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Analysis of the correlation structure of square time series
Author(s) -
Palma Wilfredo,
Zevallos Mauricio
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.1467-9892.2004.01797.x
Subject(s) - mathematics , autocorrelation , series (stratigraphy) , kurtosis , statistics , sequence (biology) , zero (linguistics) , uncorrelated , least squares function approximation , paleontology , linguistics , genetics , philosophy , estimator , biology
Abstract. This paper analyses the asymptotic behaviour of the autocorrelation structure exhibited by squares of time series with a Wold expansion where the input error is a sequence of random variables with mean zero and finite kurtosis. Two important cases are discussed: (i) when the errors are independent and, (ii) when the errors are uncorrelated but their squares are correlated. Both situations are addressed when the process exhibits short or long memory. Consequences of these results on certain models widely used in many disciplines are also discussed.