Kybernetika 47 no. 4, 501-518, 2011

On a class of estimators in a multivariate RCA(1) model

Zuzana Prášková and Pavel Vaněček

Abstract:

This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated in a small simulation study.

Keywords:

parameter estimation, multivariate RCA models, asymptotic variance matrix

Classification:

60F05, 60G10, 60G46, 62M10

References:

  1. A. Aue, L. Horváth and J. Steinebach: Estimation in random coefficient autoregressive models. J. Time Ser. Anal. 27 (2006), 60-67.   CrossRef
  2. S. Y. Hwang and I. V. Basawa: Parameter estimation for generalized random coefficient autoregressive processes. J. Statist. Plann. Inference 68 (1998), 323-337.   CrossRef
  3. I. Berkes, L. Horváth and S. Ling: Estimation in nonstationary random coefficient autoregressive models. J. Time Ser. Anal. 30 (2009), 395-416.   CrossRef
  4. P. Billingsley: The Lindeberg-Lévy theorem for martingales. Proc. Amer. Math. Soc. 12 (1961), 788-792.   CrossRef
  5. P. Bougerol and N. Picard: Strict stationarity of generalized autoregressive processes. Ann. Probab. 20 (1992), 1714-1730.   CrossRef
  6. J. Davidson: Stochastic Limit Theory. Advanced Texts in Econometrics. Oxford University Press, Oxford 1994.   CrossRef
  7. P. D. Feigin and R. L. Tweedie: Random coefficient autoregressive processes: A Markov chain analysis of stationarity and finiteness of moments. J. Time Ser. Anal. {\mi6} (1985), 1-14.   CrossRef
  8. H. Janečková and Z. Prášková: CWLS and ML estimates in a heteroscedastic RCA(1) model. Statist. Decisions 22 (2004), 245-259.   CrossRef
  9. H. L. Koul and A. Schick: Adaptive estimation in a random coefficient autoregressive model. Ann. Statist. 24 (1996), 1025-1052.   CrossRef
  10. D. F. Nicholls and B. G. Quinn: Random coefficient autoregressive models: An introduction. Lecture Notes in Statistics 11, Springer, New York 1982.   CrossRef
  11. J. Schott: Matrix Analysis for Statistics. Wiley Series in Probability and Statistics, Wiley, New York 1996.   CrossRef
  12. P. Vaněček: Rate of convergence for a class of RCA estimators. Kybernetika 6 (2006), 698-709.   CrossRef
  13. P. Vaněček: Estimators of multivariate RCA models. In: Bull. Internat. Statistical Institute LXII (M. I. Gomes at al., eds.), Instituto Nacional de Estatística, Lisbon 2007, pp. 4027-4030.   CrossRef
  14. P. Vaněček: Estimation of Random Coefficient Autoregressive Models. PhD Thesis, Charles University, Prague 2008.   CrossRef