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
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;
/* 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
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-9.824145014 -2.375539323
-11.33125468 -2.033315124
-11.04128514 1.842206169
-10.89568714 1.40799338
-10.46596445 2.962635195
-8.817024707 3.757484002
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-3.284472561 1.862678144
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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
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;
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;
