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Article Citation - WoS: 14Citation - Scopus: 16The Nexus Between the Oil Price and Its Volatility Risk in a Stochastic Volatility in the Mean Model With Time-Varying Parameters(Elsevier Sci Ltd, 2019) Balcilar, Mehmet; Ozdemir, Zeynel AbidinHigh price volatility in oil markets creates uncertainty and risk, and increased risk premium may feed back into the prices. This study investigates the dynamic nexus between oil price and its volatility for oil spot and futures markets by means of stochastic volatility in the mean model with time-varying parameters in the conditional mean. The study finds substantial time-variation about the impact of oil price volatility on oil price return in both spot and 1-month to 10-month futures markets. The oil price return volatility has a positive impact on oil price return series over the sample period form the mid-1980s to 2017s except for four very short time periods, which correspond to collapse of OPEC in 1986, invasion of Kuwait in 1990/91, Asian crisis in 1997/2000 and the Global Financial Crisis in 2008. While the oil price return volatility has a positive impact on oil prices, it has limited negative impact on oil prices during periods corresponding to these historical events. Moreover, the findings from this study point out to the existence of a negative and small effect of the lagged oil return series on its volatility for both the spot and futures markets.Article Citation - WoS: 1Citation - Scopus: 1A Unit Root Test With Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms(Springer, 2023) Omay, Tolga; Corakci, AysegulIn 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.Article Citation - WoS: 19Citation - Scopus: 12Using Double Frequency in Fourier Dickey-Fuller Unit Root Test(Springer, 2022) Cai, Yifei; Omay, TolgaWe 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.Article Citation - WoS: 9Citation - Scopus: 7Identifying the Cycles in Covid-19 Infection: the Case of Turkey(Taylor & Francis Ltd, 2023) Akdi, Yilmaz; Karamanoglu, Yunus Emre; Unlu, Kamil Demirberk; Bas, Cem; Emre Karamanoğlu, YunusThe new coronavirus disease, called COVID-19, has spread extremely quickly to more than 200 countries since its detection in December 2019 in China. COVID-19 marks the return of a very old and familiar enemy. Throughout human history, disasters such as earthquakes, volcanic eruptions and even wars have not caused more human losses than lethal diseases, which are caused by viruses, bacteria and parasites. The first COVID-19 case was detected in Turkey on 12 March 2020 and researchers have since then attempted to examine periodicity in the number of daily new cases. One of the most curious questions in the pandemic process that affects the whole world is whether there will be a second wave. Such questions can be answered by examining any periodicities in the series of daily cases. Periodic series are frequently seen in many disciplines. An important method based on harmonic regression is the focus of the study. The main aim of this study is to identify the hidden periodic structure of the daily infected cases. Infected case of Turkey is analyzed by using periodogram-based methodology. Our results revealed that there are 4, 5 and 62 days cycles in the daily new cases of Turkey.Article A Flexible Methodological Approach for Deriving Asymptotic Distributions in Nonlinear Unit Root Tests(Springer, 2026) Omay, TolgaThis 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.
