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Abstract
The Kalman filter is a time series estimation algorithm that is applied extensively in the field of engineering and recently (relative to engineering) in the field of finance and economics. However, presentations of the technique are somewhat intimidating despite the relative ease of generating the algorithm. This article presents the Kalman filter in a simplified manner and produces an example of an application of the algorithm in Excel. This scaled-down version of the Kalman filter can be introduced in the (advanced) undergraduate classroom as well as the graduate classroom.
ACKNOWLEDGMENTS
The authors thank Joseph Hartman, Jimmy Hilliard, Karl Horak, Marcos M. Lopez de Prado, Jerry Stevens, two anonymous referees, students at James Madison University and the College of Santa Fe, and members of the Social Science Research Network for helpful conversations and comments.
Notes
1See Bertus, Beyer, Godbey, and Hinkelmann, Market Behavior and Equity Prices: What Can the S&P 500 Index Derivatives Markets Tell Us? Working paper. (2006); Bertus, Denny, Godbey and Hinkelmann, Noise and Equity Prices: Evidence from the Stock Index Futures Market, Working paper. (2006); Burmeister and Wall, “Kalman filtering estimation of unobserved rational expectations with an application to the German hyperinflation,” Journal of Econometrics, 20 (1982) 255–284; Burmeister, Wall, and Hamilton, “Estimation of unobserved expected monthly inflation using Kalman filtering,” Journal of Business and Economic Statistics, 4 (1986) 147–160; Faff, Hillier, and Hillier, “Time varying beta risk: An analysis of alternative modeling techniques,” Journal of Business Finance & Accounting, 27(5) (2000) 523–554; Fink, Fink, and Lange, “The use of term structure information in the hedging of mortgage-backed securities,” The Journal of Futures Markets, 25(7) (2005) 661–678; Godbey and Hilliard, “Adjusting Stacked-Hedge Rations for Stochastic Convenience Yield: A Minimum Variance Approach,” Quantitative Finance, 7 (2007); Schwartz, “The stochastic behavior of commodity prices implications for valuations and hedging,” Journal of Finance, 52 (1997) 923–973.