A comparison of two least-squared random coefficient autoregressive models: with and without autocorrelated errors
Abstract
This paper compares a Least-Squared Random Coefficient Autoregressive (RCA) model with a Least-Squared RCA model based on Autocorrelated Errors (RCA-AR). We looked at only the first order models, denoted RCA(1) and RCA(1)-AR(1). The efficiency of the Least-Squared method was checked by applying the models to Brownian motion and Wiener process, and the efficiency followed closely the asymptotic properties of a normal distribution. In a simulation study, we compared the performance of RCA(1) and RCA(1)-AR(1) by using the Mean Square Errors (MSE) as a criterion. The RCA(1) exhibited good power estimation in both cases where the data is stationary and nonstationary. On the other hand, when data oscillates around its mean, RCA(1)-AR(1) performed better. For real world data, we applied the two models to the daily volume of the Thai gold price and found that RCA(1)-AR(1) performed better than RCA(1).
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References
[1] D.F. Nicholls, B.G. Quinn, Random coefficient autoregressive models: An introduction, Springer- Verlag Inc (Berlin; New York), (1982).
[2] D. Wang, S.K. Ghosh, Bayesian analysis of random coefficient autoregressive models, Model Assisted Statistics and Applications, 3(2), (2002), 281-295.
[3] A. Thavaneswaran, S.S. Appadoo, S. Peiris, Forecasting Volatility, Statistics & Probability Letters, 75, (2005), 1-10.
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[4] S.Y. Hwang, U.V. Basawa, Parameter estimation for generalized random coefficient autoregressive process, Journal of Statistical Planning and Inference, 68, (1998), 323-337.
View more references (7)
[5] S.A. Chandra, M. Taniguchi, Estimating Functions for Nonlinear Time Series Data, Annals of the Institute of Statistical Mathematics, 53(1), (2001), 125-136.
[6] V. Haggan, T. Ozaki, Modeling nonlinear vibrations using an amplitude-dependent autoregressive time series model, Biometrika, 68, (1981), 189-196.
[7] H. Tong, Threshold models in nonlinear time series analysis, Lecture Notes in Statistics 21, Heidelberg:Springer, (1982).
[8] K.S. Chan, H. Tong, On estimating thresholds in autoregressive models, Journal of Time Series Analysis, 7,(1986), 179-190.
[9] P.C.B. Phillips, Time series regression with a unit roots, Econometrica, 55, (1987), 227-301.
[10] D.A. Dickey, W.A. Fuller, Distribution of the estimates for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, (1979), 427-431.
[11] A. Araveeporn, The Least-Squares Criteria of the Random Coefficient Dynamic Regression Model, Journal of Statistical Theory and Practice, 6(2), (2012), 315-333