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Non‐Gaussian Filter and Smoother Based on the Pearson Distribution System

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  • Yuichi Nagahara

Abstract

The Pearson distribution system can represent wide class of distributions with various skewness and kurtosis. We develop a practical approach of using all types of its distribution system including the type‐IV distribution which was difficult to implement. We propose an easily implemented algorithm which uses less‐memory and performs at a higher speed than other typical methods: using analytic approximation of successive conditional probability density functions for prediction and filtering by the Pearson distribution system in the case of both the system and observation noise being one‐dimensional. By using the approximated probability density function and the numerical integration, we obtain mean, variance, skewness and kurtosis of the next distribution. We decide the next approximated distribution from the Pearson distribution system. We adopt these steps for the prediction, filtering and smoothing recursively. Our framework makes it possible to construct time series models with various noise distributions. We apply our non‐Gaussian filter to the estimation of non‐Gaussian stochastic volatility models of the stock returns. We compare our method with the typical method.

Suggested Citation

  • Yuichi Nagahara, 2003. "Non‐Gaussian Filter and Smoother Based on the Pearson Distribution System," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 721-738, November.
  • Handle: RePEc:bla:jtsera:v:24:y:2003:i:6:p:721-738
    DOI: 10.1111/j.1467-9892.2003.00331.x
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    References listed on IDEAS

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    1. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    2. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    3. Parrish, Rudolph S., 1983. "On an integrated approach to member selection and parameter estimation for Pearson distributions," Computational Statistics & Data Analysis, Elsevier, vol. 1(1), pages 239-255, March.
    4. Nagahara, Yuichi, 1999. "The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 251-264, July.
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    Cited by:

    1. Yuichi Nagahara, 2008. "A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(3), pages 175-184, December.
    2. Yuichi Nagahara, 2011. "Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 429-443, November.
    3. Fabio Pizzutilo, 2013. "The Distribution of the Returns of Japanese Stocks and Portfolios," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(9), pages 1249-1259, September.
    4. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.

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