Omay, Tolga

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Citation - WoS: 1
Citation - Scopus: 1
A Unit Root Test With Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms
(Springer, 2023) Omay, Tolga; Corakci, Aysegul
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.
Citation - WoS: 19
Citation - Scopus: 12
Using Double Frequency in Fourier Dickey-Fuller Unit Root Test
(Springer, 2022) Cai, Yifei; Omay, Tolga
We propose a double frequency fourier Dickey-Fuller (DF) unit root test. The asymptotic theory of the newly proposed test is first presented in this study. We conduct a series of simulations which suggest the proposed test statistic has correct size performance and gains more power when breaks are located at the beginning and end of the sample and in smooth type. In empirical analysis, we utilize the new test to examine the unit root hypothesis of relative commodity prices measured by Harvey et al. (Rev Econ Stat 92(2):367-377, 2010). The empirical results show that more relative commodity prices are stationary around a deterministic trend generated from double frequency Fourier function.
A Flexible Methodological Approach for Deriving Asymptotic Distributions in Nonlinear Unit Root Tests
(Springer, 2026) Omay, Tolga
This paper examines the challenges associated with deriving asymptotic distributions for nonlinear unit root tests. Although the prevalence of non-linear models has increased in recent years, such complex functions make deriving analytical solutions for ergodicity conditions and asymptotic distributions more challenging. The common practice of approximating nonlinear unit root tests with linear functions results in a significant loss of information. This study proposes a novel approach that utilizes the augmented Fourier transformation of the Arctan function to overcome these limitations. The fast convergence properties of the Arctan function within the Fourier framework allow for the derivation of asymptotic distributions for nonlinear unit root tests. The effectiveness of this method is demonstrated by obtaining previously elusive asymptotic distributions for the (existing nonlinear unit root tests) Leybourne et al., in Journal of Time Series Analysis, 19(1), 83-97 (1998) test and achieving improved approximations for the Kapetanios et al., in Journal of Econometrics, 112(2), 359-379 (2003) test. Furthermore, we develop a new unrestricted ESTAR unit root test and demonstrate how previously unattainable asymptotic distributions can be readily derived for this novel test. An empirical application to real exchange rates, incorporating this new test alongside the existing KSS and Kılıç inft tests, reveals that our unrestricted version captures the data generating process more effectively than its restricted counterparts and demonstrates the superior performance of high-power tests that would otherwise be analytically intractable. Therefore, this approach offers a more accurate and robust way to understand the behavior of non-linear unit root tests.

Journal	Count
Computational Economics	6
Applied Economics	5
Mathematics	3
Springer Proceedings in Business and Economics -- 4th International Conference on Banking and Fice Perspectives, ICBFP 2019 -- 2 May 2019 through 3 May 2019 -- Famagusta -- 273729	3
Environmental Modeling & Assessment	2

Omay, Tolga

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80

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1218

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74

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1075

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70

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58

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