A Class of Multivariate Micromovement Models of Asset Price and Their Bayesian Model Selection via Filtering
Laurie C. Scott, Yong Zeng
Abstract
A filtering model with counting process observations has been recently developed as a reasonable framework for the micromovement of asset price. In this paper, we first highlight such an extension to multivariate case for modeling multi-stocks and related results on Bayes estimation via filtering. For this rich class of multivariate models, we develop the Bayesian model selection using Bayes factor. Based on the unnormalized, Duncan-Mortensen-Zakai-like filtering equation, we derive a system of SPDE characterizing the evolution of the Bayes factors and prove their uniqueness. Furthermore, applying Kushner’s Markov chain approximation method, we propose a numerical scheme to derive recursive algorithms, and we prove the consistency (or robustness) of the recursive algorithms.
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1233152939
Digital Object Identifier: doi:10.1214/074921708000000345
References
[1] Barclay, M., Christie, W., Harris, J., Kandel, E. and Schultz, P. H. (1999). The effects of market reform on the trading costs and depths of nasdaq stocks. Journal of Finance 54 (1) 1–34.
[2] Bremaud, P. (1981). Point Processes and Queues: Martingale Dynamics. Springer-Verlag, New York.
Mathematical Reviews (MathSciNet):
MR636252
[3] Easley, D. and O’Hara, M. (1992). Time and the process of security price adjustment. Journal of Finance 47 577–605.
[4] Engle, R. (2000). The econometrics of ultra-high-frequency data. Econometrica 68 1–22.
[5] Ethier, S. and Kurtz, T. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.
Mathematical Reviews (MathSciNet):
MR838085
[6] Goggin, E. (1994). Convergence in distribution of conditional expectations. Annals of Probability 22 1097–1114.
Mathematical Reviews (MathSciNet):
MR1288145
Zentralblatt MATH:
0805.60017
Digital Object Identifier: doi:10.1214/aop/1176988743
Project Euclid: euclid.aop/1176988743
[7] Hasbrouck, J. (1988). Trades, quotes, inventories and information. Journal of Financial Economics 42 229–252.
[8] Kass, R. E. and Raftery, A. E. (1995). Bayes factors and model uncertainty. Journal of the American Statistical Association 90 773–795.
[9] Kouritzin, M. and Zeng, Y. (2005). Bayesian model selection via filtering for a class of micro-movement models of asset price. International Journal of Theoretical and Applied Finance 8 97–121.
Mathematical Reviews (MathSciNet):
MR2122692
Zentralblatt MATH:
1100.91046
Digital Object Identifier: doi:10.1142/S0219024905002883
[10] Kouritzin, M. and Zeng, Y. (2005). Weak convergence for a type of conditional expectation: Application to the inference for a class of asset price models. Nonlinear Analysis: Theory, Methods and Applications 60 231–239.
Mathematical Reviews (MathSciNet):
MR2101876
[11] Kurtz, T. and Protter, P. (1991). Weak limit theorems for stochastic integrals and stochastic differential equations. Annals of Probability 19 1035–1070.
Mathematical Reviews (MathSciNet):
MR1112406
Zentralblatt MATH:
0742.60053
Digital Object Identifier: doi:10.1214/aop/1176990334
Project Euclid: euclid.aop/1176990334
[12] Protter, P. (2003). Stochastic Integration and Differential Equations. Springer-Verlag, New York, 2nd ed.
[13] Russell, J. (1999). Econometric modeling of multivariate irregularly-spaced high-frequency data. Working Paper, University of Chicago.
[14] Scott, L. C. and Zeng, Y. (2006). Bayes estimation for a class of multivariate filtering micromovement models of asset price. Working Paper, University of Missouri at Kansas City.
[15] Spalding, R., Tsui, K. W. and Zeng, Y. (2005). A micro-movement model with bayes estimation via filtering: Applications to measuring trading noises and trading cost. Nonlinear Analysis: Theory, Methods and Applications 64 295–309.
Mathematical Reviews (MathSciNet):
MR2188460
[16] Xiong, J. and Zeng, Y. (2006). A branching particle approximation to the filtering problem with counting process observations. Working Paper, University of Tennessee at Knoxville.
[17] Zeng, Y. (2003). A partially-observed model for micro-movement of asset prices with bayes estimation via filtering. Mathematical Finance 13 411–444.
Mathematical Reviews (MathSciNet):
MR1995285
Digital Object Identifier: doi:10.1111/1467-9965.t01-1-00022
[18] Zeng, Y. (2004). Estimating stochastic volatility via filtering for the micromovement of asset prices. IEEE Transactions on Automatic Control 49 338–348.
Mathematical Reviews (MathSciNet):
MR2062247
Digital Object Identifier: doi:10.1109/TAC.2004.824478
[19] Zeng, Y. (2006). Statistical analysis of the filtering models with marked point process observations: Applications to ultra-high frequency data. Working Paper, University of Missouri at Kansas City.
[20] Zhang, M. Y., Russell, J. R. and Tsay, R. S. (2001). A nonlinear autoregressive conditional duration model with applications to financial transaction data. Journal of Econometrics 104 179–207.
Mathematical Reviews (MathSciNet):
MR1862032
Zentralblatt MATH:
1108.62336
Digital Object Identifier: doi:10.1016/S0304-4076(01)00063-X
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