Testing for ARCH in the presence of additive outliers

In this paper we investigate the properties of the Lagrange Multiplier [LM] test for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AOs). We show analytically that both the asymptotic size and power are adversely affected if AOs are neglected: the test rejects the null hypothesis of homoscedasticity too often when it is in fact true, while the test has difficulty detecting genuine GARCH effects. Several Monte Carlo experiments show that these phenomena occur in small samples as well. We design and implement a robust test, which has better size and power properties than the conventional test in the presence of AOs. We apply the tests to a number of US macroeconomic time series, which illustrates the dangers involved when nonrobust tests for ARCH are routinely applied as diagnostic tests for misspecification. Copyright © 1999 John Wiley & Sons, Ltd.     

Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics

Trend breaks appear to be prevalent in macroeconomic time series, and unit root tests therefore need to make allowance for these if they are to avoid the serious effects that unmodelled trend breaks have on power. Carrion-i-Silvestre et al. (2009) propose a pre-test-based approach which delivers near asymptotically efficient unit root inference both when breaks do not occur and where multiple breaks occur, provided the break magnitudes are fixed. Unfortunately, however, the fixed magnitude trend break asymptotic theory does not predict well the finite sample power functions of these tests, and power can be very low for the magnitudes of trend breaks typically observed in practice. In response to this problem we propose a unit root test that allows for multiple breaks in trend, obtained by taking the infimum of the sequence (across all candidate break points in a trimmed range) of local GLS detrended augmented Dickey–Fuller-type statistics. We show that this procedure has power that is robust to the magnitude of any trend breaks, thereby retaining good finite sample power in the presence of plausibly-sized breaks. We also demonstrate that, unlike the OLS detrended infimum tests of Zivot and Andrews (1992), these tests display no tendency to spuriously reject in the limit when fixed magnitude trend breaks occur under the unit root null.     

The unemployment structure of the US states

This paper analyses the time series properties of the unemployment rates of the US economy using a regional disaggregated level. Our results are, in general, favorable to the rejection of the presence of a unit root in these variables. However, we can also observe that this conclusion is clearly qualified by the level of disaggregation employed. We also find robust evidence in favor of the presence of some breaks in the evolution of these unemployment rates. We subsequently offer an estimation of the NAIRU, which is based on the use of the Bai–Perron procedure.     

Price-wage dynamics in a transition economy: The case of Poland

In this paper we analyse the wage-price relationship of an economy in transition characterized by important structural changes. It is known (see Perron, 1989) that structural breaks in stationary time series can induce apparent unit roots. The stationarity analysis of the series employed in the present model is conducted jointly with the assumption that the breakpoint location is unknown. We follow a testing procedure recently proposed by Zivot and Andrews (1992). Cointegration analysis of wages and prices in the presence of structural breaks finds empirical evidence in favour of two cointegrating vectors involving prices and wages. Our analysis focuses on the different structural behaviour of the price-wage dynamic relationship in the short and long term; we also demonstrate the relative importance of import prices as a source of wage-price fluctuations.     

Further Evidence on the Statistical Properties of Real GNP*

The well‐known lack of power of unit‐root tests has often been attributed to the short length of macroeconomic variables and also to data‐generating processes (DGPs) departing from the I(1)–I(0) models. This paper shows that by using long spans of annual real gross national product (GNP) and GNP per capita (133 years), high power can be achieved, leading to the rejection of both the unit‐root and the trend‐stationary hypothesis. More flexible representations are then considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that both FI and SB formulations are in general preferred to the autoregressive integrated moving average (ARIMA) [I(1) or I(0)] formulations. As a novelty in this literature, new techniques are applied to discriminate between FI and SB. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non‐stationary, highly persistent but mean‐reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.     

On economic uncertainty,stock market predictability and nonlinear spillover effects

This paper uses a k-th order nonparametric Granger causality test to analyze whether firm-level, economic policy and macroeconomic uncertainty indicators predict movements in real stock returns and their volatility. Linear Granger causality tests show that whilst economic policy and macroeconomic uncertainty indices can predict stock returns, firm-level uncertainty measures possess no predictability. However, given the existence of structural breaks and inherent nonlinearities in the series, we employ a nonparametric causality methodology, as linear modeling leads to misspecifications thus the results cannot be considered reliable. The nonparametric test reveals that in fact no predictability can be observed for the various measures of uncertainty i.e., firm-level, macroeconomic and economic policy uncertainty, vis-à-vis real stock returns. In turn, a profound causal predictability is demonstrated for the volatility series, with the exception of firm-level uncertainty. Overall our results not only emphasize the role of economic and firm-level uncertainty measures in predicting the volatility of stock returns, but also presage against using linear models which are likely to suffer from misspecification in the presence of parameter instability and nonlinear spillover effects.     

Structural breaks, rural transformation and total factor productivity growth in China

This paper carries out an empirical investigation into the contribution of rural transformation, which can produce efficiency gains over and above those associated with technical progress, to total factor productivity in China during the post-reform period 1980–2010. For the first time for China, the roles of rural transformation and technical progress are examined whilst structural breaks are taken into account. We employ Bai and Perron (Econometrica 66:47–68, 1998; J Appl Econom 18:1–22, 2003a; Econom J 6:72–78, 2003b) methods which allow for multiple structural breaks at unknown dates and can be applied for both pure and partial structural changes. We also evaluate the robustness of our results by employing alternative production functions and two capital series. Two structural breaks near the Tiananmen Square incident in 1989 and the implementation of further reforms and opening-up measures in 1995 were identified for both capital series. We found the contribution of rural transformation to total factor productivity to be significant and positive across all regimes. However, its importance to the growth of total factor productivity has been declining over time, while that of technical progress has been increasing.     

Are unemployment rates in OECD countries stationary? Evidence from univariate and panel unit root tests

This paper revisits the dynamics of unemployment rate for 29 OECD countries over the period of 1980–2013. Numerous empirical studies of the dynamics of unemployment rate are carried out within a linear framework. However, unemployment rate can show nonlinear behaviour as a result of business cycles or some idiosyncratic factors specific to labour market (Cancelo, 2007). Thus, as a testing strategy, we first perform Harvey, Leybourne, and Xiao (2008) linearity unit root test and then apply the newly ESTAR nonlinear unit root test suggested by Kruse (2011). This test has higher power than conventional unit root tests when time series exhibits nonlinear behaviour. Our empirical findings provide significant evidence in favour of unemployment rate stationarity for 25 countries. For robustness purpose, we have also used panel unit root tests without and with structural breaks. The empirical results show that unemployment hysteresis hypothesis is strongly rejected, when taking into account the cross-sectional and structural break assumptions. Thus, unemployment rate is expected to return back to their natural levels without executing any costly macroeconomic labour market policies by the OECD’s governments.     

Efficient tests for the presence of a pair of complex conjugate unit roots in real time series

We introduce a framework which allows us to draw a clear parallel between the test for the presence of seasonal unit roots and that for unit root at frequency 0 (or π$\pi$). It relies on the properties of the complex conjugate integrated of order one processes which are implicitly at work in the real time series. In the same framework as that of Phillips and Perron (Biometrica 75 (1988) 335), we derive tests for the presence of a pair of conjugate complex unit roots. The asymptotic distribution we obtain are formally close to those derived by these authors but expressed with complex Wiener processes. We then introduce sequences of near-integrated processes which allow us to study the local-to-unity asymptotic of the above test statistics. We state a result on the weak convergence of the partial sum of complex near-random walks which leads to complex Orstein–Uhlenbeck processes. Drawing on Elliott et al. (Econometrica 64 (1996) 813) we then study the design of point-optimal invariant test procedures and compute their envelope employing local-to-unity asymptotic approximations. This leads us to introduce new feasible and near efficient seasonal unit root tests. Their finite sample properties are investigated and compared with the different test procedures already available (J. Econometrics 44 (1991) 215; 62 (1994) 415; 85 (1998) 269) and those introduced in the first part of the paper.     

Testing of Fractional Cointegration in Macroeconomic Time Series*

We propose in this article a two‐step testing procedure of fractional cointegration in macroeconomic time series. It is based on Robinson's (Journal of the American Statistical Association, Vol. 89, p. 1420) univariate tests and is similar in spirit to the one proposed by Engle & Granger (Econometrica, Vol. 55, p. 251), testing initially the order of integration of the individual series and then, testing the degree of integration of the residuals from the cointegrating relationship. Finite‐sample critical values of the new tests are computed and Monte Carlo experiments are conducted to examine the size and the power properties of the tests in finite samples. An empirical application, using the same datasets as in Engle & Granger (Econometrica, Vol. 55, p. 251) and Campbell & Shiller (Journal of Political Economy, Vol. 95, p. 1062), is also carried out at the end of the article.     

Robust Dickey–Fuller tests based on ranks for time series with additive outliers

In this paper the unit root tests proposed by Dickey and Fuller (DF) and their rank counterpart suggested by Breitung and Gouriéroux (J Econom 81(1): 7–27, 1997) (BG) are analytically investigated under the presence of additive outlier (AO) contaminations. The results show that the limiting distribution of the former test is outlier dependent, while the latter one is outlier free. The finite sample size properties of these tests are also investigated under different scenarios of testing contaminated unit root processes. In the empirical study, the alternative DF rank test suggested in Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) (GH) is also considered. In Fotopoulos and Ahn (J Time Ser Anal 24(6): 647–662, 2003), these unit root rank tests were analytically and empirically investigated and compared to the DF test, but with outlier-free processes. Thus, the results provided in this paper complement the studies of the previous works, but in the context of time series with additive outliers. Equivalently to DF and Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) unit root tests, the BG test shows to be sensitive to AO contaminations, but with less severity. In practical situations where there would be a suspicion of additive outlier, the general conclusion is that the DF and Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) unit root tests should be avoided, however, the BG approach can still be used.     

Tests for Stationarity in Series with Endogenously Determined Structural Change*

We consider tests of the null hypothesis of stationarity against a unit root alternative, when the series is subject to structural change at an unknown point in time. Three extant tests are reviewed which allow for an endogenously determined instantaneous structural break, and a related fourth procedure is introduced. We further propose tests which permit the structural change to be gradual rather than instantaneous, allowing the null hypothesis to be stationarity about a smooth transition in linear trend. The size and power properties of the tests are investigated, and the tests are applied to four economic time series.     

Do TFP and the relative price of investment share a common I(1) component?

Results from cointegration tests clearly suggest that TFP and the relative price of investment (RPI) are not cointegrated. Evidence on the alternative possibility that they may nonetheless contain a common I(1) component generating long-horizon co-variation between them crucially depends on the fact that (i) structural breaks are, or are not allowed for, and (ii) the precise nature and timing of such breaks. Not allowing for breaks, evidence points towards the presence of a common component inducing positive long-horizon covariation, which is compatible with the notion that the technology transforming consumption goods into investment goods is non-linear, and the RPI is also impacted upon by neutral shocks. Allowing for breaks, evidence suggests that long-horizon covariation is either nil or negative.Assuming, for illustrative purposes, that the two series contain a common component inducing negative long-horizon covariation, evidence based on structural VARs shows that this common shock (i) plays an important role in macroeconomic fluctuations, explaining sizeable fractions of the forecast error variance of main macro series, and (ii) generates ‘disinflationary booms’, characterized by transitory increases in hours, and decreases in inflation.     

Structural breaks and GARCH models of exchange rate volatility

We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the structural breaks. We also find that it almost always pays to allow for structural breaks when forecasting exchange rate return volatility in real time. Combining forecasts from different models that accommodate structural breaks in volatility in various ways appears to offer a reliable method for improving volatility forecast accuracy given the uncertainty surrounding the timing and size of the structural breaks. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust and Powerful Tests for Nonlinear Deterministic Components

We develop a test for the presence of nonlinear deterministic components in a univariate time series, approximated using a Fourier series expansion, designed to be asymptotically robust to the order of integration of the process and to any weak dependence present. We show that our proposed test has uniformly greater local asymptotic power than the existing tests of Harvey, Leybourne and Xiao (2010) when the shocks are I(1), identical local asymptotic power when the shocks are I(0), and also improved finite sample properties. We also consider the issue of determining the number of Fourier frequencies used to specify any nonlinear deterministic components.     

A Simple Test for Cointegration in Dependent Panels with Structural Breaks*

This paper develops a very simple test for the null hypothesis of no cointegration in panel data. The test is general enough to allow for heteroskedastic and serially correlated errors, unit‐specific time trends, cross‐sectional dependence and unknown structural breaks in both the intercept and slope of the cointegrated regression, which may be located at different dates for different units. The limiting distribution of the test is derived, and is found to be normal and free of nuisance parameters under the null. A small simulation study is also conducted to investigate the small‐sample properties of the test. In our empirical application, we provide new evidence concerning the purchasing power parity hypothesis.     

Testing for Panel Cointegration with Multiple Structural Breaks*

This paper proposes a Lagrange multiplier (LM) test for the null hypothesis of cointegration that allows for the possibility of multiple structural breaks in both the level and trend of a cointegrated panel regression. The test is general enough to allow for endogenous regressors, serial correlation and an unknown number of breaks that may be located at different dates for different individuals. We derive the limiting distribution of the test and conduct a small Monte Carlo study to investigate its finite sample properties. In our empirical application to the solvency of the current account, we find evidence of cointegration between saving and investment once a level break is accommodated.     

Tests for a Break in Level when the Order of Integration is Unknown*

In this paper, we consider tests for a break in the level of a series at an unknown point in time. It is often the case that uncertainty exists concerning the order of integration of the series; consequently, we focus on tests that are applicable when the order of integration is not known. The size and power of existing tests are analysed, and a modification to one of the established sets of tests is proposed which offers improved performance in certain circumstances.     

Large shocks,small shocks,and economic fluctuations: Outliers in macroeconomic time series

We analyse fifteen post-World War II US macroeconomic time series using a modified outlier identification procedure based on Tsay (1988a). ‘Large shocks’ appear to be present in all the series we examined. Furthermore, there are three basic outlier patterns: (1) outliers seem to be associated with business cycles, (2) outliers are clustered together—both over time and across series, (3) there appears to be a dichotomy between outlier behaviour of real versus nominal series. Also, after controlling for outliers, much of the evidence of non-linearity in many of the time series is eliminated.     

Finite sample multivariate structural change tests with application to energy demand models

This paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models, in which case commonly used structural change tests remain asymptotic. As in Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68], we account for intervening nuisance parameters through a two-stage maximized Monte Carlo test procedure. Our contributions can be classified into five categories: (i) we extend tests for which a finite-sample theory has been supplied for Gaussian distributions to the non-Gaussian context; (ii) we show that Bai et al. [1998. Testing and dating common breaks in multi-variate time series. The Review of Economic Studies 65 (3), 395–432] test severely over-rejects and propose exact variants of this test; (iii) we consider predictive break test approaches which generalize tests in Dufour [1980. Dummy variables and predictive tests for structural change. Economics Letters 6, 241–247] and Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68]; (iv) we propose exact (non-Bonferonni based) extensions of the multivariate outliers test from Wilks [1963. Multivariate statistical outliers. Sankhya Series A 25, 407–426] to models with covariates; (v) we apply these tests to the energy demand system analyzed by Arsenault et al. [1995. A total energy demand model of Québec: forecasting properties. Energy Economics 17 (2), 163–171]. For two out of the six industrial sectors analyzed over the 1962–2000 period, break and further goodness-of-fit and diagnostic tests allow to identify (and correct) specification problems arising from historical regulatory changes or (possibly random) industry-specific effects. The procedures we propose have potential useful applications in statistics, econometrics and finance (e.g. event studies).