A Fractional Stationarity Test with Gradual Shifts and the Hysteresis Hypothesis in OECD Countries (original) (raw)

Centre de Referència en Economia Analítica Barcelona Economics Working Paper Series Working Paper n o 29 Testing for a Unit Root Againts Fractional Alternatives in the Presence of a Maintained Trend

2004

This paper discusses the role of deterministic components in the DGP and in the auxiliary regression model which underlies the implementation of the Fractional DickeyFuller (FDF) test for I(1) against F I(d) processes with d 2 [0; 1): Invariant tests to the presence of a drift under the null of I(1) are derived. In common with the standard DF approach in the I(1) vs: I(0) framework, we also examine the consequences of including a constant and /or a linear trend in the regression model when there is a drift under the null. A simple testing strategy entailing only asymptotically normally-distributed tests is proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OCDE countries.

No-cointegration test based on fractional differencing: Some Monte Carlo results

Journal of Statistical Planning and Inference, 1999

This paper examines the use of the t-statistic in the Geweke-Porter-Hudak regression for the estimation of the fractional di erencing parameter as a test for cointegration. The critical values of the test statistic are estimated using Monte Carlo methods. The results conÿrm that the test will over-reject the null hypothesis of no cointegration if the standard-normal critical values are used. The estimated critical values are generally robust to the nuisance parameters in the autoregressive or moving average speciÿcation of the error process of the component time series. Exceptions occur when the dependent variable in the cointegration regression follows an autoregressive process with a large positive parameter or a moving average process with a large negative parameter.

Hysteresis in unemployment for 17 OECD countries: Stationary test with a Fourier function

Economic Modelling, 2011

In this empirical study, we apply stationary test with a Fourier function proposed by to reexamine the hysteresis hypothesis in unemployment for 17 OECD countries over the 1960 to 2009 period. The hysteresis in unemployment is confirmed for most of these 17 OECD countries, with the exception of Australia, Canada, Finland, France, Sweden and the USA, when Becker et al. 's (2006) stationary test with a Fourier function is conducted.

Testing the Unemployment Hysteresis in G7 Countries: A Fresh Evidence from Fourier Threshold Unit Root Test

2020

In this study, we test the validity of unemployment hysteresis in G7 countries over the period of 1991 – 2019 using monthly data by suggesting a new unit root test that considers both structural breaks and nonlinearity that we entitled as Fourier Threshold Unit Root (FTUR) test. The results of the test show that unemployment rates of Canada, Japan, and the USA are nonlinear. Thus, for these countries we apply the FTUR test, while for the remaining series, we employ the Fourier ADF unit root test. The results of unit root tests show that unemployment hysteresis holds in Canada, France, and the United Kingdom, while NonAccelerating Inflation Rate of Unemployment applies in Germany, and Italy. We could not reject the null of a unit root for Japan and the USA only in the second regime, where the unemployment series are rising. So, we conclude that the policymakers of Japan and the USA should follow fiscal stabilization policies only in recession periods.

Local Asymptotic Distributions of Stationarity Tests

Journal of Time Series Analysis, 2006

In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non-stationary process in any finite sample which converges to a stationary process as T " 1. From the asymptotic distributions, we find that the stationarity tests have non-trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704-709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.

Is There Really Hysteresis in OECD Countries’ Unemployment Rates? New Evidence Using a Fourier Panel Unit Root Test

MPRA Paper, 2021

We investigate the hysteresis hypothesis by proposing a heterogeneous panel unit root test that allows for gradually changing trends and cross-sectional dependence (CSD) among panel members using a flexible Fourier form. Inconclusive results from previous studies are potentially due to using very restrictive specifications with homogenous break structures and/or exogenously determined abrupt breaks. We seek to address these limitations by employing general specifications that are more capable of characterising the true data generation process of unemployment and by allowing for spill-over effects using a bootstrapping procedure to accommodate CSD that must be considered in a globalized world. Extensive simulations suggest that the failure to take structural breaks and CSD into account can lead to misleading conclusions about whether the unemployment rate is stationarity. We apply our test procedure to unemployment data for 23 OECD countries and find conclusive evidence against the hysteresis hypothesis for all these countries.

The Exact Maximum Likelihood-Based Test for Fractional Cointegration: Critical Values, Power and Size

Computational Economics, 2004

The exact maximum likelihood (EML) procedure can be used as a residual-based test of the hypothesis of no cointegration against the alternative of fractional cointegration. Since the corresponding asymptotic properties have not yet been established, this paper provides simulated critical values, power and size relating to the EML-based test for fractional cointegration. Monte Carlo simulations indicate that the simulated density of the EML-based test is shifted to the left compared to the standard normal distribution and exhibits a strong excess of kurtosis in the absence of autoregressive components in the regression residuals. The power and size comparison indicates that the EML-based test is more powerful than other fractional cointegration tests (Lo, Lobato-Robinson and Geweke and Porter-Hudak) in small and medium sample sizes. Moreover, by simulating integrated time series with AR(1), and respectively MA(1), disturbances, it is shown that, whatever the sample size, the EML-based test exhibits the lowest size distortions for positive AR(1) and negative MA(1) coefficients, respectively.

Distribution-Free Tests of Fractional Cointegration

Econometric Theory, 2007

We propose tests of the null of spurious relationship against the alternative of fractional cointegration among the components of a vector of fractionally integrated time series+ Our test statistics have an asymptotic chi-square distribution under the null and rely on generalized least squares-type of corrections that control for the short-run correlation of the weak dependent components of the fractionally integrated processes+ We emphasize corrections based on nonparametric modelization of the innovations' autocorrelation, relaxing important conditions that are standard in the literature and, in particular, being able to consider simul-taneously~asymptotically! stationary or nonstationary processes+ Relatively weak conditions on the corresponding short-run and memory parameter estimates are assumed+ The new tests are consistent with a divergence rate that, in most of the cases, as we show in a simple situation, depends on the cointegration degree+ Finite-sample properties of the tests are analyzed by means of a Monte Carlo experiment+