Previous |  Up |  Next


asymmetric recursive methods; time series; Kalman filter; exponential smoothing; asymmetric time series; autoregressive model; split-normal distribution
The problem of asymmetry appears in various aspects of time series modelling. Typical examples are asymmetric time series, asymmetric error distributions and asymmetric loss functions in estimating and predicting. The paper deals with asymmetric modifications of some recursive time series methods including Kalman filtering, exponential smoothing and recursive treatment of Box-Jenkins models.
[1] K. Campbell: Recursive computation of $M$-estimates for the parameters of a finite autoregressive process. Annals of Statistics 10 (1982), 442–453. DOI 10.1214/aos/1176345785 | MR 0653519 | Zbl 0492.62076
[2] T. Cipra: Some problems of exponential smoothing. Aplikace matematiky 34 (1989), 161–169. MR 0990303 | Zbl 0673.62079
[3] T. Cipra: Robust exponential smoothing. Journal of Forecasting 11 (1992), 57–69. DOI 10.1002/for.3980110106
[4] T. Cipra and R. Romera: Robust Kalman filter and its application in time series analysis. Kybernetika 27 (1991), 481–494. MR 1150938
[5] T. Cipra and R. Romera: Recursive time series methods in $L_1$-norm. $L_1$-Statistical Analysis and Related Methods (Y. Dodge, ed.), North Holland, Amsterdam, 1992, pp. 233–243. MR 1214835
[6] T. Cipra, A. Rubio and L. Canal: Robustified smoothing and forecasting procedures. Czechoslovak Journal of Operations Research 1 (1992), 41–56.
[7] C. W. J. Granger: Prediction with a generalized cost of error function. Operational Research Quarterly 20 (1969), 199–207. DOI 10.1057/jors.1969.52 | MR 0295497 | Zbl 0174.21901
[8] E. J. Hannan: Multiple Time Series. Wiley, New York, 1970. MR 0279952 | Zbl 0211.49804
[9] P. Lefrançois: Allowing for asymmetry in forecast errors: Results from a Monte-Carlo study. International Journal of Forecasting 5 (1989), 99–110. DOI 10.1016/0169-2070(89)90067-8
[10] W. K. Newey and J. L. Powell: Asymmetric least squares estimation and testing. Econometrica 55 (1987), 819–847. DOI 10.2307/1911031 | MR 0906565
[11] H. Robbins and D. Siegmund: A convergence theorem for non negative almost supermartingales and some applications. Optimizing Methods in Statistics (J. S. Rustagi, ed.), Academic Press, New York, 1971, pp. 233–257. MR 0343355
[12] K. Sejling, H. Madsen, J. Holst, U. Holst and J.-E. Englund: A method for recursive robust estimation of $AR$-parameters. Preprint, Technical University of Lyngby, Denmark and University of Lund, Sweden, 1990.
[13] M. J. Silvapulla: On $M$-method in growth curve analysis with asymmetric errors. Journal of Statistical Planning and Inference 32 (1992), 303–309. DOI 10.1016/0378-3758(92)90013-I | MR 1190200
[14] W. E. Wecker: Asymmetric time series. Journal of the American Statistical Association 76 (1981), 16–21. DOI 10.1080/01621459.1981.10477595
Partner of
EuDML logo