TSDECOMP Call
analyzes nonstationary time series by using
smoothness priors modeling
- CALL TSDECOMP( comp, est, aic, data, <,xdata, order,
sorder,
- nar, npred, init, opt, icmp,
print>);
The inputs to the TSDECOMP subroutine are as follows:
- data
- specifies a (or ) data vector.
- xdata
- specifies a explanatory data matrix.
- order
- specifies the order of trend differencing (0, 1, 2, or 3).
The default is 2.
- sorder
- specifies the order of seasonal differencing (0, 1, or 2).
The default is 1.
- nar
- specifies the order of the AR process.
The default is 0.
- npred
- specifies the length of the forecast
beyond the available observations.
The default is 0.
- init
- specifies the initial values of parameters.
The initial values are specified as variances for trend
difference equation, AR process, seasonal difference
equation, regression equation, and partial AR coefficients.
The corresponding default variance values
are 0.005, 0.8, 1E-5, and 1E-5.
The default partial AR coefficient values are determined as
- opt
- specifies the options vector.
- opt[1]
- specifies the mean deletion option.
The mean of the original series is subtracted
from the series if opt[1]=-1.
By default, the original series is processed (opt[1]=0).
When regressors are specified, only
the opt[1]=0 option is accepted.
- opt[2]
- specifies the trading day adjustment.
The default is opt[2]=0.
- opt[3]
- specifies the year () when the series starts.
If opt[3]=0, there is no trading day adjustment.
By default, opt[3]=0.
- opt[4]
- specifies the number of seasons
within a period (speriod).
By default, opt[4]=12.
- opt[5]
- controls the transformation of the original series.
If opt[5]=1, log transformation is requested.
By default, there is no transformation (opt[5]=0).
- opt[6]
- specifies the maximum number of iterations allowed.
The default is opt[6] = 200.
- opt[7]
- specifies the update technique for the
quasi-Newton optimization technique.
If opt[7]=1 is specified, the dual Broyden, Fletcher,
Goldfarb, and Shanno (BFGS) update method is used.
If opt[7]=2 is specified, the dual Davidon,
Fletcher, and Powell (DFP) update method is used.
The default is opt[7]=1.
- opt[8]
- specifies the line search technique for
the quasi-Newton optimization method.
The default is opt[8] = 2.
- opt[8]=1
- specifies a line search method that requires the
same number of objective function and gradient
calls for cubic interpolation and extrapolation.
- opt[8]=2
- specifies a line search method that requires
more objective function calls than gradient
calls for cubic interpolation and extrapolation.
- opt[8]=3
- specifies a line search method that requires the
same number of objective function and gradient
calls for cubic interpolation and extrapolation.
- opt[8]=4
- specifies a line search method that requires the
same number of objective function and gradient calls
for cubic interpolation and stepwise extrapolation.
- opt[8]=5
- specifies a line search method that is
a modified version of opt[8]=4.
- opt[8]=6
- specifies the golden section line search method that
uses only function values for linear approximation.
- opt[8]=7
- specifies the bisection line search method that
uses only function values for linear approximation.
- opt[8]=8
- specifies the Armijo line search method that uses
only function values for linear approximation.
- opt[9]
- specifies the upper bound of the variance estimates.
If you specify opt[9]=value, the variances are
estimated with the constraint that .
When you specify the opt[9]=0
option, the upper bound is not imposed.
The default is opt[9]=0.
- opt[10]
- specifies the length of data used in backward
filtering for the Kalman filter initialization.
The default value of opt[10] is 100 if the
number of observations is greater than 100; otherwise,
the default value is the number of observations.
- icmp
- specifies which component is calculated.
- icmp=1
- requests the estimate and forecast of trend component.
- icmp=2
- requests the estimate and forecast of seasonal component.
- icmp=3
- requests the estimate and forecast of AR component.
- icmp=4
- requests the trading day adjustment component.
- icmp=5
- requests the regression component.
- icmp=6
- requests the time-varying regression coefficients.
You can calculate multiple components by specifying a vector.
For example, you can specify icmp={1 2 3 5}.
- print
- specifies the print option.
By default, printed output is suppressed (print=0).
If you specify print=1, the
subroutine prints the final estimates.
The iteration history is printed if you specify print=2.
The TSDECOMP subroutine returns the following values:
- comp
- refers to the estimate and forecast of the trend component.
- est
- refers to the parameter estimates
including coefficients of the AR process.
- aic
- refers to the AIC statistic obtained from the final estimates.
The TSDECOMP subroutine analyzes nonstationary
time series by using smoothness priors modeling
(see the section
"Smoothness Priors Modeling" for more details).
The likelihood function is maximized
with respect to hyperparameters.
The Kalman filter algorithm is used for
filtering, smoothing, and forecasting.
The TSDECOMP call decomposes the time series
as follows:
where
represents the trend component,
denotes the seasonal component,
represents the trading day adjustment component,
denotes the autoregressive process component,
denotes regression effect components,
and
represents the irregular
term with zero mean and constant variance.
The trend components are constrained as follows:
When you specify the ORDER=0 option,
the trend component is not estimated.
The maximum order of differencing is 3 (
).
The seasonal components are denoted as
a stochastically perturbed equation:
When you specify SORDER=0, the
seasonal component is not estimated.
The maximum value of
is 2 (
).
The stationary autoregressive (AR) process is
denoted as a stochastically perturbed equation:
where
is the order of AR process.
When NAR=0 is specified, the AR
process component is not estimated.
The time-varying regression coefficients are
estimated if you include exogenous variables:
where
contains
regressors except the constant
term and
.
The time-varying coefficients
follow the random walk process:
where
is an element of
the coefficient vector
.
The trading day adjustment component
is deterministically restricted.
See the section "State Space and Kalman Filter Method",
for more information.
You can estimate the time-varying coefficient model as follows:
call tsdecomp COMP=beta ORDER=0 SORDER=0 NAR=0
DATA=y XDATA=x ICMP=6;
The output matrix BETA contains
time-varying regression coefficients.