Time series test of nonlinear convergence and transitional dynamics

This paper revisits the income convergence hypothesis by using the nonlinear unit root test of Kapetanios et al. [Kapetanios, G., Shin, Y. and A. Snell, 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359–379.]. Out of the 12 OECD income gaps in which nonlinearity has been detected, two cases of long-run converging and four cases of catching up are found.     

THE REAL INTEREST RATE DIFFERENTIAL: INTERNATIONAL EVIDENCE BASED ON NON-LINEAR UNIT ROOT TESTS

This paper aims at testing international parity conditions by using non-linear unit root tests advocated by Kapetanios et al . (2003, KSS). Results from the KSS tests based on 17 countries (G7 and 10 Asian countries) overwhelmingly show that the adjustment of real interest rates towards real interest rate parity (RIP) follows a non-linear process except for the Taiwan, Hong Kong and Philippines relationships with both the USA and Japan. Overall, the empirical results are in favour of RIP using the USA and Japan as the centre countries but only if non-linearities are accounted for in the data-generating process. Our findings confirm that interest rate differentials, like the real exchange rates reported in recent literature, display a non-linear mean reversion process.     

Further evidence on the PPP analysis of the Australian dollar: Non-linearities, fractional integration and structural changes

The aim of this paper is to analyse the empirical fulfilment of the Purchasing Power Parity (PPP) theory for the Australian dollar. In order to do so we have applied recently developed unit root tests that account for asymmetric adjustment towards the equilibrium [Kapetanios, G., Shin, Y., Snell, A., 2003. “Testing for a unit root in the nonlinear STAR framework”, Journal of Econometrics, 112, 359–379] and fractional integration in the context of structural changes [Robinson, P.M., 1994. “Efficient tests of nonstationary hypotheses”, Journal of the American Statistical Association, 89, 1420–1437; Gil-Alana, L.A., 2008. “Fractional integration and structural breaks at unknown periods of time”, Journal of Time Series Analysis, 29, 163–185]. Although our results point to the rejection of the PPP hypothesis, we find that the degree of persistence of shocks to the Australian dollar decreases after the 1985 currency crisis.     

A Time-Series Investigation of the U.S. Real Health Expenditure: Evidence from Nonlinear Unit Root Tests

This paper contributes to the literature on health expenditure studies by applying the non-linear unit root tests formulated recently by Kapetanios et al. (Journal of Econometrics 112(2):359?C79, 2003) to empirically test whether the U.S. real health expenditure time-series are non-stationary or non-linear and globally stationary during a relatively long period from 1965 to 2009. For comparison purposes, it also reports the results of a battery of traditional linear unit root tests and the Lee and Strazicich??s minimum LM unit root (Review of Economics and Statistics 85(4):1082?C1089, 2003) test for structural breaks. The empirical findings of the paper show that in the United States during the period under investigation, the real health expenditure time-series are non-stationary in levels. Policy implications of the empirical findings are discussed.     

Do real interest rates converge across Latin american countries?

In this study, we apply the Sequential Panel Selection Method (SPSM), proposed by Chortareas and Kapetanios (Journal of Banking and Finance 33:390–404, 2009), to investigate and assess the non-stationary properties of the real interest rate parity (RIRP) for fourteen Latin American countries. Utilizing the SPSM, we can classify the entire panel into a group of stationary series and a group of non-stationary series. We clearly identify how many and which series in the panel are stationary processes and provide robust evidence that clearly indicate RIRP holds true for ten countries. Our findings note that these countries’ real interest rate convergence is a mean reversion toward RIRP equilibrium values in a non-linear way. Our results have important policy implications for these Latin American countries under study.     

Revisiting purchasing power parity for African countries: with nonlinear panel unit-root tests

This study applies Panel Seemingly Unrelated Regressions (SUR) Kapetanios et al. (Kapetanios–Shin–Snell (KSS), SURKSS) tests, proposed by Wu and Lee (2009), to investigate the properties of long-run Purchasing Power Parity (PPP) in 15 African countries. The empirical results from the univariate unit root and panel based unit root tests indicate that PPP does not hold for these 15 countries under study. However, Panel SURKSS tests indicate that PPP is valid for four of these 15 countries. These results have important policy implications for these 15 African countries under study.     

Sustainability of external debt: further evidence from non-linear framework

This study investigates sustainability of external debt under a two-step non-linear framework. The first step uses a general linearity test proposed by Harvey and Leybourne (2007 Harvey, David I. and Leybourne, Stephen J. 2007. Testing for time series linearity. Econometric Journal, 10: 149–165. [Crossref], [Web of Science ®] , [Google Scholar]) to determine the linearity property of external debt. The second step applies a non-linear ADF unit root test proposed by Kapetanios, Shin, and Snell (2003 Kapetanios, G., Y. Shin, and A. Snell. 2003. Testing for a unit root in the nonlinear STAR. Journal of Econometrics 112: 359–79.  [Google Scholar]) on the non-liner processes and the linear ADF test on the linear processes to examine the sustainability of external debt. The analysis of 36 debt and 55 current account ratios identifies strong evidence of non-linearity and sustainability. The results indicate superior performance of the non-linear unit root test over the ADF test in determining the stationary property of the data.     

Do real interest rates converge across East Asian countries based on China?

This study applies the sequential panel selection method (SPSM), proposed by Chortareas and Kapetanios (2009), to assess the non-stationary properties of the real interest rates relative to China for ten East Asian countries. SPSM can classify the whole panel into a group of stationary series and a group of non-stationary series. We clearly identify how many and which series in the panel are stationary processes and provide robust evidence to indicate that RIRP holds true for five countries. It implies that the choices and effectiveness of the monetary and fiscal policies in the East Asian economies will be highly influenced by external factors originating from China. Also, our findings point out that real interest rate convergence relative to China is mean reverting toward RIRP equilibrium values in a non-linear way.     

Extreme observations and non-normality in ARCH and GARCH

Most studies employing ARCH and GARCH models document the existence of severe excess kurtosis in the estimated residuals. This non-normality may be due to model misspecifications, structural changes, or outliers. We conduct simulation experiments to examine the impact of extreme observations on the estimated parameters and residuals in the ARCH models. Then, we propose an iterative algorithm to detect and correct for the non-normality generated by extreme observations and additive outliers. Results for the simulated data, US equity returns and $/£ exchange rates are presented. Correcting outliers dramatically reduces the non-normality and bias in the estimated coefficients for small samples.     

Further evidence regarding nonlinear trend reversion of real GDP and the CPI

This paper examines whether the CPI and real GDP for the US exhibit nonlinear reversion to trend as recently concluded by Beechey and Österholm [Beechey, M. and Österholm, P., 2008. Revisiting the uncertain unit root in GDP and CPI: testing for nonlinear trend reversion. Economics Letters 100, 221-223]. The wild bootstrap is used to correct for non-normality and heteroscedasticity in a nonlinear unit root test. The use of ‘wild bootstrapped’ critical values affects test conclusions in some cases. Results also are sensitive to the sample period examined.     

Are house prices in South Africa really nonstationary? Evidence from SPSM-based panel KSS test with a Fourier function

This study applies the sequential panel selection method (SPSM) to investigate the time-series properties of provincial house prices for entire, large, medium and small middle-segments of South Africa. Quarterly time-series data were collected from nine provinces in South Africa for different house-size categories over the period of 1978.Q1 to 2012.Q4. Whereas other panel-based unit-root tests are joint tests of a unit root for all members of a panel and are incapable of determining the mix of integrated of order zero (I(0)) series and integrated of order one (I(1)) series in a panel setting, the SPSM proposed by Chortareas and Kapetanios (2009) can clearly identify how many and which series in the panel are stationary processes by classifying a whole panel into a group of stationary and nonstationary series. The empirical results from several panel-based, as well as standard pure time-series, unit-root tests, indicate that house prices for the nine provinces studied here are either stationary or nonstationary. However, results from the SPSM using the panel version of the Kapetanios et al. (KSS, 2003) test with a Fourier function unequivocally indicate that house prices are stationary for the nine provinces under study. Our test results have important economic and policy implications for South Africa.     

Bootstrap LM tests for higher-order spatial effects in spatial linear regression models

This paper first extends the methodology of Yang (J Econom 185:33–59, 2015) to allow for non-normality and/or unknown heteroskedasticity in obtaining asymptotically refined critical values for the LM-type tests through bootstrap. Bootstrap refinements in critical values require the LM test statistics to be asymptotically pivotal under the null hypothesis, and for this we provide a set of general methods for constructing LM and robust LM tests. We then give detailed treatments for two general higher-order spatial linear regression models: namely the \(\mathtt{SARAR}(p,q)\) model and the \(\mathtt{MESS}(p,q)\) model, by providing a complete set of non-normality robust LM and bootstrap LM tests for higher-order spatial effects, and a complete set of LM and bootstrap LM tests robust against both unknown heteroskedasticity and non-normality. Monte Carlo experiments are run, and results show an excellent performance of the bootstrap LM-type tests.     

A new unit root test based on F-statistic in ESTAR framework

This article proposes a new F-type unit test in the exponential smooth transition autoregressive framework. We derive the asymptotic nonstandard distribution of the proposed test and explore its finite sample properties; simulation results show our test has greater power than the t_kss test proposed by Kapetanios et al.(2003). Finally, an application on the real exchange rates further underpins its superiority.     

On the joint Fourier–ESTAR testing of PPP

The purchasing power parity (PPP) is the hypothesis that the real exchange rate series are stationary. This study briefly reviews and applies six competing unit root test procedures to test PPP. Reflecting the existing literature, the results are mixed. The Kiliç test is the most favourable while the Kapetanios, Shin, and Snell (KSS) test is the least favourable to PPP and the standard ADF test lies in between. The same conclusion applies to the Fourier extensions of those three tests. The results support a recently suggested F-test for the significance of Fourier terms in unit root test equations.     

The Effects of Risk,Inflation and Dividend Yield on Common Stock Returns: The case of Korea

This study examines whether market equilibrium models of capital asset prices have any empirical validity in the Korean stock market, which is thin and relatively under-developed. In any study of the Korean stock market, the impurity of its ex post stock price and the attendant presumption of suspected non-normality of the stock return distribution cannot be ignored. This study finds that the Capital Asset Pricing Model (CAPM) has some explanatory power in the Korean stock market. In particular when data are segmented by time periods, the results tend to validate the general premises of the CAPM for the most recent period, i.e., between 1984 and 1987. [313]     

CO2 emissions converge in the 50 U.S. states — Sequential panel selection method

This study applies the sequential panel selection method (SPSM) procedure proposed by Chortareas and Kapetanios (2009) to investigate the time-series properties of CO₂ emissions for 50 U.S. states during the 1990 to 2010 period. SPSM classifies the whole panel into a group of stationary series and a group of non-stationary series. In doing so, we could clearly identify how many and which series in the panel are stationary processes. Empirical results from the SPSM using the panel KSS unit root test (Ucar and Omay, 2009) with a Fourier function, indicate that CO₂ emissions only converge in 12 out of the 50 U.S. states in our analysis.     

Estimating most productive scale size with stochastic data in data envelopment analysis

This article estimates most productive scale size in stochastic data envelopment analysis (DEA). Jahanshahloo and Khodabakhshi [Jahanshahloo, G.R. and Khodabakhshi, M., Using input–output orientation model for determining most productive scale size in DEA. Applied Mathematics and Computation 2003, 146(2–3), 849–855.] studied most productive scale size in classic data envelopment analysis. The classic data envelopment analysis requires that the values for all inputs and outputs be known exactly. However, this assumption may not be true, because data in many real applications cannot be precisely measured. One of the important methods to deal with imprecise data is considering stochastic data in DEA. Therefore, this research studies most productive scale size with considering stochastic data in DEA. To that end, input–output orientation model introduced in Jahanshahloo and Khodabakhshi [Jahanshahloo, G.R. and Khodabakhshi, M., Using input–output orientation model for determining most productive scale size in DEA. Applied Mathematics and Computation 2003, 146(2–3), 849–855.] is extended in stochastic data envelopment analysis. To solve the stochastic model, a deterministic equivalent is obtained. Although the deterministic equivalent is non-linear, it can be converted to a quadratic program. Furthermore, data of software companies is used to apply the proposed approach. Performance of software companies are evaluated based on their scale sizes in classic and stochastic data envelopment analysis.     

Testing for a unit root with covariates against nonlinear alternatives

This paper proposes a new procedure for testing the unit root null against stationary but nonlinear alternatives. This test can be viewed as a generalization of the one developed by Kapetanios et al. (2003) (the KSS test) by incorporating stationary covariates. The asymptotic distribution of the test is derived and the asymptotic critical values are tabulated. A set of Monte Carlo simulations show that our test generally achieves large power improvements over the KSS test. An illustrated empirical application indicates that our proposed test is able to unveil more evidence than the KSS test in favor of no unit root of real exchange rates in 15 Asian countries.     

Panel asymmetric nonlinear unit root test and PPP in Africa

This study revisits purchasing power parity (PPP) theory for 20 African countries using panel asymmetric nonlinear unit root test proposed by Emirmahmutoglu and Omay (2014), through the sequential panel selection method of Chortareas and Kapetanios (2009). While standard panel unit root tests fail to support the PPP, the empirical results from panel asymmetric nonlinear unit root test do support the PPP. However, additional tests reveal that support in all 20 African countries is mostly due to stationarity of the real effective exchange rates of Ghana and Rwanda where the adjustment process towards equilibrium is nonlinear and asymmetric.     

Nonparametric Sharpe Ratio

Sharpe ratio is a widely accepted tool for comparing the portfolio performance. In this paper we have proposed a nonparametric measure of the Sharpe rule. The statistical properties of this nonparametric measure and the standard Sharpe ratio are then developed under both normality and non-normality of observations. Further thebias corrected measures are given. An empirical application is also provided.