881461 -0.44993676
-12.52580825 -1.200538847
-13.31476417 -2.806794979
-13.05792537 2.09291805
-12.28034618 -1.251329036
-10.48282549 -1.462261593
-10.98708473 0.172720402
-10.11485107 0.801541763
-9.667495184 0.266030771
-9.419326655 -1.954007674
-7.882483909 -1.784209094
-7.11107608 2.485878188
-5.977310309 4.718707643
-2.646665945 0.927356778
-5.744209652 0.48346814
-5.016938515 1.297500166
-3.307728746 -1.392172919
-2.821855914 -1.831252351
-0.732530336 0.404289336
-1.744489594 0.633016563
-4.755444081 0.123962199
-5.674623055 -0.398795382
-3.238319802 -1.657523491
-2.416945888 0.608825271
-0.298594724 3.696732149
2.010414721 4.124837778
4.70816321 0.362493023
5.574253975 1.023766744
5.736939357 5.03399911
5.248275792 0.837450798
3.988911274 0.332375119
4.282487331 -0.298110937
6.272449605 3.01298861
7.617479318 1.545678428
10.31821265 -1.48730658
12.53663147 0.421536616
13.85366746 -2.502571284
13.96422042 -4.464427648
9.461151892 0.016004408
10.02815926 3.277178186
10.23897462 3.372624532
4.836516794 1.067612247
2.536618338 0.317055263
3.439866324 2.068033153
1.194968442 1.882573856
2.717377975 4.10216601
3.541979729 3.495421355
0.70800001 2.39065293
-3.247893481 -2.271242481
-4.486537152 0.393507163
-3.594593741 1.208756278
-4.092443621 1.577008943
-4.323525149 -0.115984053
-4.819458785 -0.21036253
-4.738642907 -0.157833608
-5.102144988 -0.700372716
-4.331047038 2.276439698
-4.407372429 3.033431009
-2.944929291 0.264015702
-3.219704857 0.930021468
-6.032674407 3.14147622
-4.640934036 0.607640305
-3.454426024 -0.378476275
-6.683992431 -2.082446846
-7.014397158 -0.683822661
-7.733372286 0.501635845
-5.371021872 -0.868703334
-1.128263639 0.767534575
-0.285454478 -0.360167941
1.233086849 -1.313319851
0.967966559 0.459071384
1.237233123 -0.399661966
-0.025833056 0.086309591
1.187330001 0.997297982
3.670009465 0.852109279
3.898233617 -0.2025774
3.974534663 1.008069703
3.305714497 1.072696315
1.20613566 -0.417210137
-0.214033243 3.800690264
-0.328855669 3.950419295
0.237471564 -1.082164438
1.711303997 2.571806056
0.728714866 4.037011194
0.452744834 1.836216597
-1.761807355 1.521966033
-4.842665523 2.397812827
-5.273803774 2.870412937
-7.871887617 2.55290223
-4.871813177 1.799743376
-4.206493179 2.68828524
-3.985138523 2.03609378
-2.978042422 1.840833465
-4.369371851 1.56461166
-1.664604374 0.292120209
-0.095747722 1.755568885
-0.562977099 -1.176028056
-1.258092222 -2.319704166
-5.164711372 -0.833315891
-7.816680058 -1.536710488
-9.708462182 -0.432590398
-10.84704344 1.216344132
-8.632785363 2.926967674
-6.77781862 2.131108956
-5.328915534 -0.605220755
-2.836741584 -2.550739445
-4.325782607 -0.586188729
-9.286760022 -0.445862509
-11.47583247 -2.807470221
-8.823008053 0.492004443
-11.52776715 1.338561053
-12.10901039 0.69105816
-10.77986926 3.010794213
-11.76720955 1.650883924
-15.88504146 -0.049763396
-15.64793212 -1.724700196
-15.97396022 -0.64267908
-11.62157184 -1.08415929
-8.77051874 1.114257062
-6.347559519 -1.736345494
-6.651944903 -3.162773566
-4.921633233 1.472156898
-1.752688802 4.817552765
-2.696292588 2.226679246
-2.180358125 0.766813086
-0.052379334 4.123333823
1.810163442 3.332097951
0.024745669 2.33321871
-1.28483011 0.045498197
-1.864776698 -1.030530668
-3.770123037 0.601282128
-5.015071691 -1.18577452
-7.166145916 0.838898896
-8.014760141 1.363039964
-11.48769373 0.45413392
-13.03149083 1.225282954
-12.79684215 1.803087887
-10.79239102 0.552572242
-8.694680895 0.05229022
-7.045965798 0.108022814
-3.462156766 -1.349343449
-4.286884804 0.91162508
-5.765729636 -1.073775593
-7.972166688 3.531823804
-5.743110245 3.546734071
-5.636229999 3.262500204
-4.935136028 0.86731997
-4.937595573 -0.623334056
-4.385290826 0.758433127
-3.09648832 -1.674198385
-2.213904641 -0.684450937
-2.690472726 -0.66425192
-4.643409031 -1.012446814
-5.617644095 0.670989655
-4.884493195 0.729267977
-2.283998718 3.112032087
-0.159444196 1.014601484
5.057095219 0.845131721
8.737296396 2.353605016
8.416423819 -0.492692506
7.885109131 -0.797762262
4.03477951 0.2217386
-0.065096764 -0.27758758
-0.541388378 0.548580468
-2.472023454 -0.39968977
-3.155353933 0.878204081
-0.961921292 0.544045362
3.369396283 1.873593101
7.866410544 0.065901713
6.569052769 -1.754187679
2.278806049 -6.957393372
1.450001842 -3.323911819
0.713840811 -1.559296672
-3.953860725 -2.053125793
-8.751752825 -6.339987848
-11.5367737 -4.274372764
-11.6394097 1.350610285
-10.03868157 4.444630919
-9.637593169 2.089355966
-9.961380502 3.107024978
-11.21585446 3.617702643
-14.52412941 2.145459849
-16.78618326 1.448529848
-14.48104607 0.265885468
-12.56105299 -0.715768643
-13.06975876 2.351873156
-12.06244081 0.665957804
-9.464848735 0.296855448
-7.466139882 1.65133642
-4.769490935 -1.699301282
-1.121219837 -0.865205308
0.318435417 1.131890265
-1.318399887 -0.456382204
-3.842793407 -2.58731042
-4.55297226 -1.61545838
-1.571900055 -0.35199056
0.594404699 0.977295921
2.626377486 -1.129062397
0.879880507 -0.416052878
0.544425587 -0.207635864
0.611648271 -0.607256959
-1.398382073 -0.453226378
-3.313269704 -2.687816208
-7.951657195 -0.605514721
-4.804095669 -0.689037753
-2.770291925 -1.205130634
-2.93519892 -1.025746935
-2.077699952 0.335916942
-3.117350673 3.061087598
-2.052227404 0.246559939
-0.593160509 -0.065189287
-0.342608296 3.359634745
1.514946754 3.736098773
2.823269632 1.72550059
2.422295323 -1.8770412
1.699516899 -1.880881905
0.517714743 2.393020202
1.760099368 2.360528393
2.923803181 1.746337128
3.955178864 -1.644089985
5.616938448 -1.52131788
9.226949633 -2.896375744
9.837641655 -2.749805977
8.430018154 -0.028157613
9.78018202 -0.479513159
9.000843318 -0.336914551
8.536381473 -2.805182321
8.724026576 -3.52739949
10.64048979 -2.318439371
10.99604503 -1.882701165
9.211504136 -4.004693394
7.461478191 -4.869929136
2.6456555 -4.43056656
1.067037971 -5.399811988
-0.774447032 -2.49704633
-3.017074995 -0.334410142
-3.35655728 -1.379845652
-2.555582499 -0.848191525
-4.815232323 -1.833671981
-6.810861931 -0.381310643
-8.869981774 0.074766412
-12.34259774 -0.106795093
-10.85504168 0.933340673
-11.55255331 1.126776329
-12.46800972 1.286491918
-13.52012129 3.286909617
-11.34358503 1.300508606
-11.22638177 2.212281731
-10.60192902 0.921250547
-13.55339641 1.314490687
-14.10642932 -0.638245341
-12.58207892 -0.128135948
-12.39931731 2.909442305
-5.86477294 6.393247208
-2.039811543 7.069865481
-1.774007221 2.939789468
-0.349305459 2.146529881
-1.265766896 0.497196366
-2.750940316 0.289732859
-6.916837348 0.717897535
-8.468730656 2.70838196
-9.001363449 2.512889651
-10.17823353 -0.168692496
-12.29870394 -1.972787296
-11.68516997 0.80864367
-7.952205207 0.210216148
-5.127322131 1.385633513
-1.723177699 0.66186779
-1.958114919 -1.122508667
0.081547551 -2.194591917
1.289325954 -3.039702913
2.716135962 -2.995416484
5.127796247 -1.896780778
7.644166637 0.272826194
9.576035215 -1.062874683
8.837065832 -6.409302645
5.306851737 -7.84724195
-0.936201904 -6.384359796
-3.964622274 -2.667067411
-4.253388727 -3.18293083
-5.735538338 -1.70580841
-6.542937854 -1.010395869
-5.257873397 -1.385972215
-7.573025937 -0.891156487
-9.964593932 -1.959523299
-9.661435178 -3.29937181
-5.055208851 0.299176307
-1.437752117 4.00318121
2.045208948 3.446224219
2.170575317 0.358966183
3.057909206 1.637830986
4.187785333 -0.05783476
5.796668311 0.904069155
6.798851382 1.649226427
8.650508525 2.910728722
13.54772503 1.090615985
13.86994389 -3.071327944
12.55072933 -3.755487268
12.10730573 -1.508716565
13.07153534 0.80884403
13.50857925 0.41652255
16.07420142 -5.207408059
10.88412745 -2.707335755
8.162497843 -0.69884616
6.047613475 0.353134728
7.287536827 0.623131588
5.491823084 1.685526708
6.63531044 0.152056639
9.331607832 -0.248795361
10.08825179 0.632994597
11.66945352 -2.150458834
8.898912039 -2.135584247
4.603947732 -1.602925714
3.491274005 -1.081847369
4.248369086 0.98734381
0.332874861 1.683846856
-0.033416274 0.189738555
-0.288322523 -2.025042465
1.164932625 -1.637170673
0.12086677 0.823418732
1.567550251 -2.58061027
3.545380672 1.746018432
1.588992391 4.733094046
0.854767204 3.330617544
-0.648414174 1.438512614
0.820874055 1.693199644
1.656536038 -0.771420086
-0.445390517 0.780238676
-1.114796678 1.85705935
-1.589835186 -1.484653706
-5.33562589 -1.505563654
-8.492962249 -1.289509262
-9.979482839 -0.995671558
-8.520944648 -0.737828933
-10.88670178 -1.543492072
-13.50892919 -0.556563007
-15.9435963 0.777285138
-14.47976507 5.272255955
-15.67033765 1.042182879
-14.68812695 -0.766199948
-13.38678127 3.437532662
-11.75398133 4.763995894
-8.80491112 2.966908624
-6.38371934 5.087136374
-3.022012706 6.388961893
-1.523177191 3.954918862
1.012725034 -0.113966273
-0.009921769 3.612077824
1.707434202 -0.506813394
1.069302792 1.05836938
0.284478117 -3.304951103
-0.593420082 -3.374446868
-2.856363098 -0.652435465
-5.628323365 -1.363980282
-9.210259614 -2.861349736
-7.987908291 -1.151520806
-6.383727518 2.48271645
-8.974381236 1.532613258
-7.747307096 -1.287446725
-10.19396628 1.161463951
-10.20943923 1.369965691
-10.00412728 3.649720332
-6.96751043 2.067881422
-4.438955197 1.300285988
-3.130963352 0.841357899
-3.625028176 3.660381227
-1.490614518 2.604322616
3.032224825 2.751886241
4.879502953 1.341329372
5.697235963 -0.861770863
5.307996227 -1.434392007
1.861505034 -1.449313726
1.985076734 -2.265444167
0.227556845 0.262022456
1.472756671 0.428390088
1.969201996 -0.239382059
4.49501624 0.002842184
8.076510116 0.488782359
11.37001477 0.20564918
13.11959185 -0.853497311
14.19573178 -1.312166375
12.77570833 -2.203104385
11.16632978 -2.063758144
11.00394743 -0.558596897
7.45411877 2.315703334
7.22139909 -0.299324949
3.975695026 -1.957634863
0.420388261 -3.028498776
1.825906432 -0.005345382
2.265085211 0.959296843
3.059564846 -1.257401533
4.018008694 -3.218124952
5.37970735 -3.24264524
4.455474692 -3.225754105
1.592748999 -3.950653544
3.677414753 -0.195172009
4.345618237 1.891089788
7.966088649 0.380160659
7.222993341 -1.737796
5.794802096 -1.533429388
4.960059005 0.614577564
4.608769117 -0.984070785
6.708448036 0.384162048
8.504007376 1.820736691
10.52300447 -2.738271565
11.81694133 -6.057719098
11.37295917 -3.610034581
12.3183631 -4.457972559
15.08064138 -5.133734097
14.59188991 -1.030723299
12.90718264 0.131020148
11.26766263 0.578436799
9.281429958 -2.755588365
7.839656583 -2.256553192
7.659310539 1.943513875
10.31825044 1.80999627
13.85620576 1.794036658
12.90850586 1.261875818
10.28627676 0.858081066
12.85943383 0.192868968
14.63230517 2.314047534
15.71259412 1.277292539
13.9387643 -0.727498663
12.83245712 0.91476659
14.7338781 -0.30018544
15.23101496 -2.270650812
13.82047629 -2.659048036
10.4684321 -3.134356341
4.843642612 -2.769300648
2.879341912 -1.248748953
2.831740028 -1.064001959
-1.104940355 2.296381849
-3.340217713 0.631937953
-3.565786261 0.508076702
-3.532987666 -0.491678933
-3.064205355 1.870600844
-7.528287718 0.838354266
-8.351895627 0.363245429
-5.993439502 1.982500272
-4.850683024 2.273846699
-3.653542222 -0.651279035
-2.712832341 2.002783032
-5.089303001 1.081045624
-8.087036425 -1.818920265
-5.808032646 0.297607877
0.23336911 2.962505471
3.385192743 3.261900616
5.481018273 1.352029037
2.209655656 -2.393764864
-3.225061003 -1.908327425
-7.471909201 -1.308047516
-6.802991412 0.662968836
-5.77579442 0.793992
-3.864353544 -0.577166236
-2.685133381 0.955898621
-0.67105868 2.244806838
-0.914163309 0.883397013
-0.668198872 0.959396856
-4.176705589 1.858589065
-4.699795872 3.323650883
-3.824155242 -1.03649251
-0.512168355 1.409702444
-0.939957147 2.132910259
4.48019908 -0.805647201
8.0923407 2.102076207
10.11333408 2.054628876
10.52320478 1.007853497
9.76625942 -0.830249119
7.560554245 -4.217801508
9.831664422 -2.1144917
9.676034809 2.50871241
9.5100567 -0.612835502
8.624574594 -2.535587669
6.686266598 -1.046370606
7.121637895 0.108996647
5.923738558 -0.063609805
4.371418328 1.34948267
4.776501073 2.949408898
6.423327281 2.888882265
7.233081011 4.017883061
8.363079937 2.094778029
7.839456929 2.934689137
9.145439344 0.457580043
8.022342553 0.276119939
7.090349702 1.121125624
3.534605397 1.588777742
5.170988738 -2.384931446
4.530374316 1.496465638
1.229710619 -0.153983096
-0.669327502 0.26727313
-3.601660224 -0.851073823
-2.742880885 0.695088095
-5.868323792 2.178803684
-9.192134988 0.989413
-11.23040168 0.139170083
-11.18712365 0.791845207
-11.64881348 1.40393131
-12.03281438 2.147210912
-12.33093423 -0.17699807
-13.67622417 -1.132572852
-12.60869081 3.509485309
-10.89291546 3.377227555
-8.875982857 1.800891
-9.685909117 1.581177812
-8.992308253 1.295813213
-7.67806825 2.656900744
-5.707715936 -0.081242804
-3.610640924 1.285658613
-3.83388714 -0.077191864
-5.116967239 -0.144611158
-6.13165548 2.109864907
-7.052722269 -0.559186245
-8.133043602 -0.749224952
-8.6001142 1.631514733
-5.245558214 1.702696418
-3.106244683 1.899821261
-2.630309178 4.16916213
-2.949384324 -0.645424767
-3.747579079 -1.279493407
-5.842397639 -1.535817813
-7.049401432 -1.521627426
-10.8472422 -1.247073384
-11.70103222 -1.255922107
-8.300727453 0.682705268
-4.021588805 3.237699406
-0.896550293 1.250260656
-0.494569213 -1.34350239
-3.266122766 2.587385425
-3.820000725 -0.367656365
-5.064322369 0.13831728
-7.097478292 -1.817705907
-8.270138035 -0.908120212
-7.921537327 1.798153108
-6.333235196 0.083997318
-6.03296455 1.356795783
-2.741890272 0.023481466
0.894144132 1.377024773
0.743180136 1.559363051
-3.253834324 1.907877127
-4.977531743 -0.098143948
-6.580001717 -0.49246346
-5.5801534 1.796113157
-4.250260008 6.605009558
-1.600060061 2.829236411
-0.548214297 -2.258803352
-2.375729741 -1.345744723
-4.377159103 -0.296203866
-7.256990018 -2.228403606
-7.774644316 -1.125632033
-2.16358002 3.178922874
-0.298940357 1.764932055
1.053368289 0.607563186
-1.385627116 -1.267632663
-3.490915676 -0.244657087
-2.006210537 0.443724202
-1.077153779 0.358173467
-2.202771908 -1.88500573
-4.374162194 0.819770201
-3.639814784 3.810941109
0.756690548 5.373486619
3.882827057 2.332051333
5.829512702 2.081779374
6.237741537 0.902582965
6.924857432 1.256528552
6.184512486 -2.233087585
1.293007926 -2.784624285
-6.617975364 -2.510101957
-9.311203682 0.05188146
-10.53024139 1.514027778
-8.776534816 3.027597446
-8.092191504 2.698070997
-7.34457229 4.272310138
-4.985860262 4.223254987
-5.26647975 2.358497073
-3.054535602 3.07032465
-2.602547066 -0.381067286
-6.600013181 0.244137471
-7.83353569 1.438519955
-5.630751109 2.223754286
-5.077262014 1.286546902
-9.194097065 0.446724724
-9.942642156 -2.020757491
-10.99877367 -2.149979752
-14.07344014 0.177819945
-15.23956927 4.179971584
-14.22198951 0.747664286
-15.06096405 -0.686668076
-14.59933983 -0.726227494
-13.41807886 0.53325837
-15.61449198 0.07579638
-16.6259129 1.104827651
-15.75864123 -0.965590479
-16.71800757 1.123627082
-17.25857266 2.581764242
-15.68279739 0.859577879
-16.35209795 2.598609509
-10.82603868 3.006995115
-7.265448979 4.217315481
-6.135649126 1.256720488
-2.097493569 1.517833883
3.383502008 3.924021408
6.463100531 4.069924542
5.041243171 4.644961522
2.870612229 2.175004901
1.229254868 5.381189031
-2.668506912 7.270530022
-4.108819943 3.867841226
-3.62605289 3.49992097
-5.711435241 4.980454645
-6.638667449 2.296210778
-7.95074043 3.123894373
-6.997293557 5.022928478
-8.826609558 0.880559791
-9.814706219 -0.047062455
-7.518542909 2.356151164
-6.395577962 1.105221721
-10.00905805 1.715845829
-9.620264077 2.096838262
-8.189346428 2.107889269
-8.249983907 1.105817918
-9.513685571 2.02494
-12.03801306 0.285868184
-14.68393961 1.655116235
-12.44395505 3.062316411
-12.68084591 2.191796802
-12.57027862 -1.011680471
-11.50524738 1.185326651
-11.2721527 2.693550217
-11.34429377 4.510861216
-9.858005377 3.842544961
-10.69772267 2.644808532
-7.590555527 0.08660188
-7.71953145 1.886077769
-9.078546263 -1.951926325
-11.8451822 -0.647256796
-12.10559584 -0.358208727
-10.51471743 2.115263078
-8.728913225 0.96666679
-7.362136213 0.061398293
-6.205198467 3.46261858
-5.293393462 2.919185322
-7.791946595 1.035243895
-7.281054276 -1.603856789
-11.08947761 -2.833273583
-14.39309085 -1.514691721
-17.41524054 -0.345816869
-15.96542538 1.818806874
-17.64612365 2.913242948
-18.3849947 1.403344968
-17.21625612 0.991298034
-15.87898792 3.549776714
-14.35607308 4.284935431
-14.54985278 2.88207071
-8.893625278 2.360635057
-7.991350326 4.047828047
-11.25732906 5.52554884
-15.4792026 4.377719707
-18.26722013 2.509929786
-18.83371286 4.508471384
-19.15539282 3.320213083
-21.29436338 4.813727227
-20.88146169 5.662978408
-19.78924127 2.298433771
-19.10842774 3.452330608
-16.44508317 2.765960625
-12.80801346 4.351760663
-11.26641382 2.670351706
-11.47508581 0.676175523
-11.25872939 2.575611998
-7.682382041 0.286856956
-5.967185035 -0.865455466
-7.139756454 -1.489271349
-7.531991909 -1.788969908
-6.851606778 1.478645506
-5.99572268 2.732712071
-6.491927769 0.005838485
-9.584509673 -0.442522562
-11.77019381 1.347125023
-13.63864835 4.163361061
-11.05821014 3.652919683
-8.13930181 4.269399601
-7.477541863 4.220557154
-7.091074499 5.207778038
-9.033658802 5.627505691
-5.182339685 3.930037083
-4.135128194 1.884624776
-5.563578505 0.839313487
-4.631887249 2.757877579
-4.328865762 1.32132422
-7.010076872 1.993003196
-6.41350547 0.218593189
-5.239098233 0.960715534
-5.200686731 2.013540238
-5.742457134 2.198407974
-8.890803585 2.153503703
-12.86791306 1.624155985
-16.11224722 2.258334109
-19.51056579 -0.294553177
-20.94566678 -0.269973324
-20.99383573 3.834640617
-19.74405118 5.745413894
-16.3321875 4.032613781
-12.28605706 8.189514222
-9.960957604 9.782879138
-8.084326643 5.224666814
-8.745609251 3.549557895
-7.735676761 0.221118911
-4.851167985 -0.787290084
-5.233041086 -0.207525728
-5.005679094 -3.150659968
-7.587873864 -3.500406457
-10.6187887 -0.557188252
-12.82051824 1.940507093
-13.25238098 0.472232024
-12.30749986 -0.941978871
-11.8107064 1.58878212
-10.5384815 1.595441383
-12.28669901 -0.15496616
-13.58501913 0.503870034
-10.2737363 2.171059817
-11.10872732 -0.098423029
-14.64354604 -0.403607102
-14.43692502 1.593891996
-12.81334802 5.951738208
-10.68564721 1.983660624
-9.521573008 1.468469891
-7.811706366 3.656621851
-6.532422453 3.227613812
-2.201079885 3.648624875
3.170169365 5.163536024
8.336552985 3.626398624
14.60838378 5.784766283
17.33406205 3.42169311
16.48068802 -2.524913015
12.2399774 -5.119745116
13.55815577 -0.776356969
12.97641012 2.608910202
9.674721979 -1.406500437
5.771367561 -2.436145146
1.669966337 -0.195722144
2.027866063 1.201576254
4.888186123 3.620711319
3.490353158 2.726469274
2.162055292 -0.010868248
2.000009069 0.421850684
3.710071641 1.774893984
3.926253682 -0.237510525
7.153569844 0.192460933
6.807806886 1.967089929
9.154472213 2.325639283
12.56914292 0.8294039
16.10943296 -1.668381861
13.47816435 -2.853175093
8.894023409 -0.8062844
5.92521146 -2.437020693
5.68077008 1.05877081
4.924285738 2.867601219
2.130358642 1.361905408
-5.010168314 0.22581737
-9.394152385 -3.928115964
-12.67912325 -1.997347263
-14.4794771 0.506562562
-13.34847928 2.211281162
-8.945830193 2.457548873
-6.733056707 2.708638945
-5.074097381 2.885232698
-7.562437641 3.385038765
-9.688887147 2.805022942
-9.408562857 1.609530376
-7.252470794 4.869626004
-3.248427396 2.404475689
-2.415367296 2.305760143
1.057489123 4.233359249
2.257427649 6.746653787
5.611129593 2.328765559
5.201068601 0.935950433
4.394178496 -0.118928521
2.688694419 -2.147116844
0.079621095 -0.943954857
1.338374495 1.985394203
2.927995827 3.884435411
1.270643425 2.532506557
0.782002744 2.115954745
1.030575595 1.902042626
0.777779325 0.326107709
-3.000218903 0.869003421
-4.497987909 -0.286116544
-6.579702034 1.568510459
-7.880460273 -0.295119818
-9.068834444 -1.377164989
-11.21684155 -3.674312116
-13.0534239 0.455153359
-13.91271328 3.633746142
-9.912431954 2.500653131
-6.079811644 2.023058473
-5.403859476 5.285285763
-3.915037108 2.888653145
-3.981514744 3.006472021
-1.780278082 5.323402664
-0.440479892 3.51606791
4.551402236 1.751241529
9.51775953 4.838820117
12.06205133 4.98820052
12.87746328 3.851737971
12.81137178 0.554092642
12.3419502 0.78208823
12.50821238 -0.674423217
9.304534468 -0.512119554
3.113147577 -1.752971161
-3.223876723 -1.287231527
-2.346986137 0.079765043
0.640108828 4.026418768
1.653474833 5.273229249
2.312332927 3.933467177
5.404008365 1.456645677
6.537664438 2.516834831
5.759552714 1.435686393
6.47754068 1.432388502
6.715231784 3.063972253
2.456611962 1.974843045
-0.915583228 0.757133318
-1.140776545 5.418324016
1.093749414 4.908417864
5.619642515 1.08005834
5.014145592 2.264460315
4.341799679 0.743561264
5.726918949 1.211521814
6.17165535 2.594912992
8.805057687 4.784293707
7.979566215 3.060156621
5.875414476 0.267857487
2.612289326 1.677918495
-0.54474623 0.126646276
-1.95511817 0.255766259
0.27399928 -0.376322828
3.392406014 -0.594787367
3.677729114 2.749004745
3.905747102 3.913530249
0.529329429 1.353902688
-0.146204078 1.694234275
-2.229670267 0.703628403
-4.514232778 2.888202088
-6.546319621 2.08051893
-4.580050334 -0.163218766
-2.25161567 -0.185356818
-2.256076604 3.522119327
-1.589204567 2.929817544
3.357375596 1.374207236
7.597858705 3.814494208
12.72131051 2.316003661
15.38503229 3.456828901
18.12559703 2.065422699
18.63123005 1.838090857
16.37187104 -1.009958055
10.74553445 -1.842642639
8.170921618 -1.254782135
7.089630052 1.607072593
8.681984528 3.022267495
12.1892903 1.516487601
12.15307867 0.534947028
11.25772452 -2.067395765
10.25990919 1.051402849
10.18064119 0.064488002
8.602346792 -0.904862648
7.793476885 -0.386071883
5.834350263 -0.011518773
2.640818831 -1.579542812
1.0429174 -0.58945427
-3.614703751 -3.666281694
-5.707745287 0.160256974
-7.249086411 3.387657949
-5.591443036 2.375707939
-5.154121559 4.207340402
-2.390144025 3.63940152
3.12049851 5.330308391
7.732287586 1.665071247
;
/* Compute the two periodograms */
proc spectra data = VARFIMA1D1 out = spectra;
var y1 y2;
run;
/* Convert to log scale */
data logspectra;
set spectra(firstobs=2);
/* compute Fourier frequencies */
j = _N_;
pi = constant('pi');
logfreq = log(2*pi*j/2000);
logpdg1 = log(P_01);
logpdg2 = log(P_02);
/* Introduce weights where regression will be performed */
wt = (1<= j <=100);
keep wt logfreq logpdg1 logpdg2;
run;
/* Regression for log-periodogram of y1*/
proc autoreg data = logspectra(obs = 100);
model logpdg1 = logfreq;
run;
/* Regression for log-periodogram of y1*/
proc autoreg data = logspectra(obs = 100);
model logpdg2 = logfreq;
run;
/*Plot the periodograms in log-log scale*/
ods graphics on;
proc sgplot data = logspectra;
series x = logfreq y = logpdg1 / lineattrs = (pattern = solid);
reg y = logpdg1 x = logfreq / nomarkers weight = wt lineattrs =
(thickness = 1 color = 'red' );
inset "Slope = -0.905" / position = topright textattrs = (color = 'red');
xaxis label = 'log-frequency';
yaxis label = 'log-periodogram';
title 'Log-periodogram of y1';
run;
proc sgplot data = logspectra;
series x = logfreq y = logpdg2 / lineattrs = (pattern = solid);
reg y = logpdg2 x = logfreq / nomarkers weight = wt lineattrs =
(thickness = 1 color = 'red' );
inset "Slope = -0.523" / position = topright textattrs = (color = 'red');
xaxis label = 'log-frequency';
yaxis label = 'log-periodogram';
title 'Log-periodogram of y2';
run;
data VARFIMA1D1N4;
time = _N_;
input y1 y2;
datalines;
0.55596529 2.114409393
-1.842925215 3.415027987
-1.902310801 2.615393601
-2.248005105 0.9952899
-1.386956611 -0.572170733
-6.290051188 -0.310766568
-9.824145014 -2.375539323
-11.33125468 -2.033315124
-11.04128514 1.842206169
-10.89568714 1.40799338
-10.46596445 2.962635195
-8.817024707 3.757484002
-5.862750166 1.793837649
-3.284472561 1.862678144
-3.128332138 0.433936326
0.430303362 -0.368114783
2.971947408 2.024630709
6.638185117 4.69384194
12.25116709 5.858882607
17.04096437 3.543926435
20.41679577 1.65943428
18.51841883 0.959385131
16.16660667 -2.234961913
16.1968332 0.057038179
18.43772993 -0.841499351
19.21268149 -2.572375281
20.02311956 -2.627351597
19.01172132 -1.412963269
20.27169138 -1.411172698
18.3457528 -1.40233312
15.04858583 -2.841223563
15.15106842 -3.243089527
13.85605054 -3.671478091
12.49147368 -3.374733171
14.38201242 -2.99561536
15.12143614 -2.561309891
15.76559462 -3.02872438
14.82214794 -2.41887462
12.37425271 -4.167693226
13.37312446 -2.019779426
15.12469972 -1.072619885
11.4863374 -1.182035611
7.816442146 -1.545865734
5.680708273 -1.362345421
7.238881474 0.628390503
10.12982025 3.820224713
11.86261027 5.853106419
12.52226298 4.204990417
10.51454488 2.325236828
5.788494497 0.920004459
0.954819513 -0.841178078
-0.491793852 -3.923359652
-2.798254013 -0.980792371
-5.127306324 -0.3811303
-7.292794694 -1.112021849
-6.63872168 1.48532677
-7.701037681 2.324912618
-6.048421701 1.185675561
-3.549952081 3.773101831
-2.611177678 3.900489283
-2.978391351 0.782197639
-6.503074495 1.382663428
-8.08124063 1.719009076
-7.371598277 2.952446326
-7.794619134 1.640602561
-9.094461567 3.261986746
-5.919236395 4.001846
-4.039770403 1.469082753
-1.510992772 0.248386132
-0.324484679 1.324776774
-0.71074958 3.596508538
-0.940853943 1.546151155
0.404166268 0.751260536
-0.527402926 0.306800185
-3.684081113 0.850685608
-4.298205348 -0.924027557
-5.511763734 -0.021857433
-3.048094616 -0.385993229
0.292876294 2.956489898
3.163956804 1.991456974
6.763658354 -0.972580053
9.359132829 -0.555863305
10.24917627 -3.86638022
10.30987404 -1.660729764
11.35726349 1.386419335
14.73883716 -1.38469536
14.99628156 -0.148796643
12.68420327 -0.421247464
11.8259717 -0.612098468
12.98093485 0.284795368
13.58085628 3.440512155
9.568352382 -0.756737686
7.724909992 -2.676466467
7.787418741 -1.906369204
6.414312952 -0.085981291
4.49189125 0.247328528
3.011831651 1.267382871
4.845706722 0.962288723
4.099474131 1.076872969
2.390932767 0.292170409
2.824183989 0.896892308
4.706596371 3.84192652
5.231122379 3.317620942
4.387964738 2.379516246
2.610294949 2.5986505
1.729300749 3.155218012
1.398768715 2.946561332
4.197698734 4.102635398
4.803607393 1.501113435
4.58822891 1.315779634
3.745645286 1.924455565
2.256653686 -1.159908444
-0.059050134 -1.605166854
-5.561686186 -0.656506054
-7.363011117 0.419576957
-5.457543417 2.198400043
-3.396957819 1.528905142
-3.81500093 -1.978290887
-8.920745865 -4.134842093
-14.0166281 -3.438500566
-13.23006165 1.215395181
-9.226228395 3.16585802
-6.815349719 0.633161256
-4.340202494 1.824355768
-3.52706095 1.158503353
-2.887031884 3.673333275
-0.712328099 1.574133664
-0.682134721 0.747149369
-3.518753295 -1.317034809
-5.095989193 0.433506796
-2.669790532 3.445066275
0.938589585 1.921235347
0.1532253 2.841595773
0.066382095 1.228470026
-1.930040944 1.195660277
-0.699041401 4.066151113
-0.094347441 7.324965352
1.04238908 4.840174511
2.255075154 4.057298755
1.741561776 2.487363643
4.532586772 3.875142978
8.59661415 4.18072418
13.52783891 5.337918637
17.3282251 1.686077987
18.88969779 -1.173162267
17.26724305 0.006014488
14.02334041 1.628873305
13.37439774 0.121860865
10.43149164 0.786734092
7.503930215 -0.109248204
7.129695371 -0.620230909
6.293752266 3.6557205
6.829089667 0.738740749
5.858941093 2.100279755
7.734758185 2.321302529
6.843085922 3.674399035
7.536162832 4.491517673
5.798191396 0.834817888
4.993707139 1.768730708
4.906702157 -0.548746235
4.144127248 -3.201700374
4.015232146 -0.865743522
3.531887791 -0.002876495
2.335168009 -0.850180551
1.832682706 0.075621553
2.172800834 2.04817741
2.55764747 3.308907862
5.295616707 2.406050953
7.728854052 3.307255484
7.679596999 7.070727533
6.975106524 2.654427234
8.342226747 0.889847754
12.69024066 0.537800531
13.34842679 -0.219751702
11.94825744 -0.871994828
13.20717941 1.411596748
14.72070411 2.384214765
15.28818957 -0.367447105
14.21379671 -3.401759054
12.86017179 -2.315151285
10.51228672 -0.112273256
9.286512167 0.344294417
10.31104734 -2.089330341
11.88337096 -1.568240503
12.31023892 1.76485829
11.7672971 -1.228669224
11.78853433 -0.15937714
13.13148672 0.873933237
15.88689709 0.247246512
14.482375 -0.195540095
11.94057417 -4.801269888
9.517754666 -4.646239731
3.319945555 -5.15334847
-2.317566823 -6.642518388
-4.441296888 -4.220450192
-4.681679665 -1.74000032
-6.243467704 -3.838702799
-6.503370264 -1.823567984
-5.437779045 1.328242787
-3.610229459 2.169080296
-0.723783437 -0.452029277
-0.877486374 0.38573372
-0.231450572 1.682756725
-0.65474782 2.513576785
1.507522277 5.141615587
0.312752368 3.338816977
1.120333577 1.603667492
0.852932578 1.174135051
3.790550195 -0.97748143
2.039053477 0.707741956
-1.06863296 -1.534053987
-3.360014169 -0.417623506
-4.184861606 0.6269709
-5.704199848 -0.300932893
-7.951510035 -0.504589953
-8.187079703 -0.019149481
-8.293156076 0.997621424
-8.281717875 -0.055924206
-7.704889165 0.448454665
-3.5523023 0.677475961
0.0512473 -0.763522968
1.354323074 -1.601248748
-1.701941724 -2.035610776
-4.050205878 -3.482093197
-2.866323406 -2.06845522
-2.854369007 -2.625644496
-3.538743844 -2.376050715
-6.445713569 1.23953275
-6.528174666 1.687188901
-4.01501181 2.872994949
-1.404863308 6.899240403
3.944978929 4.113354098
5.283398124 3.737103805
6.62368407 3.274578455
7.024068841 0.733019655
4.930336135 -1.421069328
3.135043635 -1.389493603
2.007416789 -2.557903329
1.53047432 -2.63796306
0.312003492 -3.339430227
-2.722816534 -3.006123001
-2.768792634 -0.737481602
-2.428296795 -1.762103682
-3.801191514 0.473957287
-6.231322761 -3.455367996
-7.609972633 -1.352107257
-9.375327479 3.275447528
-10.08887653 0.640589518
-9.155709599 -0.517605752
-9.238330294 3.141385071
-7.074885085 2.922053697
-6.461628141 1.076018473
-4.713370971 1.45838896
-3.234435168 5.137359038
-0.142632943 1.371481202
2.418226397 2.140040932
6.609924398 0.519802316
8.137568018 -1.935871383
10.8184115 -5.141337112
9.243974195 -5.818160659
7.8660264 -2.065398728
8.219879182 -2.072200509
8.969466124 -2.396586456
6.667302253 -2.846668245
4.623204833 -3.089145417
3.345510148 -2.134334544
3.447664749 1.731988416
4.252029782 1.473815851
3.791879261 0.912968272
5.477942664 0.459451728
7.311720639 -0.79984827
6.012278424 -2.597600791
7.129371097 -2.904127965
6.913469971 -1.143577028
5.146707164 -3.248727429
7.105954122 1.469776494
10.67005054 1.368419709
12.95969498 -2.066349681
14.02697735 -3.999215047
15.15761086 -2.322387056
10.57032614 -4.546598262
7.248549182 -4.581405568
7.204712122 0.345788768
10.44644028 5.149279058
13.27540868 1.345942797
12.31082888 0.308691544
12.58366049 -3.446590557
11.93778339 -1.256044285
12.89991105 -2.186139544
9.935949534 0.584212608
7.675005397 -1.141897878
3.100639764 -2.658736046
0.028276645 -0.566457811
1.686084256 3.248508053
1.030326063 4.539374251
2.997431612 1.115765522
1.640310212 1.200665042
2.014900892 1.709026626
0.880947155 1.36294136
0.006582325 0.820292251
-0.11403469 1.159943105
-1.531031097 4.53151381
-0.84147058 1.872903531
0.461103485 0.750670591
2.624957311 -0.388977165
3.964609083 1.078858189
5.657680781 0.098574376
10.01903718 2.751379093
11.49066528 2.040129942
12.93872157 -0.400367897
9.331624005 -0.391147104
6.133691342 -1.247685495
7.853151504 1.839649998
8.83173455 1.030615271
6.095075482 -1.278255666
6.853369847 0.538277647
5.642387258 4.853974941
8.848893818 3.275666558
8.160075534 2.56742688
6.861976367 0.432190993
5.362656445 5.441939845
5.442704559 4.286526042
6.054276117 2.604337678
3.915822629 0.218562266
2.235530681 -0.728221496
3.938563137 0.129278695
4.7883258 2.654905292
6.892386732 0.093278028
6.370305289 -3.142914722
6.766072194 -2.392484055
6.52389698 1.106740808
9.392521296 1.617538378
7.691642774 2.62857616
6.621613902 -0.049231298
5.248308496 -0.149597563
4.425412668 0.642242194
4.665737941 2.222468983
5.52979975 1.533222112
5.060352681 3.050167532
4.210862251 2.026537949
0.288594094 0.809877226
-1.439739489 1.870556263
-0.281368662 2.105257741
0.481512801 1.829910625
2.853862911 2.682912212
2.219576629 7.986335995
2.630644994 2.312136041
2.673262597 -0.656363805
0.607984423 1.082905129
0.37138572 0.55733153
-1.87630966 1.070103203
-4.132317673 3.126588907
-5.550083712 4.511646352
-6.960459936 0.730720694
-8.865019264 -0.537215058
-9.862091258 3.008579522
-7.572681366 3.799895275
-4.964263603 0.490304898
-4.768820456 -2.310939455
-5.711927119 -1.475696317
-8.069757392 0.582096096
-8.771522392 -0.29515353
-10.32589005 0.483015873
-12.2861467 2.096763227
-12.33817961 3.676420671
-12.97868468 3.449535978
-12.60367378 -0.994432852
-11.31603219 0.694290359
-9.792968791 1.495958231
-7.193247485 3.701867223
-3.196769483 3.926408354
1.100544963 3.340551911
4.132052984 2.44698349
2.829789517 0.674311856
3.600537679 -0.071992411
6.626306468 2.556788021
4.226199206 1.977083984
2.578014926 2.239843267
1.127762764 2.902934186
1.727467145 2.342503452
2.616201014 5.159964935
2.318130991 2.477220814
-0.622437718 -2.528970186
-2.474361036 -1.21052489
-2.258655523 3.166370762
-1.46217868 2.423332519
-2.256063158 2.240848815
-4.737910338 1.64893769
-8.695325545 3.72883108
-9.324947714 3.296794086
-9.604825347 3.445013114
-8.485226607 2.733111453
-11.99399791 3.640419656
-9.848168735 1.063096114
-4.975843515 4.290785473
-4.747876368 4.406542723
-2.596246629 0.427557974
-3.009840218 1.267797375
-2.86707489 1.147627529
-0.195787414 0.820107072
;
proc varmax data = VARFIMA1D1N4 plots = (forecasts);
model y1 y2 / noint fi p=1 q=1;
initial d(1) = 0.45, d(2) = 0.25;
output out = forec back = 36 lead = 36;
run;
proc varmax data = VARFIMA1D1N4 plots = (impulse);
model y1 y2 / noint fi p=1 q=1 print = (impulse = (all));
run;
proc varmax data=simul1 noprint;
id date interval=year;
model y1 y2 / p=1 noint;
output out=out lead=5;
run;
proc print data=out(firstobs=98);
run;
proc varmax data=simul2 outest=est;
model y1 y2 / p=2 noint noprint;
cointeg rank=1 normalize=y1;
run;
proc print data=est;
run;
data garch;
set garch;
date = intnx( 'month', '01may1972'd, _n_-1 );
format date yymms.;
run;
proc varmax data=garch;
id date interval=month;
model y1 y2 / p=1;
garch q=1 outht=ht;
output out=og lead=6;
run;
proc print data=og(obs=8);
var date y1 for1 std1 lci1 uci1 y2 for2 std2 lci2 uci2;
run;
proc print data=ht(obs=8);
run;
proc print data=og(firstobs=499);
var date y1 for1 std1 lci1 uci1 y2 for2 std2 lci2 uci2;
run;
proc print data=ht(firstobs=499);
run;
proc varmax data=simul2 outstat=stat;
model y1 y2 / p=2 noint noprint
cointtest=(johansen=(iorder=2));
cointeg rank=1 normalize=y1;
run;
proc print data=stat;
run;