Comparison of Maximum Likelihood and Least Absolute Deviate Estimation in Random Coefficients Autoregressive Model

The paper presents the calculation method of an asymptotic relative efficiency of the least absolute deviations estimate with respect to the maximum likelihood estimate for the parameter presented in the first order autoregressive model with a stochastic coefficient. The method is based on approximation of its asymptotic relative efficiency by Taylor series. The paper considers an example of the asymptotic relative efficiency calculation for the case where diffusion of the innovation process has an approximate Gaussian distribution (Tukey distribution). It is found out that if the assumptions of the Gaussian process are performed approximately, the maximum likelihood estimate is more efficient than the least absolute deviation estimate.

References

[1] Nicholls D.F., Quinn B.G. Random coefficient autoregressive models: an introduction. N.Y.-Berlin, Springer-Verlag, 1982. 154 p.

[2] Tong H. Nonlinear time series. A dynamical system approach. New York, Clarendon Press, 1990, 564 p.

[3] Diaconis P., Freedman D. Iterated random functions. SIAM Rev., 1999, vol. 41, no. 1, pp. 45-76.

[4] Aue A., Horvath L., Steinebach J. Estimation in random coefficient autoregressive models. J. Time Ser. Anal., 2006, vol. 27, no. 1, pp. 61-76.

[5] Truquet L., Yao J. On the quasi-likelihood estimation for random coefficient autoregressions. Statistics, 2012, vol. 46, no. 4, pp. 505-521.

[6] Hampel F., Ronchetti E., Rousseeuw P., Stahel W. Robust Statistics: The Approach Based on Influence Function. New York, John Wiley & Sons, 1984. 472 p.