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Time series regression models with locally stationary disturbance

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  • Junichi Hirukawa

    (Niigata University)

Abstract

Time series linear regression models with stationary residuals are a well studied topic, and have been widely applied in a number of fields. However, the stationarity assumption on the residuals seems to be restrictive. The analysis of relatively long stretches of time series data that may contain changes in the spectrum is of interest in many areas. Locally stationary processes have time-varying spectral densities, the structure of which smoothly changes in time. Therefore, we extend the model to the case of locally stationary residuals. The best linear unbiased estimator (BLUE) of vector of regression coefficients involves the residual covariance matrix which is usually unknown. Hence, we often use the least squares estimator (LSE), which is always feasible, but in general is not efficient. We evaluate the asymptotic covariance matrices of the BLUE and the LSE. We also study the efficiency of the LSE relative to the BLUE. Numerical examples illustrate the situation under locally stationary disturbances.

Suggested Citation

  • Junichi Hirukawa, 2017. "Time series regression models with locally stationary disturbance," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 329-346, October.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-017-9155-7
    DOI: 10.1007/s11203-017-9155-7
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    References listed on IDEAS

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    1. Suhasini Subba Rao, 2004. "On multiple regression models with nonstationary correlated errors," Biometrika, Biometrika Trust, vol. 91(3), pages 645-659, September.
    2. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
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    Cited by:

    1. Junichi Hirukawa & Sangyeol Lee, 2021. "Asymptotic properties of mildly explosive processes with locally stationary disturbance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 511-534, May.

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