Identification and Forecasting of Bull and Bear Markets using Multivariate Returns

Liu, Jia and Maheu, John M and Song, Yong (2023): Identification and Forecasting of Bull and Bear Markets using Multivariate Returns.

Abstract

Bull and bear market identification generally focuses on a broad index of returns through a univariate analysis. This paper proposes a new approach to identify and forecast bull and bear markets through multivariate returns. The model assumes all assets are directed by a common discrete state variable from a hierarchical Markov switching model. The hierarchical specification allows the cross-section of state specific means and variances to differ over bull and bear markets. We investigate several empirically realistic specifications that permit feasible estimation even with 100 assets. Our results show that the multivariate framework provides competitive bull and bear regime identification and improves portfolio performance and density prediction compared to several benchmark models including univariate Markov switching models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Markov switching, Multivariate analysis, Investment strategies, Market timing
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets

References

Ang, A. & Bekaert, G. (2002), ‘International asset allocation with regime shifts’, Review of Financial Studies 15, 1137–1187.

Baele, L., Bekaert, G., Inghelbrecht, K. & Wei, M. (2019), ‘Flights to Safety’, The Review of Financial Studies 33(2), 689–746.

Barnard, J., McCulloch, R. & Meng, X.-L. (2000), ‘Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage’, Statistica Sinica pp. 1281–1311.

Byrne, S. & Girolami, M. (2013), ‘Geodesic monte carlo on embedded manifolds’, Scandinavian Journal of Statistics 40(4), 825–845.

Candelon, B., Piplack, J. & Straetmans, S. (2008), ‘On measuring synchronization of bulls and bears: The case of east asia’, Journal of Banking & Finance 32(6), 1022–1035.

Chauvet, M. & Potter, S. (2000), ‘Coincident and leading indicators of the stock market’, Journal of Empirical Finance 7, 87–111.

Chen, S.-S. (2009), ‘Predicting the bear stock market: Macroeconomic variables as leading indicators’, Journal of Banking & Finance 33(2), 211–223.

Chib, S. (1996), ‘Calculating posterior distributions and modal estimates in Markov mixture models’, Journal of Econometrics 75(1), 79–97.

Geweke, J. (2007), ‘Interpretation and inference in mixture models: Simple MCMC works’, Computational Statistics & Data Analysis 51(7), 3529–3550.

Geweke, J. & Amisano, G. (2010), ‘Comparing and evaluating Bayesian predictive distributions of asset returns’, International Journal of Forecasting 26(2), 216–230.

Girolami, M. & Calderhead, B. (2011), ‘Riemann manifold Langevin and Hamiltonian Monte Carlo methods’, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73(2), 123–214.

Guidolin, M. & Timmermann, A. (2006), ‘An econometric model of nonlinear dynamics in the joint distribution of stock and bond returns’, Journal of Applied Econometrics 21(1), 1–22.

Guidolin, M. & Timmermann, A. (2007), ‘Asset allocation under multivariate regime switch- ing’, Journal of Economic Dynamics and Control 31(11), 3503–3544.

Haase, F., Neuenkirch, M. et al. (2020), Forecasting stock market recessions in the us: Predictive modeling using different identification approaches, Technical report, University of Trier, Department of Economics.

Hamilton, J. D. & Owyang, M. T. (2012), ‘The propagation of regional recessions’, The Review of Economics and Statistics 94(4), 935–947.

Harding, D. & Pagan, A. (2006), ‘Synchronization of cycles’, Journal of Econometrics 132(1), 59–79.

Holbrook, A., Lan, S., Vandenberg-Rodes, A. & Shahbaba, B. (2018), ‘Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation’, Journal of statistical computation and simulation 88(5), 982-1002.

Jasra, A., Holmes, C. C. & Stephens, D. A. (2005), ‘Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling’, Statistical Science 20(1), 50-67.

Kass, R. E. & Raftery, A. E. (1995), ‘Bayes factors’, Journal of the American Statistical Association 90(430), 773–795.

Kaufman, S. (2010), ‘Dating and forecasting turning points by Bayesian clustering with dynamic structure: a suggestion with an application to Austrian data’, Journal of Applied Econometrics 25, 309–344.

Kim, C.-J., Nelson, C. R. et al. (1999), ‘State-space models with regime switching: classical and Gibbs-sampling approaches with applications’, MIT Press Books 1.

Kole, E. & Van Dijk, D. (2017), ‘How to identify and forecast bull and bear markets?’, Journal of Applied Econometrics 32(1), 120–139.

Lunde, A. & Timmermann, A. (2004), ‘Duration dependence in stock prices: An analysis of bull and bear markets’, Journal of Business & Economic Statistics 22(3), 253–273.

Maheu, J. M. & McCurdy, T. H. (2000), ‘Identifying bull and bear markets in stock returns’, Journal of Business & Economic Statistics 18(1), 100–112.

Maheu, J. M., McCurdy, T. H. & Song, Y. (2012), ‘Components of bull and bear markets: bull corrections and bear rallies’, Journal of Business & Economic Statistics 30(3), 391–403.

Maheu, J. M., McCurdy, T. H. & Song, Y. (2021), ‘Bull and bear markets during the COVID-19 pandemic’, Finance Research Letters 42, 102091.

Marriam-Webseter (2022), ‘The history of ’bull’ and ’bear’ markets’, https://www.merriam-webster.com/words-at-play/the-origins-of-the-bear-and-bull-in-the-stock-market. Accessed: 2022-03-16.

Neal, R. M. et al. (2011), ‘MCMC using Hamiltonian dynamics’, Handbook of Markov chain Monte Carlo 2(11), 2.

Paap, R., Segers, R. & van Dijk, D. (2009), ‘Do leading indicators lead peaks more than troughs?’, Journal of Business & Economic Statistics 27(4), 528–543.

Pagan, A. R. & Sossounov, K. A. (2003), ‘A simple framework for analysing bull and bear markets’, Journal of Applied Econometrics 18(1), 23–46.

Pelletier, D. (2006), ‘Regime switching for dynamic correlations’, Journal of Econometrics 131(1), 445–473.

Pesaran, M. H., Pettenuzzo, D. & Timmermann, A. (2006), ‘Forecasting time series subject to multiple structural breaks’, The Review of Economic Studies 73(4), 1057–1084.

Song, Y. (2014), ‘Modelling regime switching and structural breaks with an infinite hidden Markov model’, Journal of Applied Econometrics 29(5), 825–842.

Tu, J. (2010), ‘Is regime switching in stock returns important in portfolio decisions?’, Management Science 56(7), 1198–1215.

Turner, C., Startz, R. & Nelson, C. (1989), ‘A Markov model of heteroskedasticity, risk, and learning in the stock market’, Journal of Financial Economics 25, 3–22.