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Least Squares Estimates And Order Determination Procedures For Autoregressive Processes With A Time Dependent Variance

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  • Dag Tjøstheim
  • Jostein Paulsen

Abstract

. We study nonstationary autoregressive processes, where the variance of the generating white noise process is allowed to depend on time. It is shown that ordinary least squares estimates are strongly consistent and with a proper scaling factor asymptotically normal, but, as can be expected, they are not efficient. Furthermore, AIC type order determination criteria, used as if the underlying process is stationary, are consistent, whereas identification of order in terms of the partial autocorrelation function may lead one astray.

Suggested Citation

  • Dag Tjøstheim & Jostein Paulsen, 1985. "Least Squares Estimates And Order Determination Procedures For Autoregressive Processes With A Time Dependent Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(2), pages 117-133, March.
    • Handle: RePEc:bla:jtsera:v:6:y:1985:i:2:p:117-133
    DOI: 10.1111/j.1467-9892.1985.tb00403.x
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    Cited by:

    1. Abdelouahab Bibi & Christian Francq, 2003. "Consistent and asymptotically normal estimators for cyclically time-dependent linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 41-68, March.
    2. Dobromił Serwa & Piotr Wdowiński, 2017. "Modeling Macro-Financial Linkages: Combined Impulse Response Functions in SVAR Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(4), pages 323-357, December.
    3. Chandler, Gabriel, 2010. "Order selection for heteroscedastic autoregression: A study on concentration," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1904-1910, December.

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