Analysis of the correlation structure of square time series

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.