* * Enders, Applied Econometric Time Series, 4th edition * Seasonal ARMA models * Application from pp 98-102 * open data quarterly.xls calendar(q) 1960:1 data(format=xls,org=columns) 1960:01 2012:04 m1nsa m2nsa cpinsa * set m1growth = log(m1nsa/m1nsa{1}) graph(footer="Figure 2.7 Level and Growth Rate of M1",overlay=line,\$ vlabel="Rate of Growth(%)",ovlabel="Billions of \$",\$ key=below,klabels=||"Rate of Growth","M1 in Billions"||) 2 # m1growth # m1nsa * * Do @BJIdent on the growth and its seasonal difference * spgraph(footer="Figure 2.8 ACF and PACF",vfields=2) @bjident m1growth set m1grsdiff = m1growth-m1growth{4} @bjident m1grsdiff spgraph(done) * * To estimate over the common range, set the <> parameter to * 1962:3. * * Model 1 * boxjenk(ar=1,sma=1,const) m1grsdiff 1962:3 2008:2 @regcrits(title="Seasonal (1,0)x(0,1) model") @regcorrs * * Model 2 * boxjenk(ar=1,sar=1,const) m1grsdiff 1962:3 2008:2 @regcrits(title="Seasonal (1,0)x(1,0) model") @regcorrs * * Model 3 * boxjenk(ma=1,sma=1,const) m1grsdiff 1962:3 2008:2 @regcrits(title="Seasonal (1,0)x(1,0) model") @regcorrs * * Re-estimate model 1 using differencing operators in the BOXJENK so we * can directly forecast log M1. Use the full available range. * set logm1nsa = log(m1nsa) * boxjenk(ar=1,sma=1,diffs=1,sdiffs=1,define=model1) logm1nsa uforecast(from=2013:1,steps=12,equation=model1) logm1forecast set m1forecast 2013:1 2015:4 = exp(logm1forecast) * graph(footer="Figure 2.9 Forecasts of M1") 2 # m1nsa 2000:1 * # m1forecast