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Goodness-of-fit test for stochastic volatility models

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  • Lin, Liang-Ching
  • Lee, Sangyeol
  • Guo, Meihui

Abstract

In this paper, we propose a goodness of fit test for continuous time stochastic volatility models based on discretely sampled observations. The proposed test is constructed by measuring deviations between the empirical and true characteristic functions obtained from the hypothesized stochastic volatility model. In this study, both the test statistics based on the fixed and decreasing sampling schemes are taken into consideration. It is shown that under the null, the proposed tests asymptotically follow a weighted sum of products of centered normal random variables. In order to evaluate the proposed tests, a simulation study is performed, in which a bootstrap method is also considered. Finally, a real data analysis is conducted for illustration.

Suggested Citation

  • Lin, Liang-Ching & Lee, Sangyeol & Guo, Meihui, 2013. "Goodness-of-fit test for stochastic volatility models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 473-498.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:473-498
    DOI: 10.1016/j.jmva.2013.01.006
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    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    2. Christensen, Kim & Thyrsgaard, Martin & Veliyev, Bezirgen, 2019. "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing," Journal of Econometrics, Elsevier, vol. 212(2), pages 556-583.
    3. Liang-Ching Lin & Sangyeol Lee & Meihui Guo, 2014. "The Bickel–Rosenblatt test for continuous time stochastic volatility models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 195-218, March.

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