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Analysis of the correlation structure of square time series

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  • Wilfredo Palma
  • Mauricio Zevallos

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.

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  • Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, July.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:529-550
    DOI: 10.1111/j.1467-9892.2004.01797.x
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    1. Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2004. "LARCH, leverage, and long memory," LSE Research Online Documents on Economics 294, London School of Economics and Political Science, LSE Library.
    2. Liudas Giraitis, 2004. "LARCH, Leverage, and Long Memory," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 177-210.
    3. Broto Carmen & Ruiz Esther, 2009. "Testing for Conditional Heteroscedasticity in the Components of Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.
    4. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    5. Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series 460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Broto, Carmen, 2006. "Using auxiliary residuals to detect conditional heteroscedasticity in inflation," DES - Working Papers. Statistics and Econometrics. WS ws060402, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2003. "LARCH, leverage and long memory," LSE Research Online Documents on Economics 2020, London School of Economics and Political Science, LSE Library.

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