Abstract
We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.
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Inoue, A. AR and MA representation of partial autocorrelation functions, with applications. Probab. Theory Relat. Fields 140, 523–551 (2008). https://doi.org/10.1007/s00440-007-0074-1
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DOI: https://doi.org/10.1007/s00440-007-0074-1
Keywords
- Partial autocorrelation functions
- Verblunsky coefficients
- Orthogonal polynomials on the unit circle
- Baxter’s condition
- Fractional ARIMA processes
- Long memory
Mathematics Subject Classification (2000)
- Primary: 62M10
- Secondary: 42C05
- Secondary: 60G10