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The limiting distribution of the least‐squares estimator in nearly integrated seasonal models
Author(s) -
Perron Pierre
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315463
Subject(s) - asymptotic distribution , mathematics , estimator , moment generating function , autoregressive model , moment (physics) , limiting , least squares function approximation , function (biology) , distribution (mathematics) , statistics , mathematical analysis , random variable , physics , mechanical engineering , classical mechanics , evolutionary biology , engineering , biology
We consider the least‐squares estimator of the autoregressive parameter in a nearly integrated seasonal model. Building on the study by Chan (1989), who obtained the limiting distribution, we derive a closed‐form expression for the appropriate limiting joint moment generating function. We use this function to tabulate percentage points of the asymptotic distribution for various seasonal periods via numerical integration. The results are extended by deriving a stochastic asymptotic expansion to order O p ( T ‐l ), whose percentage points are also obtained by numerically integrating the appropriate limiting joint moment generating function. The adequacy of the approximation to the finite‐sample distribution is discussed.