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:: Volume 16, Issue 2 (3-2020) ::
JSRI 2020, 16(2): 409-446 Back to browse issues page
Best Linear Predictors in a Stationary Second Order Autoregressive process by means of near and far observations
Mohammad Mahdi Saber
, mmsaber@eghlid.ac.ir
Abstract:   (1469 Views)
In this paper, some predictors for prediction in a stationary second order autoregressive process are introduced. The paper attempts to find the best predictor for some cases such as circumstances there exist a fixed number of observations near or far from desired time. Pitman's measure of closeness and mean square error of prediction are used in order to comparison these predictors. The Gaussian and Gamma distributions have been used for distribution of errors. Finally analysis of two real data sets has also been presented for illustrative purposes.
 
Keywords:  AR(2) model, prediction performance, Pitman's measure of closeness.
Full-Text [PDF 12365 kb]   (837 Downloads)    
Type of Study: Research | Subject: General
Received: 2020/10/27 | Accepted: 2021/05/1 | Published: 2021/09/19
References
1. Ailliot, P. (2006). Some Theoretical Results on Markov-switching Autoregressive Models with Gamma Innovations. Statistics, 343, 271-274. [DOI:10.1016/j.crma.2006.05.018]
2. Brockwell, P.J., and Davis, R.A. (1991). Time Series: Theory and Methods. 2nd ed. Springer-Verlag, New York. [DOI:10.1007/978-1-4419-0320-4]
3. Gourieroux, C., and Jasiak, J. (2006). Autoregressive Gamma Processes. Journal of Forecasting, 25, 129-152. [DOI:10.1002/for.978]
4. Hamaz, A., and Ibazizen, M. (2009). Comparison of Two Estimation Methods of Missing Values Using Pitman-closeness Criterion. Communication in Statistics: Theory and Method, 38, 2210-2213. [DOI:10.1080/03610920802521190]
5. Keating, J.P., Mason, R.L., and Sen, P.K. (1993). Pitman's Measure of Closeness: A Comparison of Statistical Estimators, SIAM, Philadelphia. [DOI:10.1137/1.9781611971576]
6. Saber, M.M., and Nematollahi, A.R. (2017). Comparison of Spatial Interpolation Methods in the First Order Stationary Multiplicative Spatial Autoregressive Models. Communication in Statistics: Theory and Method, 18, 9230-9246. [DOI:10.1080/03610926.2016.1205619]
7. Saber, M.M. (2017). Performance of Extrapolation Based on Pitman's Measure of Closeness in Spatial Regression Models with Extended Skew t Innovations. Communication in Statistics: Theory and Method, 0, 1-18.
8. Saadatmand, A., Nematollahi, A.R., and Sadooghi-Alvandi, S. M. (2016). On the Estimation of Missing~Values in AR(1) Model with Exponential Innovations. Communication in Statistics: Theory and Method, 3393-3400. [DOI:10.1080/03610926.2015.1060347]
9. Senoglu, B., and Bayrak, O.T. (2016). Linear Contrasts in One-way Classification AR(1) Model with Gamma Innovations. Hacettepe Journal of Mathematics and Statistics, 45, 1743-1754. [DOI:10.15672/HJMS.20164515996]
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Saber M M. Best Linear Predictors in a Stationary Second Order Autoregressive process by means of near and far observations. JSRI 2020; 16 (2) :409-446
URL: http://jsri.srtc.ac.ir/article-1-380-en.html


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Volume 16, Issue 2 (3-2020) Back to browse issues page
مجله‌ی پژوهش‌های آماری ایران Journal of Statistical Research of Iran JSRI
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