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A New Approach to Goodness of Fit for Ergodic Markov Processes

Author

Listed:
  • Vance Martin
  • Yoshihiko Nishiyama
  • John Stachurski
  • Yiran Xie

Abstract

We introduce a new density-based goodness of fit test for ergodic Markov processes. Our test compares the data against the class of models specified in the null hypothesis, and rejects if no model in the class yields a stationary density that matches with the data. No alternative needs to be specified in order to implement the test. Although our test compares densities, estimation of smoothing parameters is not required, and the test has nontrivial power against $1/\sqrt{n}$ local alternatives. The test provides new perspectives on some existing problems in econometric and financial modeling.

Suggested Citation

  • Vance Martin & Yoshihiko Nishiyama & John Stachurski & Yiran Xie, 2026. "A New Approach to Goodness of Fit for Ergodic Markov Processes," Papers 2608.03088, arXiv.org.
    • Handle: RePEc:arx:papers:2608.03088
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    File URL: https://arxiv.org/pdf/2608.03088
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