BJIDENT

Output     Options      Example      References

BJIDENT prints and plots descriptive statistics which are useful in identifying the process which generated a time series. The process of time series identification is described in the two references; TSP follows the notation of Box and Jenkins, who developed this technique for analyzing time series. BJEST is used for estimating the model you develop and BJFRCST for forecasting with it.

The decisions to be made in the process of identifying a time series process are 1) whether there is a seasonal component, 2) how much ordinary and seasonal differencing is required to make the series stationary, 3) and what are the minimum orders of the autoregressive and moving average polynomials required to explain adequately the time series. Subject to various option settings, BJIDENT will present plots of autocorrelations and partial autocorrelations for various levels of differencing of the input series.

BJIDENT (BARTLETT, ESACF, IAC, NAR=<order of AR for ESACF>, NDIFF=<degree of differencing>, NLAG=<number of autocorrelations to be computed>, NLAGP=<number of partial autocorrelations to be computed>, NMA=<order of MA for ESACF>, NSDIFF=<degree of seasonal differencing>, NSPAN=<span of seasonal>,  PLOT, PLOTAC, PLTRAW, NOPRINT, PREVIEW, SILENT)  <list of series> ;

Usage

BJIDENT followed by the name of a series is the simplest form of the command. No differencing of the series will be done in this case, and the output will consist of a plot of the series, and a printout and plot of the autocorrelations of the first 20 lags of the series and the first 10 partial autocorrelations.

Autocorrelations are the correlation of the series with its own values lagged once, lagged twice, and so forth for 20 lags. Partial autocorrelations are the correlations measured with the series residual after all the prior lags have been removed. That is, the second partial autocorrelation is the correlation of the series lagged twice with the part of the series which is orthogonal to the first lag.

The options on the BJIDENT command allow you to specify the differencing you want performed on the series, whether there is a seasonal component, and the output you wish to see plotted or printed. You can also increase and decrease the number of autocorrelations which are computed.

If you want to analyze the log or other transformation of your original series, as suggested by Box and Jenkins or Nelson, transform the series using a GENR statement before submitting it to BJIDENT.

Output

The output of BJIDENT begins with the plots of the raw and differenced series (if the PLOT option was requested). These plots are high resolution graphics plots in TSP/Oxmetrics, and low-resolution in other versions. Next a table of the autocorrelations is printed with their standard errors and the Ljung-Box portmanteau test, or modified Q-statistic. These modified Q-statistics are distributed independently as chi-squared random variables with degrees of freedom equal to the number of autocorrelations. The null hypothesis is that all the autocorrelations to that order are zero.

Following this table, the partial autocorrelations are printed for each series. If PLOTAC has been specified, BJIDENT then plots the autocorrelation and partial autocorrelation functions of the series and its differences with standard error bands. The inverse autocorrelations are printed if requested. Finally, the ESACF correlations, their p-values, and a table of Indicators is printed. If the PRINT option is on, a table of AR coefficient estimates is printed. The following matrices are stored:

Options

Note that for all the Box-Jenkins procedures (BJIDENT, BJEST, and BJFRCST), TSP remembers the options from the previous Box-Jenkins command, so that you only need to specify the ones you want to change.

BARTLETT/NOBART specifies that the Bartlett estimate using lower order autocorrelations is to be used for the variance of the ESACF option. NOBART will simply use 1/(T-p-q).

ESACF/NOESACF computes the extended sample ACF of Tsay and Tiao (1984). This can be useful for identifying stationary and nonstationary ARMA models. The upper left vertex of a triangle of zeroes in the Indicator matrix identifies the order of the ARMA model. The zeroes correspond to nonsignificant autocorrelations. See the examples.

IAC/NOIAC specifies whether the inverse autocorrelations are to be computed and printed.

NAR= maximum order of AR for ESACF. Default is 20.

NDIFF= the degree of differencing to be applied to the series. The default is zero (no differencing). BJIDENT will calculate statistics for all the differences of the series up to and including the NDIFFth order.

NLAG= the number of autocorrelations to be computed. The default is 20.

NLAGP= the number of partial autocorrelations to be computed. The default is 10.

NMA= maximum order of MA for ESACF. Default is 10.

NSDIFF= the degree of seasonal differencing to be applied to the series. The default is zero (no differencing). As in the case of ordinary differencing, BJIDENT will calculate statistics for all the differences of the series up to and including the NSDIFFth order.

NSPAN= the span (number of periods) of the seasonal cycle, i.e., for quarterly data, NSPAN should be 4. The default is the current frequency (that is, 1 for annual, 4 for quarterly, 12 for monthly).

PLOT/NOPLOT specifies whether all the differenced series are to be plotted.

PLOTAC/NOPLOTAC specifies whether the autocorrelations and partial autocorrelations are to be plotted.

PLTRAW/NOPLTRAW specifies whether the original "raw" series is to be plotted.

PREVIEW/NOPREVIEW (TSP/Oxmetrics only) specifies that the raw and differenced series are to be displayed in a high-resolution graphics window if the PLOT option is on.

PRINT/NOPRINT specifies whether the AR coefficients for the ESACF option are to be printed.

SILENT/NOSILENT Turns off all output. Results are still stored in @AC, @PAC, etc.

Example

This example computes the auto sales example from Nelson's book:

BJIDENT (IAC, NDIFF=1, NSDIFF=1, NSPAN=12, NLAG=48, NLAGP=20) AUTOSALE ;

The following example shows the ESACF output for Box-Jenkins Series C:

BJIDENT (ESACF, NAR=5, NMA=8) CHEM ;

The result of the above command is the following matrix:

                   MA

AR    0  1  2  3  4  5  6  7  8

0     9  9  9  9  9  9  9  9  1

1     9  9  9  9  9  1  1  0  0

2     0  0  0  0  0  0  0  0  0

3     9  0  0  0  0  0  0  0  0

4     9  9  0  0  0  0  0  0  0

5     9  9  9  0  0  0  0  0  0

A triangle of zeroes with upper left vertex at (2,0) is seen; this indicates an ARMA(2,0) model.

References

Box, George P., and Gwilym M. Jenkins, Time Series Analysis: Forecasting and Control, Holden-Day, New York, 1976.

Ljung, G. M., and Box, George, "On a measure of lack of fit in time series models," Biometrika 66, 1978, pp. 297-303.

Nelson, Charles, Applied Time Series Analysis for Managerial Forecasting, Holden-Day, New York, 1973.

Pindyck, Robert S., and Daniel L. Rubinfeld, Econometric Models and Economic Forecasts, McGraw-Hill Book Co., 1976, Chapters 13 and 14.

Tsay and Tiao. "Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models," JASA, March 1984, pp. 84-96.