Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models

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Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models (2004, unknown): “For simplicity of notation, we consider the general case where fXtg is any mean zero series such that the covariance matrix of ðX1; . . . ;XkÞ0 is invertible for each kP1: (Proposition 4.1 of Lund and Basawa (2000) shows that this invertibility holds for any causal PARMA model.)”
Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices (2007, background): “Further developments on likelihood evaluation and asymptotic theory for different estimators of periodic ARMA models have been discussed by Lund and Basawa (2000) and Basawa and Lund (2001).”
PARSIMONIOUS PERIODIC TIME SERIES MODELING (2006, background): “Lund & Basawa (2000) present an algorithm that efficiently computes X̂t and vt recursively in t for a general PARMA series.”
Changepoint Detection in Periodic and Autocorrelated Time Series (2007, background): “The equations governing the PAR(1) covariance structure are (5.4)–(5.7) in Lund and Basawa (2000).”