STRUCTURAL BREAKS AND UNIT ROOTS IN AUSTRALIAN MACROECONOMIC TIME SERIES

Abstract.  We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.     

Explosive behaviour and long memory with an application to European bond yield spreads

This article deals with the interplay of explosive behaviour and long memory. We conduct Monte Carlo simulations and study the finite‐sample properties of the popular unit root test by Phillips et al. (2011) against explosive alternatives. This test exhibits severe upward size distortions under the presence of strongly autocorrelated residuals. We propose the usage of a set of adjusted critical values which leads to a size‐controlled test with increased power. As a complement, we consider the Lagrange Multiplier test against long memory by Tanaka (1999). We study European government bond yield spreads during the financial crisis.     

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

An application of a new seasonal unit root test to inflation

In this paper, we apply the modified seasonal unit root test with seasonal level shifts at unknown time proposed by Popp (2007) to the G7 inflation rate. We also study the power properties of this test and generate critical values for a range of different break points and sample sizes. We find that there is a non-seasonal unit root in Canada's inflation rate, a semi-annual unit root in Germany's inflation rate, and no seasonal unit root at the annual frequency for any of the G7 countries.     

Reexamining the PPP hypothesis: A nonlinear asymmetric heterogeneous panel unit root test

In this study, we re-examine the PPP hypothesis in the light of the new developments in the unit root testing literature. The recent theoretical findings have pointed out that the real exchange rate series exhibit asymmetric nonlinear behavior. A unit root test applied to analyze the PPP hypothesis therefore, should also take into account this asymmetry inherent in the real exchange rate. Different unit root tests that consider the presence of these data features have been developed in the time series literature. However, a true attempt to test the PPP hypothesis should take a panel data approach. To this end, we propose a nonlinear heterogeneous panel unit root test where the alternative hypothesis allows for symmetric or asymmetric exponential smooth transition autoregressive nonlinearity and provide its finite sample properties. We apply our test to the real exchange rates of the 15 European Union countries against the US dollar. While the results of the linear and symmetric nonlinear heterogeneous panel unit root tests are against the PPP hypothesis, the asymmetric nonlinear heterogeneous panel test that we propose gives support for the PPP hypothesis as expected. Therefore, the conclusions drawn from the linear panel unit root tests or the nonlinear panel unit root tests that do not take asymmetry into account might be misleading.     

Convergence Across the United States: Evidence from Panel ESTAR Unit Root Test

Many empirical studies try to test whether there is income convergence across metropolitan areas in the continental United States. Drennan et al. (Journal of Economic Geography 4(5), 2004) claim that income among metropolitan economies is diverging for the period 1969–2001, after applying univariate unit root tests to the time series data. This paper brings new information to this area of study by using the nonlinear panel unit root test of the Exponential Smooth Auto-Regressive Augmented Dickey–Fuller (ESTAR-ADF) unit root test on the time series data for the period 1929–2005. Our results find evidence of stationarity for time series and thereby support beta and sigma convergence among states in a nonlinear setup. However, when the non-linear test encompasses cross section dependence as advocated by Cerrato et al. (2008), the evidence is attenuated.     

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.     

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.     

ARE LABOUR FORCE PARTICIPATION RATES NON‐STATIONARY? EVIDENCE FROM 130 YEARS FOR G7 COUNTRIES*

This paper applies a unit root test with a non‐linear threshold to examine whether labour force participation rates are mean reverting for G7 countries using annual data over a 130 year period. We find some evidence of mean reversion for just over half the sample; however, this result is sensitive to regime shifts. We also examine whether the labour force participation rate is trend reverting through employing a lagrange multiplier (LM) unit root test with one and two structural breaks in the intercept and slope. The LM unit root test provides no additional evidence in support of stationarity. On the basis of the unit root tests for mean reversion we conclude that there is at best mixed evidence that long‐term changes in unemployment rates translate into long‐term changes in employment rates and that the unemployment rate is a useful indicator of joblessness.     

Purchasing Power Parity-evidence from a new panel test

This paper uses a recently suggested test for unit roots in panels of time series data (Maddala and Wu, Oxford Bulletin of Economics and Statistics, 61, 631-52, 1999) to consider the Purchasing Power Parity hypothesis. The major innovation of this test is that it allows both the testing of unit root null, using the ADF test, and the stationarity null, using the KPSS test. It is found that the results are inconsistent, suggesting that either alternative hypotheses to a unit root may need to be considered or that panel based testing in this particular context may be of limited value.     

Exchange rates dynamics revisited: a panel data test of the fractional integration order

We test the possibility that exchange rates from nine developed countries have a unit root against the alternate possibility that they are fractionally integrated. Theoretically, exchange rates are only expected to follow a random walk under restrictive assumptions. However, most traditional unit root tests cannot reject a unit root in exchange rates, and time series tests that allow for fractional integration have given inconclusive results. To increase the power of the test of the integration order we develop two panel data tests of the fractional integration order. Monte Carlo simulations show that these tests are correctly sized and have relatively high power compared to other similar tests. Moreover, our empirical results show that we can reject a unit root in exchange rates with a high probability, but the integration order is close to one. This indicates that exchange rates are mean-reverting, although the reversion is slow, resulting in long swings.     

Some cautions on the use of nonlinear panel unit root tests: Evidence from a modified series-specific non-linear panel unit-root test

The purpose of this paper is to examine the relevance of applying nonlinear panel unit root test to examine the non-linear mean reversion behaviors of real exchange rates. We find that nonlinear panel unit root test may achieve lower power performance as compared to its alternative of linear panel unit test when the data generating process does not contain significant non-linear components. This finding post cautions to researchers in modeling and testing real exchanges behavior. We also develop a modified series-specific nonlinear panel unit root test and find evidence in favor of purchasing power parity hypothesis for China's four ASEAN trading partners in the period of February 1997 to August 2009.     

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.     

Are business cycles stationary fluctuations around a deterministic trend? Empirical evidence from 79 developing countries

There is a large literature that tests the univariate time series properties of the real output series following the seminal work of Nelson and Plosser (1982). Whether or not real output is characterized by a unit root process has important implications. A unit root in real output, for instance, is inconsistent with the notion that business cycles are stationary fluctuations around a deterministic trend. In this paper, we investigate the univariate time series properties of real output for 79 developing countries using the conventional augmented Dickey and Fuller (1979) unit root test, the Zivot and Andrews’ (1992) one structural break unit root test, and the Lumsdaine and Papell (1997) two structural breaks unit root test. Our main finding is that, for 40 countries, real output is stationary around a trend. This indicates that business cycles are stationary fluctuations around a deterministic trend for only 51% of the developing countries in our sample.     

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).     

Is real GDP stationary? Evidence from a panel unit root test with cross-sectional dependence and historical data

We use historical data that cover more than one century on real GDP for industrial countries and employ the Pesaran panel unit root test that allows for cross-sectional dependence to test for a unit root on real GDP. At first, we find strong evidence against the unit root null. Our results seem to be robust to the chosen group of countries and, in most cases, the sample period. However, the sequential panel selection method reveals that the rejection of the unit root null is due to the stationarity of real GDP in a few countries only. Real GDP is less stationary mostly in fixed exchange rate regimes like the Gold Standard and the Bretton Woods system.     

计量经济学方法之时间序列分析

本文介绍了一元时间序列分析中常用的AR、MA、ARMA和ARIMA等经典模型,分析了这几个经典模型的理论要点以及单位根检验的方法和程序,总结了时间序列分析在预测等方面的优势及其在复杂科学管理中的应用,并以我国一月期国债回购利率和上证180月收益率为分析对象,介绍了一元线性回归分析的基本步骤。     

Unit Root Tests for Dependent Micropanels

This paper proposes a new test for the null hypothesis of panel unit roots for micropanels with short time dimensions (T) and large cross‐sections (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model allowing for cross‐sectional dependency, which is introduced by a factor structure of the initial condition. Second, the test employs the panel AR(1) model with AR(1) coefficients that are heterogeneous for finite N. Third, the test can be used both for the alternative hypothesis of stationarity and for that of explosive roots. Fourth, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, the present paper employs cross‐sectional regressions using the first time‐series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t‐ratios for the coefficient are this paper's test statistics and have a standard normal distribution in the limit. The t‐ratios are based on the OLS estimator and the instrumental variables estimator that uses reshuffled regressors as instruments. The test proposed in this paper makes it possible to test for a unit root even at T = 2 as long as N is large. Simulation results show that test statistics have reasonable empirical size and power. The test is applied to college graduates' monthly real wage in South Korea. The number of time‐series observations for this data is only two. The null hypothesis of a unit root is rejected against the alternative of stationarity.     

Testing of Unit Root Cycles in the Swedish Economy

In this article we examine the existence of unit root cycles in 11 long Swedish macroeconomic time series. We use a version of the tests of Robinson (1994) that permits us to test this type of hypothesis, which is based on the Gegenbauer processes. The results show that, for most of the series, the unit root cycles occur approximately every six periods. However, in case of the GDP deflator and wage rates, first differences may be required before proceeding to the analysis of the cyclical structure.JEL code: C22