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Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models
Author(s) -
Shao Qin,
Lund Robert
Publication year - 2004
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.00356.x
Subject(s) - autocorrelation , mathematics , autoregressive model , partial autocorrelation function , autoregressive–moving average model , series (stratigraphy) , moving average , moving average model , computation , time series , autoregressive integrated moving average , econometrics , statistics , algorithm , paleontology , biology
This paper studies correlation and partial autocorrelation properties of periodic autoregressive moving‐average (PARMA) time series models. An efficient algorithm to compute PARMA autocovariances is first derived. An innovations based algorithm to compute partial autocorrelations for a general periodic series is then developed. Finally, periodic moving averages and autoregressions are characterized as periodically stationary series whose autocovariances and partial autocorrelations, respectively, are zero at all lags that exceed some periodically varying threshold.