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A New Random Coefficient Autoregressive Model Driven by an Unobservable State Variable

Author

Listed:
  • Yuxin Pang

    (School of Mathematics, Jilin University, Changchun 130012, China
    These authors contributed equally to this work.)

  • Dehui Wang

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110031, China
    These authors contributed equally to this work.)

Abstract

A novel random coefficient autoregressive model is proposed, and a feature of the model is the non-stationarity of the state equation. The autoregressive coefficient is an unknown function with an unobservable state variable, which can be estimated by the local linear regression method. The iterative algorithm is constructed to estimate the parameters based on the ordinary least squares method. The ordinary least squares residuals are used to estimate the variances of the errors. The Kalman-smoothed estimation method is used to estimate the unobservable state variable because of its ability to deal with non-stationary stochastic processes. These methods allow deriving the analytical solutions. The performance of the estimation methods is evaluated through numerical simulation. The model is validated using actual time series data from the S&P/HKEX Large Cap Index.

Suggested Citation

  • Yuxin Pang & Dehui Wang, 2024. "A New Random Coefficient Autoregressive Model Driven by an Unobservable State Variable," Mathematics, MDPI, vol. 12(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3890-:d:1540693
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