Nonlinear Unit Research Articles

Doubts on natural rate of unemployment: Evidence and policy implications

This study aims to revisit the nature of unemployment dynamics in Asian and OECD countries from 1998 to 2018 by employing a novel nonlinear unit root test developed by Park and Shintani (2016). We specify a threshold autoregressive (TAR) model with two specifications to detect the presence of natural rate, hysteresis, and a permanent shift of natural rate of unemployment due to economic or structural changes. Empirical evidence is important to give guidance for policymakers to make effective stabilization policies when having doubts on the natural rate hypothesis. The findings in this study confirm the presence of hysteresis unemployment in many Asian and OECD countries while some countries are found to have a permanent shift of natural rate, thereby giving support to more activist stabilization policies.

Testing for market efficiency in cryptocurrencies: evidence from a non-linear conditional quantile framework

ABSTRACT This study tests for the weak-form market efficiency of 15 cryptocurrency prices. The conventional unit root tests and stationary test results reveal that most cryptocurrency markets are efficient markets. However, the non-linear quantile unit root test proposed by Li and Park (2018) rejects the unit root null hypothesis over the whole quantile level. To derive more informative ideas, we split the whole quantile interval to several sub-intervals and find asymmetric behaviour of the market efficiency across the lower and upper sub-intervals in several cryptocurrency markets. Moreover, non-linear quantile unit root tests for Chainlink, Bitcoin Cash, Binance Coin, EOS, Tron, and Stellar indicate that markets for these cryptocurrencies are efficient at the upper sub-intervals.

MXene‐Based Broadband Ultrafast Nonlinear Activator for Optical Computing

AbstractOptical neural networks (ONNs) are particularly advantageous owing to their inherent parallelism and low energy consumption. However, one of the obstacles to the implementation of ONNs is the lack of optical nonlinearity. In this study, optical nonlinear activators for ONNs are prepared by combining Ti3C2Tx MXene with microfibers and their principles are verified. Activation functions obtained from experimental measurements are used to simulate multiclassification and super‐resolution reconstruction tasks with performance comparable to that of activation functions commonly used in computers. Four necessary criteria are proposed and validated for evaluating the performance of the nonlinear activator: recovery time, deviation from linearity, the activation function close to identity mapping, and reconfigurability of the configuration. Theoretically, the nonlinear activator can compute 100 times faster than commonly used electronic computers and can be used as a nonlinear activation unit for ONNs to help the integration of ONNs with artificial intelligence.

Are CO2 Emissions Stationary After All? New Evidence from Nonlinear Unit Root Tests

Are CO2 Emissions Stationary After All? New Evidence from Nonlinear Unit Root Tests

Convergence of per capita energy consumption around the world: New evidence from nonlinear panel unit root tests

This paper investigates the existence of stochastic and deterministic convergence in per capita energy consumption among the countries forming four income-level groups and a full sample of 110 countries over the 1971–2019 period. For that purpose, we employ six state-of-the-art nonlinear panel unit root tests with nonlinear dynamics that range from state-dependent nonlinearities such as ESTAR, AESTAR and TAR dynamics to time-dependent nonlinearities of structural break form. We find consistent evidence supporting stochastic convergence among high-income and upper-middle-income countries according to two of the six panel tests. Concerning the stronger notion of deterministic convergence, three tests point to deterministic convergence among high-income countries, and only one supports this hypothesis among upper-middle-income countries. Lack of convergence across all country groups carries important policy implications concerning the achievement of SDG7 of the global 2030 Agenda for Sustainable Development that affects every single country in the planet.

Dynamics of Exchange Rate Fluctuations in Turkey: Evidence from Symmetric and Asymmetric Causality Analysis

This study examines the factors affecting exchange rate fluctuations in Turkey by employing the quarterly data from 2008 to 2020. In this context, linear and nonlinear unit root tests were used to determine the stationarity levels of the variables. Then, symmetric and asymmetric causality analysis was preferred to ascertain the relationship between the variables. Symmetric causality analysis results indicated a causality relationship from the exchange rate to the long-term debt stock, from the credit default swap (CDS) to the exchange rate, and from the exchange rate to the uncertainty index. The asymmetric causality analysis showed a causality relationship from positive shocks in the short-term debt stock to negative shocks in the exchange rate. Also, it was proven that there exists a causality relationship from negative shocks in the short-term external debt stock to positive and negative shocks in the exchange rate. Another result demonstrated a causality relationship between positive shocks in the exchange rate to negative shocks in the long-term debt stock. In addition, it was found that negative shocks in net capital investment were the cause of negative shocks in the exchange rate, while it was determined that there was a causality relationship from positive shocks in the net reserves to positive shocks in the exchange rate. In conclusion, the asymmetric causality relationship from positive shocks in CDS to positive shocks in exchange rates was detected.

Impact of coal rents, transportation, electricity consumption, and economic globalization on ecological footprint in the USA.

Over the last three decades, the world has been facing the phenomenon of the ecological deficit as the ecological footprint is continuously rising due to the persistent decline of the per-capita bio-capacity. Moreover, there is a substantial increase in globalization and electricity consumption for the same period, and transportation is contributing to economic prosperity at the cost of environmental sustainability. Understanding the determinants of ecological footprint is thus critical for suggesting appropriate policies for environmental sustainability. As a result, this study analyzes the impacts of economic globalization, transportation, coal rents, and electricity consumption in ecological footprint in the context of the USA over the period 1995 to 2018. The data have been extracted from “Global Footprint Network,” “Swiss Economic Institute,” and “World Development Indicators.” The current study has also applied the flexible Fourier form nonlinear unit root test to examine the stationarity among variables. For the empirical estimation, a novel technique, the “quantile auto-regressive distributive lag model,” is applied in the study to deal with the nonlinear associations of the variables and to evaluate the long-term stability of variables across quantiles. The study’s findings indicate that coal rents, transportation, and globalization significantly and positively contribute to the deterioration of ecological footprints at different quantile ranges in the short and long run. Electricity consumption is found to have a positive and significant impact at lower quantile ranges in the long run but not have a significant impact in the short run. The study suggested that lowering the dependence of the transport sector on fossil fuels, more use of hydroelectricity, and stringent strategies to curb coal consumption would be helpful to reduce the positive influence of these variables on ecological footprints in the USA.Graphical abstract

Ecological Sustainability in Emerging Market Economies: Linear and Nonlinear Unit Root Analysis

Üretimde kullanılan güç (enerji) mekanizmasındaki radikal değişim ile sanayi kapitalizmine geçişin kapısı aralanmıştır. 18. yüzyıla kadar insan ve hayvan gücü temelinde gerçekleştirilen üretim, buharlı makinelerin fabrika sistemine entegre edilmesiyle doğanın diğer güçlerinden de yararlanma imkânını beraberinde getirmiştir. 19. yy’ın son çeyreğine gelindiğinde güç kaynağı olarak kömür, petrol ve doğalgaz gibi yüksek karbon içerikli fosil yakıt kullanımına geçilmiştir. Günümüze değin üretim sürecine koşut olarak fosil yakıt kullanım miktarındaki yoğunluk karbondioksit (CO2) salınımını önemli ölçüde yükseltmiş, bu durum sıcaklığın atmosferde tutulmasına yardımcı olan sera gazı konsantrasyonunu arttırmıştır. Atmosferik sera gazı konsantrasyonundaki ilerleyiş yer kürenin normalin üzerinde ısınmasının koşullarını oluşturmuş ve iklim değişikliğine davetiye çıkartmıştır. İnsanlık son yarım yüzyılda iklim değişikliğinin neden olduğu pek çok doğal felaketle karşılaşmıştır. Genel olarak ekolojik krizler özel olarak iklim değişikliğinin arka planında kuşkusuz kar odaklı üretim biçiminin önemli bir payı söz konusudur. Kapitalist üretim biçimindeki plansızlık doğal çevre üzerinde negatif dışsallık yaratmış, küresel ısınma ve iklim değişikliği gibi yakıcı ekolojik sorunların ortaya çıkmasına zemin oluşturmuştur. Çalışmanın amacı, kapitalist üretim ilişkisinin varlığı altında sürdürülebilirlik anlayışının sınırlarını tartışmaya açmaktır. Bu çerçevede 1980-2019 yılları arasında 10 yükselen piyasa ekonomisindeki (Brezilya, Çekya, Macaristan, Malezya, Meksika, Polonya, Güney Afrika, Tayvan, Tayland ve Türkiye) ekolojik sürdürülebilirlik düzeyi doğrusal ve doğrusal olmayan birim kök test yöntemleriyle araştırılmıştır. Nitekim daha güvenilir sonuçlar vereceği düşünülen Kruse (2011) ve Hu ve Chen (2016) doğrusal olmayan birim kök testi sonuçlarına göre Çekya ve Tayland dışındaki diğer sekiz yükselen piyasa ekonomisinde ekolojik sürdürülebilirliğin sağlanmadığı tespit edilmiştir. Dolayısıyla ülke ve zaman boyutu dikkate alındığında kapitalizm ile sürdürülebilirlik anlayışı arasında paradoksal bir ilişkinin varlığı ortaya konmuştur.

Doğrusal Olmayan Birim Kök Testleri Kullanılarak 21 OECD Ülkesinde Sağlık Harcamaları Yakınsamasının Test Edilmesi

Objective: The purpose of this study is to analyze the stochastic time series behaviour of health expenditure in the 21 OECD countries between 1975 and 2019 using a variety of state-of-the-art (cutting-edge) unit root tests.
 Methods: In this study, the linear ADF unit root test and eight relevant nonlinear unit root tests are used to empirically estimate whether the 21 OECD countries’ health expenditure data show convergence.
 Results: The empirical findings are in support the stationarity of health expenditure in 20 of the 21 OECD countries.
 Conclusions: Health convergence hypothesis is confirmed in most OECD countries, indicating that health expenditure shocks have solely temporary effects on country-level health expenditure. The empirical study provides significant policy implications. The empirical part of the study indicated that policy measures chosen by the policymakers cannot be made without considering possible nonlinearities in health expenditure data. More investment in the policy proposals stated in the conclusion section in the low regime years, as well as the continuation of current ones in the high regime periods, have been determined to offer appropriate conditions for health spending convergence. Furthermore, it has been determined that structural changes outside of the regime have resulted in a change in health expenditure convergence in countries such as Japan and South Korea. It is essential to invest in these countries while taking into account the periods of structural change.

The nonlinearity and nonlinear convergence of CO2 emissions: Evidence from top 20 highest emitting countries.

Carbon dioxide (CO2) is the most prevalent greenhouse gas that triggers climate change, which in turn leads to catastrophic effects on trade, business, human health, and other areas. Understanding the characteristics and tendency of CO2 emissions will improve policy making and mitigation strategies. Understanding the linearity or nonlinearity and convergence or divergence of CO2 emissions is essential for selecting appropriate modeling techniques and for designing reliable policies. Therefore, this paper investigates the nonlinearity and nonlinear convergence of CO2 emissions among the world's top 20 highest emitting countries, which account for 80% of the world's total emissions. To check the nonlinearity of CO2 emissions, the McLeod-Li nonlinearity test, the Terasvirta nonlinearity test, and the Brock-Dechert-Scheinkman-LeBaron nonlinearity test are employed. The convergence or divergence of CO2 emissions is checked by using the Kilic nonlinear unit root test, the Hu and Chen nonlinear unit root test, and the Park and Shintani nonlinear unit root test. The findings revealed that the CO2 emissions process in all the 20 countries is nonlinear; 17 countries exhibit convergence in CO2 emissions while the other 3 countries diverged from 1960 to 2018. Based on the results, the nonlinear nature of CO2 emissions requires special attention from scholars when selecting estimation techniques for CO2 emissions. For countries with convergence, emissions trends can be used to forecast future values of CO2 emissions. Moreover, strong policy actions are required to achieve convergence in the countries with divergence.

Re-Investigating the degree of persistence of U.S. economic policy uncertainty using the Fourier non-linear quantile unit root test

ABSTRACT This research tests the mean reversion properties of the U.S. EPU (economic policy uncertainty) index and its 11 sub-categories using the Fourier non-linear quantile unit root test over the period 1985M1-2020M12. The results indicate the following. (1) The U.S. EPU index responds asymmetrically to shocks, in which positive shocks are more long-lasting than negative shocks. (2) Monetary, fiscal, and trade policies and also national security and regulation series behave like unit root processes in all quartiles, whereas by contrast financial regulation and sovereign debt exhibit stationary behaviour over all quantiles. (3) Government spending, health care, national security, and entitlement programmes present stationary processes in low/high quantiles.

Analyzing Persistence Degree of Shocks to Co2 Emission of U.S. States: Application of Linear and Nonlinear Fourier Quantile Unit Root Tests

Analyzing Persistence Degree of Shocks to Co2 Emission of U.S. States: Application of Linear and Nonlinear Fourier Quantile Unit Root Tests

Popularity of Unit Root Tests: A Review

This study undertakes a systematic literature review on recent developments in unit root tests. We highlight popular unit root tests developed since 2010 based on the number of citations. We observe from the literature that the most popular unit root test is the Narayan and Popp unit root test and the least popular test is the quantile nonlinear unit root test, mainly because it was developed only recently. The use and popularity of the recently developed unit root tests can be judged only after 5 to 10 years.

Linearity Test with Unit Root in TV-ESTAR Framework

Firstly, this paper proposes F statistic whose limit distribution and critical values are also provided to test nonlinearity and structure change with unit root in TV-ESTAR model framework. The results show that the distribution of F statistic is nonstandard. Then, this paper analyzes finite sample characteristics of F statistics through the Monte Carlo simulation and founds F statistics has better power than kss statistics in Kapetanios et al to test nonlinear unit root with structure change.

Avrupa Birliği Ülkelerinde Cari İşlemler Hesabinin Sürdürülebilirlik Analizi: FADF ve FKSS Birim Kök Testleri

This paper examines the sustainability of the current account in 27 European Union countries over the period 2005Q1-2020Q3. First, series which is considered as the ratio of the current account to gross domestic product, was applied to the traditional unit root test ADF and the nonlinear unit root test KSS. According to the ADF test, the current account was stationary in 9 countries and according to the KSS test, current account was stationary in 5 countries. Later, nonlinear FADF and FKSS unit root tests based on Fourier were applied. According to the unit root tests results, series were found stationary in 10 countries for FADF and 3 countries for FKSS. ADF and KSS test results are valid for countries whose trigonometric terms are insignificant. According to these results, it can be said that Fourier terms should be taken into account in unit root tests on the current account.

High Persistence and Nonlinear Behavior in Financial Variables: A More Powerful Unit Root Testing in the ESTAR Framework

In this study, we consider the hybrid nonlinear features of the Exponential Smooth Transition Autoregressive-Fractional Fourier Function (ESTAR-FFF) form unit root test. As is well known, when developing a unit root test for the ESTAR model, linearization is performed by the Taylor approximation, and thereby the nuisance parameter problem is eliminated. Although this linearization process leads to a certain amount of information loss in the unit root testing equation, it also causes the resulting test to be more accessible and consistent. The method that we propose here contributes to the literature in three important ways. First, it reduces the information loss that arises due to the Taylor expansion. Second, the research to date has tended to misinterpret the Fourier function used with the Kapetanios, Shin and Snell (2003) (KSS) unit root test and considers it to capture multiple smooth transition structural breaks. The simulation studies that we carry out in this study clearly show that the Fourier function only restores the Taylor residuals of the ESTAR type function rather than accounting forthe smooth structural break. Third, the new nonlinear unit root test developed in this paper has very strong power in the highly persistent near unit root environment that the financial data exhibit. The application of the Kapetanios Shin Snell- Fractional Fourier (KSS-FF) test to ex-post real interest rates data of 11 OECD countries for country-specific sample periods shows that the new test catches nonlinear stationarity in many more countries than the KSS test itself.

An Asymmetric Investigation of Remittance and Trade Openness Impact on Inequality: Evidence From Selected South Asian Countries.

This study’s motivation is to explore the relationship pattern between remittance, trade openness, and inequality of selected south Asian countries for the 1976–2018 period. The study performed non-linear tests, including unit root tests, non-linearity applying ordinary least squares (OLS) and BDS tests, non-linear autoregressive distributed lagged (NARDL) tests, and asymmetry causality tests to assess their association. Study findings with non-linear unit root tests suggest that the research variables follow the non-linear process of becoming stationary from non-stationary. The non-linear OLS and BDS test results confirm the existence of non-linearity among research variables, implying rejection of the null hypothesis of “no non-linearity.” Furthermore, the results of the Wald test in NARDL confirm the availability of asymmetric links among variables. Besides this, the results of NARDL confirm the long-run asymmetric relationship between remittances, trade openness, and inequality in all sample nations. Findings suggest that both positive and negative shocks in remittances and trade openness is critical to either instituting or vexing the present state of inequality in the economy in the long term. In the directional relationship with asymmetry causality, the study shows that the feedback hypothesis holds to explain the asymmetric causal effects that are positive shocks in remittances and trade openness toward inequality.

Auxiliary model-based multi-innovation PSO identification for Wiener–Hammerstein systems with scarce measurements

In many actual systems, it is often difficult to obtain complete input and output data. Thus, the problem of scarce measurements usually appears in the identification of these systems. This article investigates the parameter estimation of Wiener–Hammerstein systems with scarce measurements. A Wiener–Hammerstein system comprises an input linear unit, a nonlinear unit, and an output linear unit. The nonlinear unit in this paper is described by the saturation and dead-zone characteristics respectively. To solve the incomplete data problem caused by scarce measurements, the auxiliary model is applied. Then the auxiliary model-based improved particle swarm optimization (PSO) algorithm is derived. Furthermore, the multi-innovation technology is introduced to improve the convergence speed and estimation accuracy, and the auxiliary model-based multi-innovation improved PSO is proposed. Finally, the simulations of two numerical examples and the application of the turntable servo system indicate that the proposed multi-innovation method is applicable to Wiener–Hammerstein models with scarce measurements, the estimation accuracy and convergence speed are greatly improved.

FourierBirim Kök Testleri Temelinde Ekolojik Açık, Ekonomik Büyüme ve Özel Sektör Kredilerinin Analizi: Türkiye Örneği

This study aims to investigate the sustainability of three different variables – ecological deficit, economic growth, and private sector credits – that have an important role for the examination of the infrastructure of economic processes. In this direction, the sustainability of those variables in the Turkish economy has been analyzed through linear – ADF and KPSS – and non-linear – Fourier ADF, Fourier KPSS, Fourier GLS – unit root tests for three different periods covering1987-2007 (pre-global crisis), 2008-2017 (global crisis), and 1987-2017 (whole period). The empirical findings show that the series of ecological deficit and economic growth are stationary at the level and the private sector credit is stationary at first difference within the framework of traditional/linear unit root tests. In addition, the test statistics of the series in sub-periods provides that the series are to a large extent stationary at the level in the presence of the implication ofFourier-type non-linear unit root tests, whereas the test statistics of whole periods emphasize that economic growth and private sector credits tend to return to the average at the first difference, contrary to the ecological deficit in which it is stationary at the level.

Dynamics and wave propagation in nonlinear piezoelectric metastructures

This paper reports dynamical effects in one-dimensional locally resonant piezoelectric metastructures leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to expand the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB-based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way toward fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.