Sspace—179
Series Element Functions
@elem(ser, j)........function to access the j-th observation of the series SER, where j identifies the date or observation.
Series Examples
You can declare a series in the usual fashion:
series b=income*@mean(z)
series blag=b(1)
Note that the last example above involves a series expression so that B(1) is treated as a one-period lead of the entire series, not as an element operator. In contrast:
scalar blag1=b(1)
evaluates the first observation on B in the workfile.
Once a series is declared, views and procs are available:
a.qqplot
a.statby(mean, var, std) b
To access individual values:
scalar quarterlyval = @elem(y, "1980:3") scalar undatedval = @elem(x, 323)
Sspace
State space object. Estimation and evaluation of state space models using the Kalman filter.
Sspace Declaration
sspace |
...................create sspace object (p. 482). |
To declare a sspace object, use the sspace keyword, followed by a valid name.
Sspace Method
ml ........................maximum likelihood estimation or filter initialization (p. 369).
Sspace Views
cellipse ................. |
Confidence ellipses for coefficient restrictions (p. 236). |
coefcov ................. |
coefficient covariance matrix (p. 244). |
endog ................... |
table or graph of actual signal variables (p. 285). |
grads .................... |
examine the gradients of the log likelihood (p. 315). |
label ..................... |
label information for the state space object (p. 330). |
180—Appendix A. Object, View and Procedure Reference
output.................. |
table of estimation results (p. 380). |
residcor................ |
standardized one-step ahead residual correlation matrix (p. 421). |
residcov ............... |
standardized one-step ahead residual covariance matrix (p. 421). |
resids ................... |
one-step ahead actual, fitted, residual graph (p. 422). |
results.................. |
table of estimation and filter results (p. 423). |
signalgraphs......... |
display graphs of signal variables (p. 471). |
spec ..................... |
text representation of state space specification (p. 479). |
statefinal.............. |
display the final values of the states or state covariance (p. 485). |
stategraphs........... |
display graphs of state variables (p. 484). |
stateinit................ |
display the initial values of the states or state covariance (p. 486). |
structure .............. |
examine coefficient or variance structure of the specification |
|
(p. 492). |
wald .................... |
Wald coefficient restriction test (p. 530). |
Sspace Procs
append................. |
add line to the specification (p. 205). |
displayname......... |
set display name (p. 276). |
forecast ................ |
perform state and signal forecasting (p. 300). |
makeendog .......... |
make group containing actual values for signal variables (p. 351). |
makefilter ............ |
make new Kalman Filter(p. 352). |
makegrads ........... |
make group containing the gradients of the log likelihood (p. 353). |
makemodel .......... |
make a model object containing equations in sspace (p. 358). |
makesignals ......... |
make group containing signal and residual series (p. 361). |
makestates ........... |
make group containing state series (p. 362). |
sspace.................. |
declare sspace object (p. 482). |
updatecoefs .......... |
update coefficient vector(s) from sspace (p. 521). |
Sspace Data Members
Scalar Values
@coefcov(i,j) ....... |
covariance of coefficients i and j. |
@coefs(i)............. |
coefficient i. |
@eqregobs(k) ...... |
number of observations in signal equation k. |
@sddep(k)........... |
standard deviation of the signal variable in equation k. |
@ssr(k) ............... |
sum-of-squared standardized one-step ahead residuals for equa- |
|
tion k. |
@stderrs(i) .......... |
standard error for coefficient i. |
@tstats(t)............. |
t-statistic value for coefficient i. |
Sspace—181
Scalar Values (system level data)
@aic..................... |
Akaike information criterion for the system. |
@hq ..................... |
Hannan-Quinn information criterion for the system. |
@logl ................... |
value of the log likelihood function. |
@ncoefs ............... |
total number of estimated coefficients in the system. |
@neqns ................ |
number of equations for observable variables. |
@regobs ............... |
number of observations in the system. |
@sc...................... |
Schwarz information criterion for the system. |
@totalobs ............. |
sum of “@eqregobs” from each equation. |
Vectors and Matrices
@coefcov.............. |
covariance matrix for coefficients of equation. |
@coefs ................. |
coefficient vector. |
@stderrs............... |
vector of standard errors for coefficients. |
@tstats ................. |
vector of t-statistic values for coefficients. |
State and Signal Results
The following functions allow you to extract the filter and smoother results for the estimation sample and place them in matrix objects. In some cases, the results overlap those available thorough the sspace procs, while in other cases, the matrix results are the only way to obtain the results.
Note also that since the computations are only for the estimation sample, the one-step- ahead predicted state and state standard error values will not match the final values displayed in the estimation output. The latter are the predicted values for the first out-of-esti- mation sample period.
@pred_signal........ |
matrix or vector of one-step ahead predicted signals. |
@pred_signalcov... |
matrix where every row is the @vech of the one-step ahead pre- |
|
dicted signal covariance. |
@pred_signalse..... |
matrix or vector of the standard errors of the one-step ahead pre- |
|
dicted signals. |
@pred_err ............ |
matrix or vector of one-step ahead prediction errors. |
@pred_errcov ....... |
matrix where every row is the @vech of the one-step ahead pre- |
|
diction error covariance. |
@pred_errcovinv .. |
matrix where every row is the @vech of the inverse of the one- |
|
step ahead prediction error covariance. |
@pred_errse ......... |
matrix or vector of the standard errors of the one-step ahead pre- |
|
diction errors. |
@pred_errstd ........ |
matrix or vector of standardized one-step ahead prediction errors. |
182—Appendix A. Object, View and Procedure Reference
@pred_state ......... |
matrix or vector of one-step ahead predicted states. |
@pred_statecov.... |
matrix where each row is the @vech of the one-step ahead predi- |
|
cated state covariance. |
@pred_statese ...... |
matrix or vector of the standard errors of the one-step ahead pre- |
|
dicted states. |
@pred_stateerr..... |
matrix or vector of one-step ahead predicted state errors. |
@curr_err ............ |
matrix or vector of filtered error estimates. |
@curr_gain.......... |
matrix or vector where each row is the @vec of the Kalman gain. |
@curr_state ......... |
matrix or vector of filtered states. |
@curr_statecov .... |
matrix where every row is the @vech of the filtered state covari- |
|
ance. |
@curr_statese ...... |
matrix or vector of the standard errors of the filtered state est- |
|
mates. |
@sm_signal ......... |
matrix or vector of smoothed signal estimates. |
@sm_signalcov .... |
matrix where every row is the @vech of the smoothed signal cova- |
|
riance. |
@sm_signalse ...... |
matrix or vector of the standard errors of the smoothed signals. |
@sm_signalerr ..... |
matrix or vector of smoothed signal error estimates. |
@sm_signalerrcov matrix where every row is the @vech of the smoothed signal error
|
covariance. |
@sm_signalerrse .. |
matrix or vector of the standard errors of the smoothed signal |
|
error. |
@sm_signalerrstd. matrix or vector of the standardized smoothed signal errors. |
|
@sm_state ........... |
matrix or vector of smoothed states. |
@sm_statecov ...... |
matrix where each row is the @vech of the smoothed state covari- |
|
ances. |
@sm_statese ........ |
matrix or vector of the standard errors of the smoothed state. |
@sm_stateerr....... |
matrix or vector of the smoothed state errors. |
@sm_stateerrcov.. |
matrix where each row is the @vech of the smoothed state error |
|
covariance. |
@sm_stateerrse .... |
matrix or vector of the standard errors of the smoothed state |
|
errors. |
@sm_stateerrstd... |
matrix or vector of the standardized smoothed state errors . |
@sm_crosserrcov . matrix where each row is the @vec of the smoothed error crosscovariance.
Sspace Examples
The one-step-ahead state values and variances from SS01 may be saved using:
Sym—183
vector ss_state=ss01.@pred_state
matrix ss_statecov=ss01.@pred_statecov
Sym
Symmetric matrix (symmetric two-dimensional array).
Sym Declaration
sym ...................... |
declare sym object (p. 496). |
Declare by providing a name after the sym keyword, with the optionally specified dimension in parentheses:
sym(10) symmatrix
You may optionally assign a scalar, a square matrix or another sym in the declaration. If the square matrix is not symmetric, the sym will contain the lower triangle. The sym will be sized and initialized accordingly.
Sym Views
area ...................... |
area graph of the columns of the matrix (p. 211). |
bar ....................... |
single or multiple bar graph of each column against the row index |
|
(p. 219). |
cor........................ |
correlation matrix by columns (p. 255). |
cov ....................... |
covariance matrix by columns (p. 259). |
errbar ................... |
error bar graph view (p. 287). |
hilo ...................... |
high-low(-open-close) chart (p. 320). |
label ..................... |
label information for the symmetric matrix (p. 330). |
line....................... |
single or multiple line graph of each column against the row index |
|
(p. 334). |
pie........................ |
pie chart view (p. 406). |
scat ...................... |
scatter diagrams of the columns of the sym (p. 435). |
sheet .................... |
spreadsheet view of the symmetric matrix (p. 469). |
spike .................... |
spike graph (p. 479). |
stats...................... |
descriptive statistics by column (p. 487). |
xy......................... |
XY graph with one or more X columns plotted against one or more |
|
Y (p. 556). |
xyline ................... |
XY line graph (p. 558). |
xypair................... |
XY pairs graph (p. 556). |