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A Unit Root Test with Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms

Author

Listed:
  • Tolga Omay

    (Atilim University)

  • Aysegul Corakci

    (Çankaya University)

Abstract

In this study, we investigate the performance of different optimization algorithms in estimating the Markov switching (MS) deterministic components of the traditional ADF test. For this purpose, we consider Broyden, Fletcher, Goldfarb, and Shanno (BFGS), Berndt, Hall, Hall, Hausman (BHHH), Simplex, Genetic, and Expectation-Maximization (EM) algorithms. The simulation studies show that the Simplex method has significant advantages over the other commonly used hill-climbing methods and EM. It gives unbiased estimates of the MS deterministic components of the ADF unit root test and delivers good size and power properties. When Hamilton’s (Econometrica 57:357–384, 1989) MS model is re-evaluated in conjunction with the alternative algorithms, we furthermore show that Simplex converges to the global optima in stationary MS models with remarkably high precision and even when convergence criterion is raised, or initial values are altered. These advantages of the Simplex routine in MS models allow us to contribute to the current literature. First, we produce the exact critical values of the generalized ADF unit root test with MS breaks in trends. Second, we derive the asymptotic distribution of this test and provide its invariance feature.

Suggested Citation

  • Tolga Omay & Aysegul Corakci, 2024. "A Unit Root Test with Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1837-1856, September.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:3:d:10.1007_s10614-023-10501-4
    DOI: 10.1007/s10614-023-10501-4
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    References listed on IDEAS

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    More about this item

    Keywords

    Markov switching model; Unit root; Optimization algorithm;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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