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.     

Does real U.K. GDP have a unit root? Evidence from a multi-century perspective

ABSTRACT

We employ linear and nonlinear unit-root tests to examine the stationarity of five multi-century historical U.K. series of real output compiled by the Bank of England. Three series span 1270 to 2016 and two series span 1700 to 2016. These datasets represent the longest span of historical real output data available and, thus, provide the environment for which unit-root tests are most powerful. A key feature of our test is its simultaneous allowance for two types of nonlinearity: time-dependent (structural breaks) nonlinearity and state-dependent (asymmetric adjustment) nonlinearity. The key finding of the test, contrary to what other more popular nonlinear unit-root tests suggest, provides strong evidence that the main structure of the five series is a stationary process characterized by an asymmetric nonlinear adjustment and a permanent break affecting both the intercept and the trend. A major policy implication of this finding is fiscal and/or monetary stabilization policies have only temporary effects on the output levels of the United Kingdom.     

Normality test for multivariate conditional heteroskedastic dynamic regression models

In this paper, we study the Jarque-Bera test for the normality of the innovations of multivariate GARCH models. It is shown that the test is distribution free and its limiting null distribution is a chi-square distribution.     

Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications

Testing for cointegration in the presence of nonlinear adjustments or structural breaks is important for examining the equilibrium relationship among economic variables. It is known that standard cointegration tests perform poorly when a cointegration relationship has nonlinear adjustments or structural breaks. However, it is not clear how some cointegration tests allowing for nonlinearity perform under other classes of nonlinear cointegration models. This paper investigates which cointegration tests help detect a cointegration relationship with nonlinear adjustments or structural breaks. Our Monte Carlo simulation results demonstrate that the cointegration test with threshold adjustment generally has better power performance under most cointegration relationships with nonlinearity. We also provide empirical applications to the money demand and term structure of the U.S. interest rates. The empirical results show that the test allowing for threshold adjustment provides strong evidence of the cointegration relationships of money demand and the term structure of interest rates.     

A panel data test for poverty traps

This article develops a threshold panel data nonlinearity test for poverty traps. The new testing strategy extends the work on nonlinearity tests for panel data by considering threshold nonlinearities in the fixed-effects components. Monte Carlo simulations are conducted to evaluate the finite-sample performance of these tests. The tests are applied to the relationship between Gross Domestic Product (GDP) per capita and capital stock per capita. Our application to a panel of countries for the period 1973 to 2007 uncovers the presence of two regimes determined by the level of capital stock per capita. The conclusions from our test also support the existence of a poverty trap determined by a capital stock per capita level at the 11% quantile of its pooled worldwide distribution.     

Does inflation cause gold market price changes? evidence on the G7 countries from the tests of nonparametric quantile causality in mean and variance

This article utilizes the newly proposed nonparametric causality-in-quantiles test to examine the predictability of mean and variance of changes in gold prices based on inflation for G7 countries. The causality-in-quantiles approach permits us to test for not only causality in mean but also causality in variance. We start our investigation by utilizing tests for nonlinearity. These tests identify nonlinearity, showing that the linear Granger causality tests are subject to misspecification error. Unlike tests of misspecified linear models, our nonparametric causality-in-quantiles tests find causality in mean and variance from inflation to gold market price changes between the 0.20 quantile and the 0.70 quantile, implying that very low- and high-price changes in gold markets are not related to inflation. These changes should be related to other sources, such as financial shocks and exchange market shocks. We find support that gold serves as a hedge against inflation, but only in the mid-quantile ranges, i.e. quantiles from 0.20 to 0.70. Our results show that gold does not serve as a hedge against inflation during periods when gold market price changes are very low or very high, which are respectively quiet and highly volatile periods.     

A note on spurious nonlinear regression

This paper explores the power of two tests for nonlinearity against spurious nonlinear regression. Results show that while the BDS test is susceptible to spuriousness, an approach introduced by Peña and Rodriguez [Peña, D. and Rodriguez, J., 2005, Detecting nonlinearity in time series by model selection criteria, International Journal of Forecasting 21, 731–748.] is powerful, regardless of sample size.     

A robust test for multivariate normality

The size of the Jarque-Bera test for multivariate normality can be severely distorted in small samples. An alternative test procedure, that turns out to have good size and power properties, is suggested.     

Alternative unit root testing strategies using the Fourier approximation

Two alternatives to  and  Fourier unit root testing strategy, which incorporates pretesting for nonlinearity, are considered. One is based on the union of rejection (UR) approach, and the other is a hybrid strategy that combines the UR approach with the use of extra information from nonlinearity pretesting. Simulation results show that the two proposed strategies, especially the hybrid, frequently outperform the original pretesting strategy.     

Testing nonlinearities in economic growth in the OECD countries: an evidence from SETAR and STAR models

This study estimates the Self Exciting Threshold Autoregressive (SETAR) and Smooth Transition Autoregressive (STAR) models and examines the nonlinear and regime switching dynamics of economic growth for a set of 10 OECD countries. The null of linearity in SETAR model is tested using the recursive polynomial F test of Tsay and the bootstrap based supremum, average and exponential average Lagrange Multiplier (LM) tests of Hansen. The F test of Tsay rejects the null of linearity for all the countries, except Spain and Switzerland. The SETAR model of Hansen reinforces the evidence and suggests the rejection of linear model. The STAR model rejects the null of linearity against STAR nonlinearity for all the countries, except Denmark and Switzerland. The sequential F tests for the conditional nulls suggest the LSTAR nonlinearity for Australia, Belgium, France, Sweden and UK, and the ESTAR nonlinearity for Canada, Spain and the USA.     

A new test for analysing hysteresis in European unemployment

This article proposes a new unit root test to analyse unemployment hysteresis. The test is able to incorporate cross-sectional dependence, unattended nonlinearity and unknown structural breaks in the time-series data. This study used data on unemployment in five European countries. The findings indicated that conventional unit root tests failed to reject the null hypothesis of hysteresis for all countries. However, the newly proposed unit root test was able to reject the null hypothesis for the Spanish unemployment rate.     

What drives the nonlinearity of time series: A frequency perspective

It is well-known that economic and financial time series are characterized by nonlinearities. The literature does not agree, however, on the actual causes of such nonlinearities. In this paper, I investigate whether dynamics at different frequencies present different degree of nonlinearity, and how much they may influence any nonlinearity in the aggregate original series. This paper finds strong evidence in support of the idea that nonlinearities are mostly found at high frequencies.     

Asymmetric behavior of inflation differentials in the euro area: Evidence from a threshold unit root test

This paper tests the existence of persistent inflation rate differentials in the euro area by employing linear as well nonlinear unit root tests. Besides linear unit root tests, a two-regime threshold unit root test examines the conjecture that inflation rate differentials follow a nonlinear two-regime process towards a threshold, switching from the persistent regime to the transitory one and vice versa. The results imply that threshold nonlinearity is confirmed in 10 out of the 16 cases. However, we have found unit root regime-switching behavior only in six out of the 16 cases under investigation. This finding implies that these inflation rate differentials were persistent when they were low (regime 1), but transitory when they were high (regime 2). This asymmetric behavior can possibly be explained by the different degree of pressure exercised on governments, which is accompanied with different inflation rate differentials. On the contrary, despite the evidence of nonlinearity, the majority of the inflation rate differentials are found to be monotonically persistent. Our results have strong implications for policy makers. In particular, the documented persistency in the inflation rate differentials might have long-run costs in terms of price and macroeconomic stability.     

Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

Testing misspecified non-nested factor demand systems: Some Monte Carlo results

Empirical factor demand analysis is a topic in which a choice must be made among several competing non-nested functional forms. Each of the commonly used factor demand systems, such as Translog, Generalized Leontief, Quadratic, and Generalized McFadden, exhibits statistical inadequacy when tested for the absence of residual autocorrelation, homoskedasticity and normality. This does not necessarily imply that the whole system is invalid, especially if misspecification affects only a subset of the equations forming the entire system. Since there is no theoretical guidance on how to select the model which is most able to capture the relevant features of the data, formal testing procedures can be useful. In the literature, paired and joint univariate non-nested tests (e.g. Davidson-MacKinnon's J and P tests, Bera-McAleer test and Barten-McAleer test) have been discussed at length, whereas virtually no attention has been paid to multivariate non-nested tests. In this paper we show how multivariate non-nested tests can be derived from their univariate counterparts, and we apply these tests to compare alternative factor demand systems. Since the outcome of a non-nested test is likely to be influenced by the type of misspecification affecting the competing models, we investigate the empirical performance of a multivariate non-nested test using new Monte Carlo experiments. The competing models are compared indirectly via a statistically adequate model which is considered as if it were the DGP. Under such circumstances, the distribution of the non-nested test of an incorrect null, when it is evaluated at the DGP, tends to be closer to the distribution of the test under the correct null, at least in small samples. A non-nested test is expected to select the model which is closest to the DGP. Moreover, we investigate the empirical behaviour of a non-nested test when the DGP has, in turn, autoregressive, heteroskedastic and non-normal errors. Finally, we provide some suggestions for the applied researcher. First version received: November 1999/Final version received: May 2001     

Capital flows and current account dynamics in Turkey: A nonlinear time series analysis

The paper offers an analysis of current account dynamics and its sustainability in Turkey using quarterly data. The focus is on the nonlinear characterization of the long run intertemporal budget constraint and the stationarity tests. Several well-known tests are applied to identify nonlinearity in the current account time series. The analysis reveals that while the classical unit root tests based on linear specification give rise to conflicting results as to the nonstationarity of the current account deficit series, a threshold unit root test due to Caner and Hansen (2001) fails to reject the null of nonstationarity, implying that the intertemporal budget constraint would not be satisfied in the long run.     

TESTING THE SEQUENTIAL LOGIT MODEL AGAINST THE NESTED LOGIT MODEL*

In this paper, we show that the sequential logit (SL) model, in which a choice process is characterized as a sequence of independent multinomial logit models, is a limiting case of the nested logit (NL) model. For testing the SL model against the NL model, we propose Wald, likelihood ratio and Lagrange multiplier tests after suitably reparameterizing the NL model. It is found that when the NL model parameters are “weakly identified”, the Wald test severely underrejects the true model, whereas the sizes of the LR and LM tests are not significantly affected.     

Tests for cointegration rank and the initial condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Such initial conditions are known to affect the power of univariate unit root tests diversely, whereas their impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on the power of tests for cointegration rank, such as Johansen??s widely used likelihood ratio test, tests with prior adjustment for deterministic terms, and a test based on the eigenvalues of the companion matrix. We find that the power of the likelihood ratio test is increasing in the magnitude of the initial condition, whereas the power of the other tests is generally decreasing. We exploit these findings in an application to price convergence.     

Market timing: Recent development and a new test

Henriksson-Merton's market timing test suffers nontrivial size distortion when the event forecast is autocorrelated. A new test is suggested to detect the dependence of two autocorrelated binary time series. It complements the existing tests due to better test power.     

Can we reject linearity in an HAR-RV model for the S&P 500? Insights from a nonparametric HAR-RV

This article tests the linearity assumption underlying the popular heterogeneous autoregressive model for realized volatility (HAR-RV). We implement a consistent model specification test that is robust to both distributional and model misspecification. We find that, using a nonparametric HAR-RV (NPHAR-RV), we are unable to reject the null of linearity.