Startseite Analyzing the Full BINMA Time Series Process Using a Robust GQL Approach
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Analyzing the Full BINMA Time Series Process Using a Robust GQL Approach

  • Naushad Mamode Khan EMAIL logo , Yuvraj Sunecher und Vandna Jowaheer
Veröffentlicht/Copyright: 6. August 2016
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

We investigate a new bivariate-integer valued moving average time series process where the innovation series follow the bivariate Poisson assumption under stationary moments and constant cross-correlations. Furthermore, due to the complication involved in specifying the joint likelihood function, this paper considers a robust generalized quasi-likelihood approach to estimate the mean, serial and dependence parameters. Unlike previous estimation techniques such as the Generalized Least Squares, this estimation approach here involves a two-step Newton-Raphson iterative procedure where in the first step, the serial and cross correlations are estimated while in the second step, these dependence estimates are used to compute iteratively the vector of regression coefficients. The consistency of the estimates under this approach is checked through several simulation experiments under different combinations of low and high serial and cross-correlations.

References

Al Osh, M., and A. Alzaid. 1987. “First-Order Integer-Valued Autoregressive Process.” Journal of Time Series Analysis 8:261–75.10.1111/j.1467-9892.1987.tb00438.xSuche in Google Scholar

Brannas, K.. 1995. “Explanatory Variable in the Ar(1) Count Data Model,” Umea University, Department of Economics, No. 381.Suche in Google Scholar

Brannas, K., and A. Quoreshi. 2010. “Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks.” Applied Financial Economics 20 (18):1429–40.10.2139/ssrn.540922Suche in Google Scholar

Chan, K., and J. Ledolter. 1995. “Monte Carlo Em Estimation for Time Series Models Involving Counts.” Journal of the American Statistical Association 90 (429):242–52.10.1080/01621459.1995.10476508Suche in Google Scholar

Durbin, J., and S. Koopman. 2000. “Time Series Analysis of Non-Gaussian Observations Based on State Space Models From Both Classical and Bayesian Perspectives.” Journal of the Royal Statistical Society, B 62:3–56.10.1111/1467-9868.00218Suche in Google Scholar

Jung, R., M. Kukuk, and A. Tremayne. 2006. “Time Series of Count Data:,Modelling, Estimation and Diagnostics.” Computational Statistics and Data Analysis 51 (4):2350–64.10.1016/j.csda.2006.08.001Suche in Google Scholar

Jung, R., and R. Liesenfeld. 2001. “Estimating Time Series Models for Count Data Using Efficient Importance Sampling.” Allgemeines Statistical Archives 85 (4):387–407.10.1007/s10182-001-8176-zSuche in Google Scholar

Jung, R., and A. Tremayne. 2003. “Testing for Serial Dependence in Time Series Models of Counts.” Journal of Time Series Analysis 24:65–84.10.1111/1467-9892.00293Suche in Google Scholar

Kocherlakota, S., and K. Kocherlakota. 2001. “Regression in the Bivariate Poisson Distribution.” Communications in Statistics-Theory and Methods 30:815–27.10.1081/STA-100002259Suche in Google Scholar

McKenzie, E.. 1986. “Autoregressive Moving-Average Processes with Negative Binomial and Geometric Marginal Distrbutions.” Advanced Applied Probability 18:679–705.10.2307/1427183Suche in Google Scholar

Quoreshi, A.. 2006a. “Bivariate Time Series Modeling of Financial Count Data.” Communication in Statistics-Theory and Methods 35:1343–58.10.1080/03610920600692649Suche in Google Scholar

Quoreshi, A.. 2008. “A Vector Integer-Valued Moving Average Model for High Frequency Financial Count Data.” Economics Letters 101:258–61.10.1016/j.econlet.2008.08.027Suche in Google Scholar

Steutel, F., and K. Van Harn. 1979. “Discrete Analogues of Self-Decomposability and Statibility.” The Annals of Probability 7:3893–9.Suche in Google Scholar

Sutradhar, B.. 2003. “An Overview on Regression Models for Discrete Longitudinal Responses.” Statistical Science 18:377–93.10.1214/ss/1076102426Suche in Google Scholar

Sutradhar, B.. 2011. Dynamic Mixed Models for Familial Longitudinal Count Data. New York: Springer-Verlag.10.1007/978-1-4419-8342-8Suche in Google Scholar

Sutradhar, B., and K. Das. 1999. “On the Efficiency of Regression Estimators in Generalised Linear Models for Longitudinal Data.” Biometrika 86:459–65.10.1093/biomet/86.2.459Suche in Google Scholar

Sutradhar, B., V. Jowaheer, and P. Rao. 2014. “Remarks on Asymptotic Efficient Estimation for Regression Effects in Stationary and Non-Stationary Models for Panel Count Data.” Brazilian Journal of Probability and Statistics 28 (2):241–54.Suche in Google Scholar

Yahav, I., and G. Shmueli. 2011. “On Generating Multivariate Poisson Data in Management Science Applications.” Applied Stochastic Models in Business and Industry 28 (1):91–102.10.1002/asmb.901Suche in Google Scholar

Published Online: 2016-8-6

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 4.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jtse-2015-0019/html
Button zum nach oben scrollen