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Periodic AR and ARMA Time Series

Periodic AR and ARMA Time Series. PARMA time series of period T – a zero mean time series with finite second moments that satisfies the following stochastic difference equation. In vector form…. Example of a PAR of order 1 as vector AR:. And order 4 or more….

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Periodic AR and ARMA Time Series

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  1. Periodic AR and ARMA Time Series • PARMA time series of period T – a zero mean time series with finite second moments that satisfies the following stochastic difference equation K. Ensor, STAT 421

  2. In vector form… Example of a PAR of order 1 as vector AR: K. Ensor, STAT 421

  3. And order 4 or more… K. Ensor, STAT 421

  4. Autocorariances and “stationarity” • Covariances are periodic • The process is “periodic stationary” if the covariances for season v do not depend on n. K. Ensor, STAT 421

  5. Autocorrelations and Partials • Defined for each season • Behavior for each season is the same as that for a general stationary ARMA model (e.g. see Shao and Lund, JTSA, 2004) K. Ensor, STAT 421

  6. K. Ensor, STAT 421

  7. K. Ensor, STAT 421

  8. K. Ensor, STAT 421

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