Hierarchical Markov Normal Mixture Models with Applications to Financial Asset Returns
AbstractMotivated by the common problem of constructing predictive distributions for daily asset returns over horizons of one to several trading days, this article introduces a new model for time series. This model is a generalization of the Markov normal mixture model in which the mixture components are themselves normal mixtures, and it is a specific case of an artificial neural network model with two hidden layers. The article characterizes the implications of the model for time series in two ways. First, it derives the restrictions placed on the autocovariance function and linear representation of integer powers of the time series in terms of the number of components in the mixture and the roots of the Markov process. Second, it uses the prior predictive distribution of the model to study the implications of the model for some interesting functions of asset returns. The article uses the model to construct predictive distributions of daily S&P 500 returns 1971-2005, US dollar - UK pound returns 1972-1998, and one- and ten-year maturity bonds 1987-2006. It compares the performance of the model for these returns with ARCH and stochastic volatility models using the predictive likelihood function. The model's performance is about the same as its competitors for the bond returns, better than its competitors for the S&P 500 returns, and much better than its competitors for the dollar-pound returns. In and out of sample validation exercises with predictive distributions identify some remaining deficiencies in the model and suggest potential improvements. The article concludes by using the model to form predictive distributions of one- to ten-day returns during volatile episodes for the S&P 500, dollar-pound and bond return series.
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Bibliographic InfoPaper provided by University of Brescia, Department of Economics in its series Working Papers with number 0705.
Date of creation: 2007
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Web page: http://www.unibs.it/atp/page.1019.0.0.0.atp?node=224
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Other versions of this item:
- John Geweke & Gianni Amisano, 2011. "Hierarchical Markov normal mixture models with applications to financial asset returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 1-29, January/F.
- Geweke, John & Amisano, Gianni, 2007. "Hierarchical Markov normal mixture models with applications to financial asset returns," Working Paper Series 0831, European Central Bank.
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, vol. 133(1), pages 273-305, July.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
- Andrew W. Lo, 1986.
"Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data,"
NBER Technical Working Papers
0059, National Bureau of Economic Research, Inc.
- Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
- Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
- Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Diebold, Francis X. & Inoue, Atsushi, 2001.
"Long memory and regime switching,"
Journal of Econometrics,
Elsevier, vol. 105(1), pages 131-159, November.
- Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 12(4), pages 371-89, October.
- Tom Doan, . "RATS programs to replicate Jacquier, Polson, Rossi (1994) stochastic volatility," Statistical Software Components RTZ00105, Boston College Department of Economics.
- Gallant, Ronald & Tauchen, George, 1989.
"Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications,"
Econometric Society, vol. 57(5), pages 1091-1120, September.
- Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
- Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984.
"Pseudo Maximum Likelihood Methods: Theory,"
Econometric Society, vol. 52(3), pages 681-700, May.
- John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
- Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
- Geweke, John & Whiteman, Charles, 2006. "Bayesian Forecasting," Handbook of Economic Forecasting, Elsevier.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
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