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Least squares estimation for critical random coefficient first-order autoregressive processes

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  • Hwang, S.Y.
  • Basawa, I.V.
  • Yoon Kim, Tae

Abstract

Critical random coefficient AR(1) processes are investigated where the random coefficient is binary, taking values -1 and 1. Asymptotic behavior of least squares estimator for the mean of the random coefficient is discussed. Ordinary least squares estimator is shown to be consistent. Weighted least squares estimator turns out to be asymptotically normally distributed. This enables us to present a unified limit result for the weighted least squares estimator valid for the stationary, explosive and critical cases. Also, a test of criticality is discussed.

Suggested Citation

  • Hwang, S.Y. & Basawa, I.V. & Yoon Kim, Tae, 2006. "Least squares estimation for critical random coefficient first-order autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 310-317, February.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:3:p:310-317
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    References listed on IDEAS

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    1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    1. Voyant, Cyril & Muselli, Marc & Paoli, Christophe & Nivet, Marie-Laure, 2012. "Numerical weather prediction (NWP) and hybrid ARMA/ANN model to predict global radiation," Energy, Elsevier, vol. 39(1), pages 341-355.
    2. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    3. Božidar Popović & Saralees Nadarajah & Miroslav Ristić, 2013. "A new non-linear AR(1) time series model having approximate beta marginals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 71-92, January.
    4. Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2476-2483, December.

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