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Regression theory for near-integrated time series. (English) Zbl 0744.62128
A concept of “ near integrated processes” is introduced, to develop an asymptotic theory relevant to multiple discrete-time stochastic processes that include ARIMA processes, stationary ARMA processes with roots close to the unit circle, and mildly explosive processes. The approach taken is related to the Pitman one, in which local alternatives converge as the sample size increases to a “null” value, in this case that of unit roots.
A vector autoregression is studied in which the innovations are strongly mixing. Convergence properties of sample moments and least squares estimates are derived. Noncentral distributions of multivariate tests for unit roots are analyzed. The results are extended to models with drift, and applied to time series regressions with near-integrated regressors.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H10 Multivariate distribution of statistics
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