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THE AUTOCORRELATION FUNCTION OF SEASONAL ARMA MODELS
Author(s) -
Peña Daniel
Publication year - 1984
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.1467-9892.1984.tb00392.x
Subject(s) - autocorrelation , mathematics , multiplicative function , partial autocorrelation function , moving average model , scalar (mathematics) , autocorrelation matrix , statistics , autocorrelation technique , autoregressive–moving average model , autocovariance , function (biology) , econometrics , mathematical analysis , time series , autoregressive model , autoregressive integrated moving average , fourier transform , geometry , evolutionary biology , biology
. This note obtains the theoretical autocorrelation function of an ARMA model with multiplicative seasonality. It is shown that this function can be interpretated as the result of the interaction between the seasonal and regular autocorrelation patterns of the ARMA model. The use of this result makes easier the identification of the structure of the model, is helpful in choosing between a multiplicative or additive seasonal component and leads to a better understanding of the properties of the estimated autocorrelation function of scalar ARMA processes.