* Choose "File-Clear Program" before you do the following.

All 1000

******** U = white noise Process  ***************************

* U = White noise process

set U = %ran(1)
correlate(partial=PACF, QSTATS) U / ACF
graph(key=below,style=bar,nodates,min=-1.0,max=1.0,number=1) 2
# ACF
# PACF

******** Y = AR(1) Process ***************************

* Generating the data and plot

set y = 0
set y 2 * =  0 + 0.5 * y{1} + %ran(1)

graph(key=below, header = 'y(t): AR(1) Model with alpha = 0.5') 1
# y

* Finding ACF and plot

correlate(QSTATS, Partial=PACF) y / ACF

graph(key=below,style=bar,nodates,min=-1.0,max=1.0,number=1, $
 header = 'ACF of y(t): AR(1) Model with alpha = 0.99') 2
# ACF
# PACF

* Estimating the model

boxjenk(constant, ar=1) y / resids

* Checking the residual

cor(partial=pacf,qstats,number=48,span=8,dfc=%nreg) resids / ACF

graph(key=below,style=bar,nodates,min=-1.0,max=1.0,number=1, $
 header = 'ACF of Residauls: AR(1) Model with alpha = 0.5') 2
# ACF
# PACF

******** Y = MA(1) Process  ***************************

* Generating the data and plot

set U = %ran(1)
set y = 0 + U + 0.5 * u{1}

graph(key=below, header = 'y(t): MA(1) Model') 1
# y

* Finding ACF and plot

correlate(QSTATS) Y / ACF

graph(key=below,style=bar,min=-1.0,max=1.0,number=1, $
  header = 'ACF and PACF of y(t): MA(1) Model with theta = 0.5') 2
# ACF
# PACF

* Estimating the model

boxjenk(constant, ma=1) y / resids

* Checking the residual

cor(partial=pacf,qstats,number=48,span=8,dfc=%nreg) resids / ACF

graph(key=below,style=bar,nodates,min=-1.0,max=1.0,number=1, $
 header = 'ACF and PACF of residuals: MA(1) Model with theta = 0.5') 2
# ACF
# PACF