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Approximate Factor Models with a Common Multiplicative Factor for Stochastic Volatility

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  • Roberto Leon-Gonzalez

    (National Graduate Institute for Policy Studies, Tokyo, Japan)

  • Blessings Majon

    (National Graduate Institute for Policy Studies, Tokyo, Japan)

Abstract

Common factor stochastic volatility (CSV) models capture the commonality that is often observed in volatility patterns. However, they assume that all the time variation in volatility is driven by a single multiplicative factor. This paper has two contributions. Firstly we develop a novel CSV model in which the volatility follows an inverse gamma process (CSV-IG), which implies fat Student’s t tails for the observed data. We obtain an analytic expression for the likelihood of this CSV model, which facilitates the numerical calculation of the marginal and predictive likelihood for model comparison. We also show that it is possible to simulate exactly from the posterior distribution of the volatilities using mixtures of gammas. Secondly, we generalize this CSV-IG model by parsimoniously substituting conditionally homoscedastic shocks with heteroscedastic factors which interact multiplicatively with the common factor in an approximate factor model (CSV-IG-AF). In empirical applications we compare these models to other multivariate stochastic volatility models, including different types of CSV models and exact factor stochastic volatility (FSV) models. The models are estimated using daily exchange rate returns of 8 currencies. A second application estimates the models using 20 macroeconomic variables for each of four countries: US, UK, Japan and Brazil. The comparison method is based on the predictive likelihood. In the application to exchange rate data we find strong evidence of CSV and that the best model is the IG-CSV-AF. In the Macro application we find that 1) the CSV-IG model performs better than all other CSV models, 2) the CSV-IG-AF is the best model for the US, 3) the CSV-IG is the best model for Brazil and 4) exact factor SV models are the best for UK and JP.

Suggested Citation

  • Roberto Leon-Gonzalez & Blessings Majon, 2024. "Approximate Factor Models with a Common Multiplicative Factor for Stochastic Volatility," GRIPS Discussion Papers 24-02, National Graduate Institute for Policy Studies.
    • Handle: RePEc:ngi:dpaper:24-02
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    References listed on IDEAS

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    1. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    2. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    3. Aubrey Poon, 2018. "Assessing the Synchronicity and Nature of Australian State Business Cycles," The Economic Record, The Economic Society of Australia, vol. 94(307), pages 372-390, December.
    4. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    5. Anna Pajor, 2006. "Bayesian Analysis of the Conditional Correlation Between Stock Index Returns with Multivariate SV Models," Papers physics/0607176, arXiv.org.
    6. Mumtaz, Haroon, 2018. "A generalised stochastic volatility in mean VAR," Economics Letters, Elsevier, vol. 173(C), pages 10-14.
    7. Haroon Mumtaz, 2018. "A generalised stochastic volatility in mean VAR," Working Papers 855, Queen Mary University of London, School of Economics and Finance.
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    1. Roberto Leon-Gonzalez & Blessings Majoni, 2023. "Exact Likelihood for Inverse Gamma Stochastic Volatility Models," GRIPS Discussion Papers 23-07, National Graduate Institute for Policy Studies.

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