Simulation study of testing an intervention effect in arima (1,0,0,L,δ) model / Illias Mamat

In order to test whether or not the intervention effect, δ which occurs between the pre-time series and the post-time series in an intervention time series model is different from zero, under appropriate assumptions. the t- statistics test suggested by Glass, Wilson, and Gottman (2) may be used. In this study. the first order autoregressive ARIMA (1,0,0,L,δ) intervention model. which contains the same pre- and post- intervention first-order autoregressive parameter Ø, is chosen in order to study the validity of the t-statistics. The variable Z will represent the series measured across n equally spaced units of time. This series is labelled as Z1,Z2-····,Zn. We shall assume the intervention effect occurs between times n1 and n1 + 1. where n1 < n. and where L is the level of the pre- intervention time series Z1,Z2 , Zn1' and (L+δ) is the level of post-intervention time series Znl+1, ,Zn. Zinkgraft and Wilson [5] simulated the performance of this t- procedure under the null hypothesis assumption that Ho : δ = 0 (no change) and reported that this procedure may not preserve an δ - level of significance. As the result of the simulation study in [5], the observed α - values for n1 + n2 =20 and Ø =0.6 are: 0.077,0.178. and 0.259, compared to theoretical values of: 0.01,0.05 and 0.10 respectively. Also from this simulation study the observed (α - values) for n1 + n2 = 50 and Ø= 0.6 are: 0.034.0.112 and 0.185. These observed values are also greater than the theoretical values: 0.01, 0.05 and 0.10 respectively. Based on this preliminary and sketchy evidence, this study is being done to see whether this t-statistics can really control the type-1 error (α) for a wider category of Ø values: Ø= 0.0. 0.3, 0.6 and 0.9. and a wider choice of sample sizes. The same procedure in [5] will be used.