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Forecasting stochastic Volatility using the Kalman filter: An Application to Canadian Interest Rates and Price-Earnings Ratio

Author

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  • Francois-Éric Racicot

    () (Département des sciences administratives, Université du Québec (Outaouais), LRSP et Chaire d'information financière et organisationnelle)

  • Raymond Théoret

    () (Département de finance, Université du Québec (Montréal), Université du Québec (Outaouais), et Chaire d'information financière et organisationnelle)

Abstract

In this paper, we aim at forecasting the stochastic volatility of key financial market variables with the Kalman filter using stochastic models developed by Taylor (1986, 1994) and Nelson (1990). First, we compare a stochastic volatility model relying on the Kalman filter to the conditional volatility estimated with the GARCH model. We apply our models to Canadian short-term interest rates. When comparing the profile of the interest rate stochastic volatility to the conditional one, we find that the omission of a constant term in the stochastic volatility model might have a perverse effect leading to a scaling problem, a problem often overlooked in the literature. Stochastic volatility seems to be a better forecasting tool than GARCH(1,1) since it is less conditioned by autoregressive past information. Second, we filter the S&P500 price-earnings (P/E) ratio in order to forecast its value. To make this forecast, we postulate a rational expectations process but our method may accommodate other data generating processes. We find that our forecast is close to a GARCH(1,1) profile.

Suggested Citation

  • Francois-Éric Racicot & Raymond Théoret, 2011. "Forecasting stochastic Volatility using the Kalman filter: An Application to Canadian Interest Rates and Price-Earnings Ratio," RePAd Working Paper Series UQO-DSA-wp032011, Département des sciences administratives, UQO.
  • Handle: RePEc:pqs:wpaper:032011
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    File URL: http://www.repad.org/ca/qc/uq/uqo/dsa/forecasting.pdf
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    3. Torben G. Andersen & Luca Benzoni, 2009. "Stochastic volatility," Working Paper Series WP-09-04, Federal Reserve Bank of Chicago.
    4. Fornari, Fabio & Mele, Antonio, 2006. "Approximating volatility diffusions with CEV-ARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(6), pages 931-966, June.
    5. François-Éric Racicot & Raymond Théoret, 2010. "Hedge Fund Returns, Kalman Filter, and Errors-in-Variables," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 38(3), pages 377-378, September.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
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    Cited by:

    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
    2. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.

    More about this item

    Keywords

    Stochastic volatility; Kalman filter; P/E ratio forecast; Interest rate forecast.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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