Estimating SUR Tobit Model while errors are gaussian scale mixtures: with an application to high frequency financial data

Qian, Hang (2009): Estimating SUR Tobit Model while errors are gaussian scale mixtures: with an application to high frequency financial data.

Abstract

This paper examines multivariate Tobit system with Scale mixture disturbances. Three estimation methods, namely Maximum Simulated Likelihood, Expectation Maximization Algorithm and Bayesian MCMC simulators, are proposed and compared via generated data experiments. The chief finding is that Bayesian approach outperforms others in terms of accuracy, speed and stability. The proposed model is also applied to a real data set and study the high frequency price and trading volume dynamics. The empirical results confirm the information contents of historical price, lending support to the usefulness of technical analysis. In addition, the scale mixture model is also extended to sample selection SUR Tobit and finite Gaussian regime mixtures.

• Item Type: MPRA Paper
• Language: English
• Keywords: Tobit; Gaussian mixtures; Bayesian
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C34 - Truncated and Censored Models ; Switching Regression Models; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Amemiya, Takeshi, "Regression Analysis When the Dependent Variable Is Truncated Normal," Econometrica 41 (1973), 997-1016.

Amemiya, Takeshi, "Multivariate Regression and Simultaneous Equation Models When the Dependent Variables Are Truncated Normal," Econometrica 42:6 (1974), 999-1012.

Arias, Carlos, and Thomas Cox, "Estimation of a US Dairy Sector Model by Maximum Simulated Likelihood," Applied Economics 33 (2001), 1201-1211.

Arslan, Olcay, "Family of Multivariate Generalized T Distributions," Journal of Multivariate Analysis 89 (2004), 329-337.

Birnbaum, Z.W., and P.L. Meyer, "On the Effect of Truncation in Some or All Co-ordinates of a Multi-normal Population," Journal of the Indian Society of Agricultural Statistics 5 (1953), 17-28.

Borsch-Supan, Axel, and Vassilis Hajivassiliou, "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models," Journal of Econometrics 58 (1993), 347-368.

Brock, William, Josef Lakonishok, and Blake LeBaron, "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance 47:5 (1992), 1731-64.

Butler, J.S., and Robert Moffitt, "a Computationally Efficient Quadrature Procedure for the One Factor Multinomial Probit Model," Econometrica 50 (1982), 761-764.

Campbell, John, Andrew Lo, and Craig MacKinlay, the Econometrics of Financial Markets (Princeton: Princeton University Press, 1997).

Chib, Siddhartha, and Edwards Greenberg, "Hierarchical Analysis of SUR Models with Extensions to Correlated Serial Errors and Timevarying Parameter Models," Journal of Econometrics 68 (1995), 339-60.

Chib, Siddhartha, and Edwards Greenberg, "Bayesian Analysis of the Multivariate Probit Model," Biometrika 85 (1998), 347-361.

Cornick, Jorge, Thomas Cox, and Brain Gould, "Fluid Milk Purchases: a Multivariate Tobit Analysis," American Journal of Agricultural Economics 76:1 (1994), 74-82.

Dempster, Arthur, Nan Laird, and Donald Rubin, "Maximum Likelihood from Incomplete Data Via the EM Algorithm," Journal of the Royal Statistical Society 39:1 (1977), 1-38.

Fama, E., "the Behavior of Stock Market Prices," Journal of Business 38 (1965), 34-105.

Genz, Alan, "Numerical Computation of Rectangular Bivariate and Trivariate Normal and T Probabilities," Statistics and Computing. Vol. 14, No 3 (2004), 251-260.

Geweke, Johns, "Efficient Simulation from the Multivariate Normal and Student T Distribution Subject to Linear Constraints”. In Computer Science and Statistics Proceedings of the Twenty-Third Symposium on the Inference, American Statistical Association, (1991), 571-578.

Heien, Dale, and Cathy Wessells, "Demand Systems Estimation with Microdata: a Censored Regression Approach," Journal of Business and Economic Statistics 8 (1990), 365-71.

Huang, Cliff, Frank Sloan, and Killard Adamache, "Estimation of Seemingly Unrelated Tobit Regressions via the EM Algorithm," Journal of Business and Economic Statistics 5 (1987), 425-430.

Huang, River, "Estimation of the SUR Tobit Model via the MCECM Algorithm," Economics Letters 64 (1999), 25-30. Huang, River, "Bayesian Analysis of the SUR Tobit Model," Applied Economics Letters 8 (2001), 617- 622.

Hajivassiliou, Vassilis, Daniel McFadden, and Paul Ruud, "Simulation of Multivariate Normal Rectangle Probabilities and Their Derivatives Theoretical and Computational Results," Journal of Econometrics 72 (1996), 85-134.

Hamilton, James, Time Series Analysis (Princeton: Princeton University Press, 1994).

Kao, Chihwa, Lung-fei Lee, and Mark Pitt, "Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints," Annals of Economics and Finance 2 (2001), 215-55.

Keane, Michael, "A Computationally Practical Simulation Estimator for Panel Data," Econometrica 62 (1994), 95-116.

Lee, Lung-Fei, and Mark Pitt, "Microeconomic Demand Systems with Binding Nonnegativity Constraints: the Dual Approach," Econometrica 5 (1986), 1237-42.

Lo, Andrew, Harry Mamaysky, and Jiang Wang, "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," Journal of Finance 55:4 (2000), 1705-1770.

Newcomb, S., "A Generalized Theory of the Combination of Observations So as to Obtain the Best Result," American Journal of Mathematics 8 (1886), 343-366.

Nobile, Agostino, "Comment: Bayesian Multinomial Probit Models with a Normalization Constraint," Journal of Econometrics 99:2 (2000), 335-345.

Peiro, Amado, "the Distribution of Stock Returns: International Evidence," Applied Financial Economics 4:6 (1994), 431-39.

Praetz, Peter, "The Distribution of Share Price Changes," Journal of Business 45 (1972), 49-55.

Pudney, Stephen, Modelling Individual Choice: the Econometrics of Corners, Kinks and Holes (New York: Basil-Blackwell, 1989).

Schnedler, Wendelin, "Likelihood Estimation for Censored Random Vectors," Econometric Reviews 24:2 (2005), 195-217.

Shonkwiler, Scott, and Steven Yen, "Two-step Estimation of a Censored System of Equations," American Journal of Agricultural Economics 81 (1999), 972-82.

Su, Shew-Jiuan, and Steven Yen, "A Censored System of Cigarette and Alcohol Consumption," Applied Economics 32:6 (2000), 729-37.

Tallis, G.M., "The Moment Generating Function of the Truncated Multinormal Distribution," Journal of the Royal Statistical Society 23 (1961), 223-229.

Taylor, Mark, and Helen Allen, "The Use of Technical Analysis in the Foreign Exchange Market," Journal of International Money and Finance 11:3 (1992), 304-314.

Wales, T.J., and Alan Woodland, "Estimation of Consumer Demand Systems with Binding Non-Negativity Constraints," Journal of Econometrics 21 (1983), 263-285.

Yen, Steven, and Biing-Hwan Lin, "Quasi-maximum Likelihood Estimation of a Censored Equation System with a Copula Approach: Meat Consumption by US Individuals," Agricultural Economics 39 (2008), 207-217.