* ARCH model
* Data = WPI

cal 1960 1 4             ;* set calendar to begin 1960:Q1
all 0 1992:2             ;* data runs until 1992:Q2
open data wpi.wk1      ;* data is assumed to be on drive a:\
data(format=wks,org=obs) / wpi

set lwpi = log(wpi)

* ACF plot of the raw data
cor(partial=pacf,qstats,number=36,span=12,dfc=4) lwpi
source(noecho) bjident.src
@bjident lwpi

* Since it appears non-stationary, we take a first difference.
set dlwpi = lwpi - lwpi{1} ;* transform data
set y = dlwpi

cor(partial=pacf,qstats,number=36,span=12,dfc=4) y
source(noecho) bjident.src
@bjident y

* Estimating ARMA model(1,4) for the differenced data

boxjenk(constant,ar=1,ma=4) y / U
cor(partial=pacf,qstats,number=36,span=12,dfc=4) U

* Testing for arch effects
set u2 = u*u
lin u2
# constant u2{1 to 4}

* Estimating GARCH models

*source(noecho) garch.src
*@GARCH y / res1 Ht1   ; * Choose ar=1, ma=4, p=1, q=1, det=const

* ar=1, ma=4, p=1, q=1, det=const
garch(p=1,q=1,regressors,hseries=h1) / y
# constant y{1}  %mvgavge{1 to 4}

*asymmetric model
garch(p=1,q=1,regressors, asymmetric, hseries=h2) / y
# constant y{1} %mvgavge{1 to 4}

*asymmetric model
garch(p=1,q=1,regressors, exponenial, hseries=h3) / y
# constant y{1} %mvgavge{1 to 4}

graph(header="Plots of h(t)", key = below) 3
# h1
# h2
# h3

****************************************************

cal(q) 1960:1
all 2008:2

open data quarterly.xls
data(format=xls,org=obs)

set y = cpicore
log y / ly
dif ly / dly

set growth = 100*dly

gra(hea='Inflation Rate using CPI Core',overlay=line, $
patterns,key=below,nokbox,ovl='billions of $',vla='rate of growth') 2 ;# growth ; # y

garch(p=1,q=1,hseries=hvar) / growth
gra(hea='Plot of h(t) and inflation') 2; # growth; #hvar

garch(p=1,q=1,exp,asymmetric, hseries=hvar2, regressors) / growth
# constant %mvgavge{1}

gra(hea='Plot of h(t) and inflation, EGARCH(1,1), MA(1)') 2; # growth; #hvar2