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AUTOREGRESSIVE MOVING AVERAGE PROCESSES WITH NON‐NORMAL RESIDUALS
Author(s) -
Davies Neville,
Spedding Trevor,
Watson William
Publication year - 1980
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.1467-9892.1980.tb00304.x
Subject(s) - kurtosis , skewness , mathematics , autoregressive–moving average model , autoregressive model , series (stratigraphy) , econometrics , statistics , stationary process , paleontology , biology
. ARMA processes with non‐normal residuals have applications in surface metrology and have recently been shown by Nelson and Granger (1979) to occur in modelling economic time series. In this paper we obtain the theoretical relationship between the skewness and kurtosis of an ARMA process and the corresponding parameters of its generating noise series and consider some of the implications of these results. Simulation methods for any ARMA process with given skewness and kurtosis, using Johnson transformations are briefly discussed.