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Limiting Distribution of the Score Statistic under
Moderate Deviation from a Unit Root in MA(1)
Abstract
This paper derives the asymptotic distribution of Tanaka's score statistic under moderate deviation from a unit root in a moving average model of order one or MA(1). We classify the limiting distribution into three types depending on the order of deviation. In the fastest case, the convergence order of the asymptotic distribution continuously changes from the invertible process to the unit root. In the slowest case, the limiting distribution coincides with the invertible process in a distributional sense. This implies that these cases share an asymptotic property. The limiting distribution in the intermediate case provides the boundary property between the fastest and slowest cases.
