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How does innovation’s tail risk determine marginal tail risk of a stationary financial time series?

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Abstract

We discuss the relationship between the marginal tail risk probability and the innovation’s tail risk probability for some stationary financial time series models. We first give the main results on the tail behavior of a class of infinite weighted sums of random variables with heavy-tailed probabilities. And then, the main results are applied to three important types of time series models: infinite order moving averages, the simple bilinear time series and the solutions of stochastic difference equations. The explicit formulas are given to describe how the marginal tail probabilities come from the innovation’s tail probabilities for these time series. Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.

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Authors and Affiliations

  1. LMAM and Department of Financial Mathematics, School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Pan Jiazhu

  2. Department of Business Studies, The Hong Kong Polytechnic University, Hong Kong

    Yu Bosco W. T.

  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong

    Pang W. K.

Authors
  1. Pan Jiazhu
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  2. Yu Bosco W. T.
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  3. Pang W. K.
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Correspondence to Pan Jiazhu.

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Pan, J., Yu, B.W.T. & Pang, W.K. How does innovation’s tail risk determine marginal tail risk of a stationary financial time series?. Sci. China Ser. A-Math. 47, 321–338 (2004). https://doi.org/10.1360/02ys0317

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  • DOI: https://doi.org/10.1360/02ys0317

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