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Article A Computationally Efficient Approximation for Fractional Differencing: First-Order Operators(Pergamon-Elsevier Science Ltd, 2026) Omay, Tolga; Baleanu, DumitruThis paper introduces the First-Order Fractional Differencing (FOFD) operator that substantially reduces the computational burden of fractional differencing for large-scale applications. While the standard Gr & uuml;nwald-Letnikov (GL) operator requires O(T2) operations for a series of length T, and recent FFT-based methods achieve O(T log T), our FOFD operator requires only O(T) operations through a simple two-point recursion. We develop an optimal weight calibration framework that ensures this computational efficiency does not compromise statistical accuracy, deriving a general formula wopt = d & sdot; (1-0.9 rho)beta(p) that adapts to the persistence structure of autoregressive processes. Empirical applications demonstrate substantial improvements: for the Chicago Fed National Financial Conditions Index with extreme persistence (rho= 0.992), optimal weight calibration reduces approximation error by 93% while preserving the autocorrelation structure of the GL operator. For a series of 10,000 observations, our method requires 20,000 operations compared to 530,000 for FFT-based methods and 50 million for standard implementations-enabling fractional differencing in real-time and high-frequency contexts previously infeasible due to computational constraints. The method's simplicity, requiring no specialized libraries and providing direct implementation through our calibration formula, makes it immediately accessible to practitioners while maintaining the long-memory properties essential for financial time series modeling.Article Citation - WoS: 11Citation - Scopus: 11Comparison of Optimization Algorithms for Selecting the Fractional Frequency in Fourier Form Unit Root Tests(Routledge Journals, Taylor & Francis Ltd, 2021) Omay, Tolga; Emirmahmutoglu, Furkan; Hussain Shahzad, Syed JawadWe compare the performance of unit root tests which include flexible Fourier trends in their testing processes. The algorithms considered are those of Broyden, Fletcher, Goldfarb and Shanno (BFGS), Berndt, Hall, Hall and Hausman (BHHH), Simplex, Genetic and grid search (GS). The simulation results indicate that derivative-free methods, such as Genetic and Simplex, have advantages over hill-climbing methods, such as BFGS and BHHH in providing accurate fractional frequencies for fractional frequency flexible Fourier form (FFFFF) unit root test. When the parameters are estimated under the alternative hypothesis of the FFFFF type of unit root test, the grid search and derivative-free methods provide unbiased and efficient estimations. We also provide the asymptotic distribution of the FFFFF unit root test. We extend the FFFFF unit root test to a panel version in order to increase the power of the test. Finally, the empirical analyses of healthcare convergence show that derivative-free methods, hill climbing and extensive grid searches can be used interchangeably. However, for big data and accurate estimation of the frequency parameters, the Simplex methodology using the bootstrap process is preferred.Article Citation - WoS: 6Citation - Scopus: 4Is real per capita state personal income stationary? New nonlinear, asymmetric panel-data evidence(Wiley, 2020) Emirmahmutoglu, Furkan; Gupta, Rangan; Miller, Stephen M.; Omay, TolgaThis paper re-examines the stochastic properties of U.S. state real per capita personal income, using new panel unit-root procedures. The new developments incorporate non-linearity, asymmetry, and cross-sectional correlation within panel-data estimation. Including nonlinearity and asymmetry finds that 43 states exhibit stationary real per capita personal income whereas including only nonlinearity produces 42 states that exhibit stationarity. Stated differently, we find that two states exhibit nonstationary real per capita personal income when considering nonlinearity, asymmetry, and cross-sectional dependence.Article Citation - WoS: 11Testing the Hysteresis Effect in the Us State-Level Unemployment Series(Routledge Journals, Taylor & Francis Ltd, 2020) Omay, Tolga; Ozcan, Burcu; Shahbaz, MuhammedThis paper re-examines the stochastic time series behaviour of the monthly unemployment rate in 50 states of the United States (US) for the period 1976-2017 using a number of state-of-the-art unit root tests. The new developments incorporate structural break, nonlinearity, asymmetry, and cross-sectional correlation within panel-data estimation including the use of a sequential panel selection method. While not previously considered, sequential panel selection enabled us to determine and separate the stationary and nonstationary series in the sample. The empirical findings are in support of the stationarity of unemployment rate in 47 states. The findings confirm a natural rate hypothesis for the labour markets in the most US states, indicating that labour market shocks have solely temporary effects on state-level unemployment. This empirical study provides significant state-specific policy implications.Article Hisse Senedi Getirileri, Bitcoin Getirileri ve Riskten Kaçınma Arasındaki İlişki: Çok Değişkenli Bir Garch Modelinden Kanıtlar(Sosyoekonomi Soc, 2021) Sivrikaya, Ayşen; İren, Perihan; Omay, TolgaBu çalışma, çok değişkenli bir GARCH modeli kullanarak ABD Dow Jones Borsasında işlem gören hisse senedi getirileri, Bitcoin getirileri ve bunların belirsizlikleri arasındaki ilişkileri araştırmaktadır. Özellikle, yüksek ve düşük olmak üzere farklı risk iştahının ve getirilerde belirsizliğin yüksek olduğu dönemlerde Bitcoin ve ABD hisse senedi getirilerinin verdiği tepkileri karşılaştırmaktadır. Sonuçlar, Bitcoin getirisinin riskten kaçınılan veya yüksek belirsizliğin olduğu dönemlerde hisse senedi gibi tepki verdiğini, ancak iki getiri arasındaki ilişkinin sürdürülebilir olmadığını göstermektedir. Öte yandan, ABD borsa yatırımcıları tüm örneklem dönemi boyunca riskten kaçınma davranışını gösterirken, Bitcoin yatırımcıları aynı davranışı göstermemektedir.Article Citation - WoS: 10Citation - Scopus: 11Is There Convergence in Renewable Energy Deployment? Evidence From a New Panel Unit Root Test With Smooth and Sharp Structural Breaks(Pergamon-elsevier Science Ltd, 2023) Corakci, Aysegul; Omay, TolgaThis study examines whether the contribution of renewable energy to the total primary energy supply converges in a panel of 24 OECD countries over the period 1960-2020. To this end, a new panel unit root test that allows for both sharp and smooth breaks is proposed to test for the stochastic convergence hypothesis. Although renewable energy convergence is not rejected when the newly proposed test is applied to the full panel of OECD countries, it found only moderate support within the members of the panel using a sequential panel selection methodology. In fact, in two high-income OECD countries, the contribution of renewable energy to the primary energy supply shows no sign of convergence: Poland and Iceland. Therefore, the renewable energy shares seem to be converging to a common steady state in only a group of OECD countries over the long run. This uneven pattern of convergence, in turn, suggests that the OECD countries are still far away from developing a common sustainable renewable energy target, calling for urgent international policy cooperation to encourage the divergent econo-mies to seek out the menu of policies that ensure the worldwide success of renewable energy transformation.Article Citation - WoS: 9Citation - Scopus: 11Current Account and Credit Growth: the Role of Household Credit and Financial Depth(Elsevier Science inc, 2020) Ekinci, Mehmet Fatih; Ekinci, Mehmet Fatih; Omay, Tolga; Omay, Tolga; Ekinci, Mehmet Fatih; Omay, Tolga; Economics; EconomicsUnderstanding the impact of financial variables on the current account balance is one of the priorities of academic literature and policymakers. Evidence from a broad panel of advanced and emerging countries shows that an increase in credit growth is associated with a significant deterioration in the current account balance. When we examine the roles of the components of credit, we find that an increase in household credit causes a significant decline in the current account balance, whereas an increase in business loans has no significant effect. Therefore, our findings indicate that the significant negative impact of credit growth on the current account balance is driven by household credit. Furthermore, we show that total and household credit growth rates have a stronger negative effect on the current account balance for lower levels of financial depth. Our results suggest that targeted policy measures that curb household credit growth might be more effective to reduce external imbalances particularly at the early stages of financial deepening.Article Citation - WoS: 47Citation - Scopus: 47Global Risk Aversion and Emerging Market Return Comovements(Elsevier Science Sa, 2018) Demirer, Riza; Omay, Tolga; Yuksel, Asli; Yuksel, AydinUtilizing the recently developed measure of global risk aversion by Xu (2017), we show that global risk aversion is a significant determinant of international equity correlations, consistently across all emerging markets examined. The positive effect of risk aversion on emerging market comovements is particularly strong for South Africa and Turkey and is consistent with contagion effects. The results underscore the importance of non-cash flow shocks in models of contagion and portfolio risk. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 6Oil and Stock Prices: New Evidence From a Time Varying Homogenous Panel Smooth Transitionvecmfor Seven Developing Countries(Wiley, 2022) Ceylan, Resat; Ivrendi, Mehmet; Shahbaz, Muhammed; Omay, TolgaThis paper investigates the relationship between international oil price and stock prices applying the time varying causality testing over the period of 2000(M1)-2017(M3). The panel unit root and panel cointegration tests considering cross-section dependence are also employed. A time varying panel smooth transition vector error correction (TV-PSTRVEC) model is a developed and estimated for testing the presence of non-linear short-run and long-run causality, and cointegrating relationship between stock and oil prices. The empirical findings indicate that short and long-run causalities between oil price and stock prices are time-dependent. Moreover, oil price cause stock prices in the long-run. In the short-run, neutral effect exists between oil price and stock prices. These two findings are evidence of a strong exogeneity of oil price in time-dependent regimes which is also supporting the recent arguments and empirical findings.Article Citation - WoS: 31Citation - Scopus: 35Fractional Unit-Root Tests Allowing for a Fractional Frequency Flexible Fourier Form Trend: Predictability of Covid-19(Springer, 2021) Omay, Tolga; Baleanu, DumitruIn this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.
