The introduction of seasonal unit roots and cointegration to test index aggregation optimality: An application to a Spanish farm price index

In this paper we present a methodological proposal of the way integration and cointegration analysis can best be used to test if the level of aggregation of an index is adequate. Using this proposal, we enquire the extent to which a Spanish aggregate farm price index captures the behavior of its components. First version received: October 1994/final version received: September 1998     

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.     

Quantile nonlinear unit root test with covariates and an application to the PPP hypothesis

In this article, we employ the methods initiated by Hansen (1995) to develop new quantile nonlinear unit root tests with covariates. The limiting distributions of our proposed tests are derived, which are dependent on nuisance parameter reflecting the correlation between the equation error and the covariates. To deal with this inferential difficulty, two alternative procedures based on either consistent estimate of the nuisance parameter or bootstrap implementation of the test are proposed. Monte Carlo simulations show that the proposed tests perform very well in finite samples and large power gains can be achieved by including correlated covariates in the testing equation. The proposed tests are applied to the PPP hypothesis. The empirical results indicate that the real exchange rates are not constant unit root processes.     

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.     

Standard and seasonal long memory in volatility: an application to Spanish inflation

The historical series of many economic variables, such as inflation, are characterized by a strong persistent behaviour in the form of long memory, not only in the long run or at zero frequency but often also at seasonal frequencies. In financial series, long memory is not apparent in levels but strong persistence in higher order moments such as volatility has been proven to be a stylized fact in stock returns. Interest in economic time series has, however, focused on the persistence of levels and little attention has been paid to higher order dependence, which can be important for assessing the stability of the series. We propose a semiparametric analysis of the standard and seasonal persistence of the volatility of a monthly Spanish inflation series. The conclusions can be summarized in three main results. First volatility shows strong persistence implying an unstable trend in prices, but its structure depends on the proxy used, the absolute values, the squares or the logarithms of squares. Second, the structure of the persistence of volatility changed with the first oil crisis in 1973, with a persistent trend in both periods, in contrast with levels. Third, the Taylor effect, which is well documented in financial series, does not apply in this series.     

The seasonal unit root structure in New Zealand Macroeconomic variables

ADF unit root tests are generally applied to macroeconomic data prior to testing theoritical models to ensure that all relevant variables are integrated of the same order. Not only is it important to test that these variables are integrated of the same order but also that a cointegrating relationship exists; failure to do so raise the specture of false inference associated with the spurious regression problem. The seasonal nature of quarterly data adds a further proplem which has generally been overcome by seasonally adjusting the data using procedure such as the census X-11 rather than suppressing it, have attempted to determine whether the seasonal component in each variable exhibits stochastic non-stationary. This paper analysisunit roots in a seasonal setting and compares the recently developed tests for seasonal unit roots as well as the standard augmented Dickey-Fuller zerop frequency unit root tests. Of the variables tested relatively few paper to be integrated at the seasonal frequenciues and, as other studies suggest,determinstic seasonal effects are typically more important than stochastic ones.     

The behaviour of seasonal unit root tests under neglected local drifts

This paper analyses the limit distributions of the seasonal unit root test procedures proposed by Dickey, Hasza and Fuller (1984) and Hylleberg, Engle, Granger and Yoo (1990), when local trends at different frequencies are present in data generation processes, but ignored in the test regressions used. The findings presented explicitly show that neglected deterministic trends have negative effects on the distributions of the test statistics. Analytical observations and Monte Carlo simulations reveal that seasonal unit root test statistics become severely undersized as the values of standardized local trends increase. Hence, failure to consider local trends may often bear the undesirable effect of biasing decisions towards non-rejection of unit roots.Received: February 2001, Accepted: September 2001, JEL Classification: C12, C22Paulo M. M. Rodrigues: I am thankful to two anonymous referees for their detailed and useful comments and suggestions.     

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.     

Rational expectations and fixed-event forecasts: An application to UK inflation

This paper tests a version of the rational expectations hypothesis using ‘fixed-event’ inflation forecasts for the UK. Fixed-event forecasts consist of a panel of forecasts for a set of outturns of a series at varying horizons prior to each outturn. The forecasts are the prediction of fund managers surveyed by Merrill Lynch. Fixed-event forecasts allow tests for whether expectations are unbiased in a similar fashion to the rest of the literature. But they also permit the conduct of particular tests of forecast efficiency - whether the forecasts make best use of available information - that are not possible with rolling-event data. We find evidence of a positive bias in inflation expectations. Evidence for inefficiency is much less clear cut.First version received: June 2002/ Final version received: November 2003We would like two anonymous referees and an editor for comments that have significantly improved the paper. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of England.     

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).     

Flexible Fourier unit root test of unemployment for PIIGS countries

In this empirical study, we apply the flexible Fourier unit root test proposed by Enders and Lee (2012) to re-examine the hysteresis hypothesis of unemployment for PIIGS (Portugal, Ireland, Italy, Greece, and Spain) countries over the period from 1960 to 2011. We find that the Fourier unit root test has greater power than a linear method if the true data generating process of unemployment is a stationarity, non-linear process of an unknown form with structural change. The hysteresis in unemployment is confirmed for all PIIGS countries, with the exception of Portugal and Spain, when the Fourier unit root test is conducted.     

Trend stationary of inflation rates: evidence from LM unit root testing with a long span of historical data

The article applies the LM univariate unit root test recently developed by Lee and Strazicich (2003 Lee, J and Strazicich, MC. 2003. Minimum Lagrange multiplier unit root test with two structural breaks. The Review of Economics and Statistics, 85: 1082–9. [Crossref], [Web of Science ®] , [Google Scholar], 2004 Lee, J and Strazicich, MC. 2004. Minimum LM unit root test with one structural break, Department of Economics, University of Central Florida. Working Paper Series [Google Scholar]) to re-examine the validity of trend stationary in the inflation rates of 11 OECD and Asian countries using a longer span of historical data. Our empirical findings are favourable to the trend stationary of the inflation rates when we control the structural breaks in series, and therefore they point to the absence of hyperinflation in the majority of the countries. The results indicate that shocks to inflation rates are temporary and soon converge, with the inflation rates being trend stationary. Hence, most structural breaks in the inflation rate occur around the Great Depression, World War I, World War II, and energy shock periods. For the convergence effect, we repeat the unit root tests utilized above for smaller sub-samples so as to provide a robust analysis. The outcomes show that by selecting a longer data span, we can catch more powerful convergent evidence. Overall, some policy implications are obtained in this article.     

An econometric test of inflation neutrality using observable variables only

A modification to Startz (1981) test of some basic assertions of the resurgent neoclassical school of macroeconomics is undertaken. The assertions suggest the neutrality of the real economy with respect to anticipated inflation and the advantage of the new test is that it can be implemented using observable variables only. Results similar to Startz's were obtained when the test was rerun.     

Testing hysteresis effect in U.S. state unemployment: new evidence using a nonlinear quantile unit root test

We revisit hysteresis effect in the unemployment rate of each of the 52 states of the United States using nonlinear quantile unit root test over the period 1976M1–2016M7. Our results indicate that unemployment rate of the U.S. economy as a whole displays hysteresis effect over recessionary periods. Nineteen out of 52 states display hysteresis behaviour over the period 1976–2016. For the remaining 33 states, we find four types of behaviours. Some states display stationarity behaviour almost in all quantiles. Some display hysteresis over recessionary periods and in contrast some display hysteresis over expansion period.     

Fourier nonlinear quantile unit root test and PPP in Africa

We test the PPP hypothesis in 29 African countries using a newly developed nonlinear Quantile unit root test with a Fourier function which accounts for smooth breaks. Simulation indicates that the proposed new test has higher power than the conventional Quantile unit root test as proposed by Koneker and Xiao (2004). Our empirical results provide support for the PPP hypothesis in 21 out of 29 African countries, a unique discovery using their real effective exchange rates. It appears that incorporating Fourier function to nonlinear Quantile unit root test gets us closer and closer to solving the PPP puzzle in Africa.     

Specification sensitivities in the Markov-switching unit root test for bubbles

The aim of this article is to provide some empirical guidelines for the practical implementation of the Markov-switching augmented Dickey–Fuller (MSADF) test proposed by Hall et al. (J Appl Econom 14:143–154, 1999) for detecting explosive bubble behavior. We conduct simulation studies to compare the performance of the MSADF test under different error variance specifications, namely the constant variance and regime-dependent variance assumptions. An empirical application to the money base, consumer price and exchange rate in Argentina reveals the practical importance of the error variance specification on the MSADF test outcomes.     

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.     

Revisiting the US money demand function: an application of the Lagrange multiplier structural break unit root test and the bounds test for a long-run relationship

In this article, we examine the issue of a levels relationship and stability of the US money demand function over the period 1959:01 to 2004:02. We use the Lagrange multiplier structural break unit root test and the bounds testing approach to a long-run relationship in levels of the variables, namely real money demand, nominal interest rate and real income. We find greater evidence for a long-run relationship in levels and stability of the US money demand function when we use M2 as a proxy for money demand. However, we find little evidence for a long-run relationship between M1 and M2 with their determinants for the recent period, spanning the last decade or so.