An old estimator of the autocorrelation coefficient (***)

[NicolasR]

Hello,

This program estimates the usual (HAT) autocorrelation coefficient (already supported by Eviews) and estimates the autocorrelation using the "STAR" estimator p(tau)*. The only difference with HAT estimator, is that the STAR divides by (T-Tau), the HAT divides by T. Both have the same asympotic propertys, but in finite samples the can differ substantialy.

Code: Select all

'ACF HAT and STAR '------------------------------------- !T=50 !M=!T-1 'Maximum orden of autocorrelations, Max=T-1 '------------------------------------- pagecreate u 1 !T mode quiet genr x=nrnd genr x=x-@mean(x) stomna(x,xv) scalar R0=@var(x) table ACF_table ACF_table(1,1)="ACF HAT AND STAR" ACF_table(2,1)="Tau" ACF_table(2,2)="ACF Hat" ACF_table(2,3)="ACF STAR" for !Tau=1 to !M genr rezago=x(-!Tau) stomna(rezago,lag) for !h=1 to !T if lag(!h)=NA then statusline ACF: !Tau !h lag(!h)=0 endif next scalar ACF_gorro=((1/!T)*@transpose(xv)*lag)/R0 ACF_table(2+!Tau,1)=!Tau ACF_table(2+!Tau,2)=ACF_gorro scalar ACF_estrella=((1/(!T-!Tau))*@transpose(xv)*lag)/R0 ACF_table(2+!Tau,3)=ACF_estrella next ACF_table.setformat(b) f.3 ACF_table.setformat(c) f.3

References

Priestley, M. B. (1981). Spectral analysis and time series: probability and mathematical statistics (No. 04; QA280, P7.).