Autoregressive-integrated-moving average models of each series, which incorporated the weighting scheme just described for the pre-1992 portion of each new TMS series, were estimated. Prices were expressed in nominal terms and transformed into natural logarithms. The transformed nominal price series were all nonstationary. Nonstationarity was tested by running augmented Dickey-Fuller tests for unit roots for the undifferenced series. The ADF test specification included an intercept. The number of difference terms to include in each series’ test was determined by the minimum of the Akaike information criterion, choosing from among nine specifications (0 to 8 lagged difference terms).
ARMA(p,q) models of each series were then estimated, including a dummy corresponding to the first quarter of 1992, when the new regions first took effect, and testing for whether the dummy coefficient was statistically different from zero at five percent significance. Again, the specification of each series’ ARMA(p,q) was determined by the minimum of the Akaike information criterion.
