A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries

Existing tests of the unit root hypothesis against the alternative hypothesis of exponential smooth transition autoregressive (ESTAR) nonlinearity implicitly assume symmetry under the alternative. This paper proposes a simple unit root test against the alternative of symmetric or asymmetric ESTAR nonlinearity. In the event that the unit root hypothesis is rejected, a simple test of symmetric versus asymmetric ESTAR nonlinearity is also proposed. The asymptotic distributions of the test statistics are straightforward to establish and finite-sample performance is studied with Monte Carlo simulations. An empirical application involving the real exchange rates of four Nordic countries against the U.S. dollar illustrates the usefulness of the new tests.     

Examining the evidence of purchasing power parity by recursive mean adjustment

This paper revisits the empirical evidence of purchasing power parity under the current float by recursive mean adjustment (RMA) proposed by So and Shin (1999). We first report superior power of the RMA-based unit root test in finite samples relative to the conventional augmented Dickey–Fuller (ADF) test via Monte Carlo experiments for 16 linear and nonlinear autoregressive data generating processes. We find that the more powerful RMA-based unit root test rejects the null hypothesis of a unit root for 16 out of 20 current float real exchange rates relative to the US dollar, while the ADF test rejects only 5 at the 10% significance level. We also find that the computationally simple RMA-based asymptotic confidence interval can provide useful information regarding the half-life of the real exchange rate.     

On the power of bootstrap tests for stationarity: a Monte Carlo comparison

This paper studies the behavior of recently proposed bootstrap tests for the null hypothesis of stationarity when the data are generated under the alternative hypothesis of a unit root. Using Monte Carlo experiments and empirical examples, it is shown that the power of these tests critically depends on the type of bootstrap employed. Specifically, while tests based on the stationary bootstrap have power functions that are increasing with respect to sample size, those based on the sieve bootstrap have non-monotonic power functions. We argue that this difference arises from the fact that the latter procedure does not impose the null hypothesis when generating the bootstrap samples while the former ensures that the bootstrap samples are stationary, conditional on the original data. Our results therefore suggest that while both forms of bootstrap are effective at providing improved distributional approximations under the null hypothesis, it is important to pay careful attention to the particular type of bootstrap being employed when attempting to distinguish between the unit root and stationarity hypotheses as the choice of bootstrap can have crucial implications for the power of the resulting tests.     

Quantile unit root test and the PPP in Africa

In this study, we apply the Quantile unit root test and revisit the Purchasing Power Parity (PPP) in 20 African countries using real effective exchange rates over the period 1971Q1 to 2012Q4. While traditional unit root tests fail to reject unit root hypothesis in most of the countries, results from Quantile unit root test reject unit root null hypothesis in Ghana, Mauritius, Niger, South Africa, and Togo, providing support for the PPP at least in these five countries. We further estimate the half-life based on Quantile autoregressive (QAR) model to be about 4.57–7.96 quarters (1–2 year).     

BAYESIAN ANALYSIS OF GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY AND STOCHASTIC VOLATILITY: MODELING LEVERAGE,JUMPS AND HEAVY‐TAILS FOR FINANCIAL TIME SERIES*

This paper develops a Bayesian model comparison of two broad major classes of varying volatility model, the generalized autoregressive conditional heteroskedasticity and stochastic volatility models, on financial time series. The leverage effect, jumps and heavy‐tailed errors are incorporated into the two models. For estimation, the efficient Markov chain Monte Carlo methods are developed and the model comparisons are examined based on the marginal likelihood. The empirical analyses are illustrated using the daily return data of US stock indices, individual securities and exchange rates of UK sterling and Japanese yen against the US dollar. The estimation results indicate that the stochastic volatility model with leverage and Student‐t errors yield the best performance among the competing models.     

ESTIMATING MULTICOUNTRY VAR MODELS*

This article presents a method to estimate the coefficients, to test specification hypotheses, and to conduct policy exercises in multicountry Vector Autoregressive (VAR) models with cross‐unit interdependencies, unit‐specific dynamics, and time variations in the coefficients. The framework of analysis is Bayesian: A prior flexibly reduces the dimensionality of the model and puts structure on the time variations, Markov chain Monte Carlo (MCMC) methods are used to obtain posterior distributions, and marginal likelihoods to check the fit of various specifications. Impulse responses and conditional forecasts are obtained with the output of an MCMC routine. The transmission of certain shocks across countries is analyzed.     

A Unit Root Test With Multiple Trend Breaks: A Theory and an Application to US and Japanese Macroeconomic Time-Series

This study develops a unit root test that allows for an alternative hypothesis with multiple trend breaks of unknown dates, and proves that tests with fewer than the true number of breaks fail, incorrectly, to reject the null asymptotically. The asymptotic distributions of appropriate t -statistics under the unit root null are determined. In empirical applications, this test rejects the null for the Nelson–Plosser velocity of the USA, the postwar quarterly real output series of the USA and Japan, and Japanese real consumption, but not for real consumption of the USA. The finite-sample properties are examined with Monte Carlo experiments.
JEL Classification Numbers: C32, C12, E32.     

Testing for unit roots with income distribution data

In this paper I test the unit root hypothesis for US log GNP using the information available in income distribution data. The percentile data of an income distribution are shown to follow the same autoregressive pattern as does mean income. Under the null hypothesis of a unit root log GNP is cointegrated with the percentile data. A sequence of augmented HEGY-Tests, however, presents strong evidence against the unit root hypothesis for the distribution data and hence for log GNP. Using a full information estimation procedure for the percentiles under the alternative yields an estimate of the autoregressive coefficient which is in principle testable by an approximate Dickey-Hasza-Fuller test. The appropriate critical values are found by bootstrap methods. Again, inference is clearly unfavorable for the unit root hypothesis.An earlier version of this paper was presented at the ESEM 1993 in Uppsala. I thank Prof. Jürgen Wolters, seminar participants at the Free University of Berlin and an anonymous referee of this journal for valuable comments. The usual disclaimer applies.     

What do we know about real exchange rate nonlinearities?

Nonlinear modeling of adjustments to purchasing power parity has recently gained much attention. However, a huge body of the empirical literature applies ESTAR models and neglects the existence of other competing nonlinear models. Among these, the Markov Switching AR model has a strong substantiation in international finance. Our contribution to the literature is fivefold: First, ESTAR and MSAR models from a unit root perspective are compared. To this end, a new unit root test against MSAR is proposed as the second contribution. Thirdly, the case of misspecified alternatives in a Monte Carlo setup with real world parameter constellations is studied. The ESTAR unit root test is not indicative, while the MSAR unit test is robust. Fourthly, the case of correctly specified alternatives is considered and low power of the ESTAR but not for the MSAR unit root test is observed. Fifthly, an empirical application to real exchange rates suggests that they may indeed be explained by Markov Switching dynamics rather than ESTAR.     

Are Flexible Exchange Rate Regimes more Volatile? Panel GARCH Evidence for the G7 and Latin America

This paper investigates empirically the relationship between exchange rate (ER) regimes and volatility of real exchange rate depreciation (RERD), comparing the G7 and 17 Latin American (LA17) countries, during 1970–2010. We estimate a panel autoregressive model with generalized autoregressive conditional heteroskedasticity (GARCH) errors and regime‐specific effects on both the conditional mean and conditional variance. For the G7, we find that, relative to the fixed ER regime, only the freely floating regime shows higher RERD volatility; under the managed floating regime the RERD is equally volatile and under the crawling peg it is actually less volatile. Instead, in the case of the LA17, more flexible ER regimes are associated with more volatile RERD rates, with higher volatility under the managed floating regime than under the crawling peg and with extremely high volatility under the “freely falling” ER regime.     

Markov regime-switching Beta-t-EGARCH

We suggest a Markov regime-switching (MS) Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model for U.S. stock returns. We compare the in-sample statistical performance of the MS Beta-t-EGARCH model with that of the single-regime Beta-t-EGARCH model. For both models we consider leverage effects for conditional volatility. We use data from the Standard Poor’s 500 (S&P 500) index and also a random sample that includes 50 components of the S&P 500. We study the outlier-discounting property of the single-regime Beta-t-EGARCH and MS Beta-t-EGARCH models. For the S&P 500, we show that for the MS Beta-t-EGARCH model extreme observations are discounted more for the low-volatility regime than for the high-volatility regime. The conditions of consistency and asymptotic normality of the maximum likelihood estimator are satisfied for both the single-regime and MS Beta-t-EGARCH models. All likelihood-based in-sample statistical performance metrics suggest that the MS Beta-t-EGARCH model is superior to the single-regime Beta-t-EGARCH model. We present an application to the out-of-sample density forecast performance of both models. The results show that the density forecast performance of the MS Beta-t-EGARCH model is superior to that of the single-regime Beta-t-EGARCH model.     

Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process

The paper considers nonlinear logistic smooth transition autoregressive (LSTAR) process and aims to detect the unit root under the null hypothesis of a random walk process against the alternative of a stationary LSTAR process and to estimate the parameters of the process in Bayesian framework using MCMC. The simulation study is carried out for investigating the performance of the Bayes estimators for parameters and Bayesian unit root test and it has been observed that the estimates of parameters of the LSTAR process are close to the true parameter values. It has been observed that the Bayesian unit root test performs well and the power of the test is high even for the boundary cases having root close to unity, at least when the sample size is large. Since the LSTAR models are widely applied for real exchange rate modeling, the theoretical results are illustrated empirically for the real exchange rates of ten OCED countries.

     

Pricing and hedging options with GARCH-stable proxy volatilities

This article considers modelling nonnormality in return with stable Paretian (SP) innovations in generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) volatility dynamics. The forecasted volatilities from these dynamics have been used as a proxy to the volatility parameter of the Black–Scholes (BS) model. The performance of these proxy-BS models has been compared with the performance of the BS model of constant volatility. Using a cross section of S&P500 options data, we find that EGARCH volatility forecast with SP innovations is an excellent proxy to BS constant volatility in terms of pricing. We find improved performance of hedging for an illustrative option portfolio. We also find better performance of spectral risk measure (SRM) than value-at-risk (VaR) and expected shortfall (ES) in estimating option portfolio risk in case of the proxy-BS models under SP innovations.

Abbreviation: generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH)     

Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution To the Purchasing Power Parity Puzzles

We fit nonlinearly mean-reverting models to real dollar exchange rates over the post-Bretton Woods period, consistent with a theoretical literature on transactions costs in international arbitrage. The half lives of real exchange rate shocks, calculated through Monte Carlo integration, imply faster adjustment speeds than hitherto recorded. Monte Carlo simulations reconcile our results with the large empirical literature on unit roots in real exchange rates by showing that when the real exchange rate is nonlinearly mean reverting, standard univariate unit root tests have low power, while multivariate tests have much higher power to reject a false null hypothesis.     

Testing for nonlinear panel unit roots under cross-sectional dependency — With an application to the PPP hypothesis

In this paper we propose a number of nonlinear panel unit root tests that are robust to cross-sectional dependency. These tests may be used to test the null hypothesis of non-stationarity against the alternative that some or all of the time series in the system of equations follow a stationary exponential smooth transition autoregressive (ESTAR) process. In contrast to previous research we relax the assumption that the cross-correlation structure is driven by a common-factor and consider an endogenous correlation structure. Based on the size and power results from the Monte Carlo simulations we recommend using the Wald version of our cross-sectional dependent robust nonlinear panel unit root (CDR-NPU) method.Finally, in an empirical application we demonstrate that our more powerful nonlinear method, in contrast to previous methods, can provide support for PPP even in smaller samples. In consistency with the univariate tests in Bahmani-Oskooee et al. (2008) our CDR-NPU tests support the theory that less industrialized economies exhibit stronger and more distinct nonlinear adjustment patterns towards PPP.     

House price dynamics,conditional higher-order moments,and density forecasts

Most studies on housing price dynamics are only concerned with the conditional mean and variance, but overlook other higher-order conditional moments and the structural change characteristics inherent in housing prices. In order to take into account these two important issues, this study utilizes the generalized Markov switching GARCH model to explore house price dynamics and conditional distribution for US market over 1975Q1–2007Q4. The housing return follows two distinct dynamics: the bust regime and the boom regime. The volatility pattern is different in the bust and boom regimes. In addition, the conditional densities derived by the regime-switching model change dramatically over time and are significantly different from normal distribution. More importantly, the regime-switching model can detect in advance a weak US housing market such as the one that occurred in the middle of 2007. The in-sample fitting ability of regime-switching model, which incorporates higher-order moments, has significant improvements compared to the single-regime AR and AR-GARCH models. For the out-of-sample Value-at-Risk forecasting performance, the ability of regime-switching AR-GARCH model to forecast one-step-ahead density is better compared to the single-regime AR-GARCH model.     

Re-examining the real interest rate parity hypothesis (RIPH) using panel unit root tests with asymmetry and cross-section dependence

This paper investigates the validity of the real interest rate parity hypothesis (RIPH) using a panel unit root approach. For this purpose, first we estimate the possible nonlinear data-generating processes of the real interest rate differential series and using these estimates determine which panel unit root test is better for analyzing the RIPH. To this end, smooth transition autoregressive and threshold autoregressive (TAR) models are estimated for two different panels of countries: G7 and post-Soviet transition economies. The results show that the data displays both strong asymmetry and high transition speed. Therefore, secondly, we propose a new panel unit root test where the alternative is stationary with asymmetric TAR adjustment, and provide their empirical power properties. Finally, we demonstrate that our newly proposed test is able to provide conclusive evidence in favor of the RIPH in contrast to the other panel unit root tests considered.     

Testing for a unit root in the presence of stochastic volatility and leverage effect

Previous studies have shown that the stationary and nonstationary time-varying volatilities have different implications on the unit root test. In this paper, we provide a Bayesian unit root test for an AR(1) model with stochastic volatility and leverage effect. Monte Carlo simulations show that the proposed Bayesian unit root test statistic achieves good finite sample properties and is robust to the stationarity of stochastic volatility.     

A nonlinear approach to testing the unit root null hypothesis: an application to international health expenditures

In this article, we examine the unit root null hypothesis for per capita total Health Expenditures (HEs), per capita private HEs and per capita public HEs for 29 Organization for Economic Co-operation and Development (OECD) countries. The novelty of our work is that we use a new nonlinear unit root test that allows for one structural break in the data series. We find that for around 45% of the countries, we are able to reject the unit root hypothesis for each of the three HE series. Moreover, using Monte Carlo simulations, we show that our proposed unit root model has better size and power properties than the widely used Augmented Dickey–Fuller (ADF) and Lagrange Multiplier (LM) type tests.     

Asymmetric effect of advertising on the Chinese stock market

In this paper, we investigate whether investor attention to advertising has an asymmetric effect on Chinese stock returns by using a multivariate Markov switching model with time-varying regime transition probabilities. Using the Chinese stock market as a setting, we obtain lagged conditional volatility from generalized autoregressive conditional heteroskedasticity (GARCH) for modelling the time-varying transition probabilities of the regime-switching process to capture changes in the market regime. Our evidence documents that the high advertising portfolio does earn higher abnormal return than the low advertising portfolio in low-volatility periods. In high-volatility periods, however, the abnormal return is insignificant when the firm increases advertising spending. Our results support the behavioural model argument that in high-volatility period, advertising information diffuses slowly due to cognitive dissonance. Thus, the effect of advertising on stock returns is asymmetric, and it shows statistical significance in low-volatility periods.