** Chapter 21 ** for W.H. Greene, Econometric Analysis 6th ed. *****************
* (c) Noel Roy 2003, 2008
*
*                        TIME-SERIES MODELS
*
*===============================================================================
* 21.2 STATIONARY STOCHASTIC PROCESSES
*
* Example 21.1 (p. 729) ACF and PACF for a Series of Bond Yields.
*
READ (TableF21-1.prn) Date Yield /SKIPLINES=1 
*
* Replicate Figure 21.1
TIME 1990 12 Month 
TIMEFMT %Y.%m
AXISFMT %Y.%m
GRAPH Yield Month /NOKEY TIMEFMT AXISFMT
*
* The ARIMA command provides features for the Box-Jenkins approach to the
* analysis of autoregressive integrated moving average models of univariate 
* time series. There are 3   forms of the command: IDENTIFICATION, ESTIMATION, 
* and FORECASTING. The specified options determine which form of the ARIMA 
* command is in effect.
*  ...................... IDENTIFICATION PHASE ..............................
*   In general, the format is:
*    ARIMA vars / options
*   where vars is a list of variables. 
*
* The NLAG= option specifies the number of lags to consider in 
* the calculation of the autocorrelations (the default is 24). The NLAGP= 
* option specifies the number of lags to consider in the calculation of the 
* partial autocorrelations (the default is 12). The PLOTAC option plots the 
* sample autocorrelation function. The PLOTPAC option plots the sample
* partial autocorrelation function. The + symbols mark the 95% confidence 
* bounds (+ and - 2 standard deviations) for the autocorrelations. Additional 
* options are documented in Chapter 10 of the SHAZAM Manual.
*
* Generate the ACF and PACF in Table 21.1.
ARIMA YIELD / PLOTAC PLOTPAC  NLAG=14 NLAGP=14 
*
*  .......................... ESTIMATION PHASE ...............................
*   In general, the format is:
*    ARIMA var / NAR= NMA= options
*   where var is a variable, NAR= specifies the order of the AR process, and
*    NMA= specifies the order of the MA process (REQUIRED).
*
* An AR(2) model is estimated by running ARIMA with options NAR=2, NMA=0.
*
ARIMA YIELD / NAR=2 NMA=0 RESID=U COEF=GAMMA
* Calculate the roots of the AR(2) process to check stationarity.
GEN1 ROOT1=.5*(GAMMA(1)+SQRT(GAMMA(1)**2+4*GAMMA(2)))
GEN1 ROOT2=.5*(GAMMA(1)-SQRT(GAMMA(1)**2+4*GAMMA(2)))
PRINT ROOT1 ROOT2
* Plot the ACF and PACF of the residuals as in Table 21.2.
ARIMA U /PLOTAC PLOTPAC NLAG=14 NLAGP=14 
*
*  ........................ FORECASTING PHASE ................................
*   In general, the format is:
*    ARIMA var / COEF= NAR= NMA= FBEG= FEND= options
*   where var is a variable. 
STOP
*
*===============================================================================
* Updated November 19, 2008