Innovations algorithm asymptotics for periodically stationary time series with heavy tails

  • Authors:

  • Paul L. Anderson;Laimonis Kavalieris;Mark M. Meerschaert

  • Affiliations:

  • Department of Mathematics, Albion College, MI, USA;Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand;Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2008

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Abstract

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the underlying noise sequence has infinite fourth moment but finite second moment. In this case, the sample covariances on which the innovations algorithm are based are known to be asymptotically stable. The asymptotic results developed here are useful to determine which model parameters are significant. In the process, we also compute the asymptotic distributions of least squares estimates of parameters in an autoregressive model.