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Order selection for heteroscedastic autoregression: A study on concentration

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  • Chandler, Gabriel

Abstract

We consider an autoregressive model where the variance is allowed to be a function of time, unconditional on the past. Pötscher (1989) has proven that, regardless of the shape of the variance function, order selection can be made consistently. However, this procedure does not account for the non-stationary behavior. We consider the concentration of the variance function and its effect on order selection. We show that an order free estimate of the variance function can be constructed and propose an order selection criterion based on this estimate. Consistency is established and simulation results verify a large increase in the probability of selecting the correct order for finite samples.

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  • Chandler, Gabriel, 2010. "Order selection for heteroscedastic autoregression: A study on concentration," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1904-1910, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1904-1910
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    References listed on IDEAS

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    1. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
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    4. 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.
    5. Piotr Fryzlewicz & Theofanis Sapatinas & Suhasini Subba Rao, 2006. "A Haar--Fisz technique for locally stationary volatility estimation," Biometrika, Biometrika Trust, vol. 93(3), pages 687-704, September.
    6. Peter C. B. Phillips & Ke‐Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 289-308, March.
    7. Chandler, Gabriel & Polonik, Wolfgang, 2006. "Discrimination of Locally Stationary Time Series Based on the Excess Mass Functional," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 240-253, March.
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    Cited by:

    1. Schnaubelt, Matthias, 2019. "A comparison of machine learning model validation schemes for non-stationary time series data," FAU Discussion Papers in Economics 11/2019, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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