Fits an ARIMA model, with forecast and residual checks (G. Tunnicliffe Wilson & S.J. Welham).
Options
PRINT = string tokens |
Controls printed output (description, monitoring, model); default desc, moni, mode |
|---|---|
GRAPHICS = string token |
What type of graphics to use (lineprinter, highresolution); default high |
WINDOWS = scalar or variate |
Windows to be used for residual plots: a scalar N indicates that plots are to be produced on separate pages in window N (as currently defined), whereas a variate specifies four separate windows to be redefined (within the procedure) for plotting four graphs on one page; default 1 |
PENS = variate |
The three pens to be used (after being defined appropriately) for drawing the plots; default !(1,2,3) |
Parameters
SERIES = variates |
Holds the time series to which the model is to be fitted |
|---|---|
LENGTH = scalars or variates |
Specifies the units to be used from each series: a scalar N indicates that the first N units of the series are to be used, a variate of length 2 gives the index of the first and last units of the subseries to be used; by default the whole series is used |
ORDERS = variates |
Variate holding the orders for the ARIMA model to be fitted to each series |
PARAMETERS = variates |
Variate specifying the initial values for the parameters (to be used by the TFIT directive) |
TSM = TSMs |
TSM to store each fitted model, also to supply values for orders and parameters if ORDERS and PARAMETERS are unset |
RESIDUALS = variates |
Variate to save the residuals from fitting the model to each series |
Description
BJESTIMATE fits an ARIMA model of specified orders to a time series given by the SERIES parameter. If only part of the series is to be used, this should be specified by the parameter LENGTH, using either a scalar N to indicate that the first N values should be used, or a variate of length 2 holding the positions of the first and last units of the subseries to be included. If only a subseries is used in the estimation, forecasts of any later series values are plotted to act as a check on the fitted model. The fit of the model is examined using the procedure BJIDENTIFY on the residual series; this residual series is plotted, together with its sample autocorrelations, partial autocorrelations and periodogram. The residuals from the fitted model can be saved using the RESIDUALS parameter.
The orders of the ARIMA model can be specified by the ORDERS parameter; alternatively, if parameter TSM has been set to the identifier of a TSM structure to save the results, ORDERS can be omitted and the orders will be taken from those of the TSM. Likewise, the PARAMETERS parameter can be set to a variate of initial values for the TFIT directive, used by the procedure to fit the model; if PARAMETERS is unset these will again be taken from the setting of the TSM parameter, if available. Any unset initial values are determined automatically by TFIT.
Printed output is controlled by the option PRINT; by default, a description of the series, monitoring of the estimation process and the fitted model are printed.
Graphical output is controlled by the options GRAPHICS, WINDOWS and PENS. Option GRAPHICS controls whether plots are produced for line-printer output or on the current high-resolution graphics device; by default high-resolution plots are given. Option WINDOWS controls the way in which the high-resolution plots are arranged. First of all there may be a graph of forecasts; this is plotted on a new page (i.e. a cleared screen), using the first window specified. Then procedure BJIDENTIFY is called to produce four different plots of residuals. If WINDOWS is set to a scalar N, the graphs are all produced in window N on separate pages; the FRAME directive can be used to set the attributes of window N before calling the procedure. Alternatively, WINDOWS can be set to a variate of length four; the attributes of the four windows specified are then redefined within the procedure so that four graphs are produced on the same page. By default WINDOWS=1. The PENS option controls which pens are used for the plots; the attributes of these pens are modified appropriately within the procedure. By default pens 1-3 are used, but these can be changed by setting option PENS to a variate of length 3 containing the numbers of the three different pens required.
Options: PRINT, GRAPHICS, WINDOWS, PENS.
Parameters: SERIES, LENGTH, ORDERS, PARAMETERS, TSM, RESIDUALS.
Method
The model is fitted using the default settings of directive TFIT, and forecasts are constructed for increasing leadtimes using the directive TFORECAST. BJIDENTIFY is called to display time series statistics for the residual series after fitting the required ARIMA model.
Action with RESTRICT
Input structures must not be restricted. Restriction of the input SERIES to a contiguous set of units can be achieved using the LENGTH parameter.
See also
Directive: TFIT.
Procedures: BJFORECAST, BJIDENTIFY.
Commands for: Time series.
Example
CAPTION 'BJESTIMATE example', !t(\
'Data from Andrews & Herzberg (1985), Data, A Collection',\
'of Problems from Many Fields for the Student and Research',\
'Worker, Springer-Verlag, pp. 369-370.'); STYLE=meta,plain
VARIATE [VALUES=8.075,7.819,7.366,8.113,7.380,7.134,7.222,7.768,\
7.386,6.965,6.478,8.105,8.060,7.684,7.580,7.093,\
6.129,6.026,6.679,7.414,7.112,7.762,7.645,8.639,\
7.667,8.080,6.678,6.739,5.569,5.049,5.642,6.808,\
6.636,8.241,7.968,8.044,7.791,7.024,6.102,6.053,\
5.941,5.386,5.811,6.716,6.923,6.939,6.705,6.914] Profit
TSM Model; ORDERS=!(2,0,1,0,1,1,4);\
PARAMETERS=!(1,-0.1,0.2,1.6,-0.8,0.99,0.9)
VARIATE [VALUES=1...4] Windows
BJESTIMATE [PRINT=description,model; WINDOWS=Windows]\
Profit; LENGTH=40; TSM=Model
" If the TSM was not to be saved, the orders would need
to be supplied by the ORDERS parameter: i.e.
BJESTIMATE Profit; LENGTH=40; ORDERS=!(2,0,1,0,1,1,4) "
PRINT Model