Unit Root Tests under Various Model Specifications

Many financial time series are nonstationary and are modeled as ARIMA processes; they are integrated processes (I(n)) which can be made stationary (I(0)) via differencing n times. I(1) processes have a unit root in the autoregressive polynomial. Using OLS with unit root processes often leads to spurious results; a cointegration analysis should be used instead. Unit root tests (URT) decrease spurious cointegration. The Augmented Dickey Fuller (ADF) URT fails to reject a false null hypothesis of a unit root under the presence of structural changes in intercept and/or linear trend. The Zivot and Andrews (ZA) (1992) URT was designed for unknown breaks, but not under the null hypothesis. Lee and Strazicich (2003) argued the ZA URT was biased towards stationarity with breaks and proposed a new URT with breaks in the null. When an ARMA(p,q) process with trend and/or drift that is to be tested for unit roots and has changepoints in trend and/or intercept two approaches that can be taken: One approach is to use a unit root test that is robust to changepoints. In this paper we consider two of these URT's, the Lee-Strazicich URT and the Hybrid Bai-Perron ZA URT(Herranz, 2016.) The other approach we consider is to remove the deterministic components with changepoints using the Bai-Perron breakpoint detection method (1998, 2003), and then use a standard unit root test such as ADF in each segment. This approach does not assume that the entire time series being tested is all I(1) or I(0), as is the case with standard unit root tests. Performances of the tests were compared under various scenarios involving changepoints via simulation studies. Another type of model for breaks, the Self-Exciting-Threshold-Autoregressive (SETAR) model is also discussed.

Weekly series of agricultural prices usually exhibit seasonal variations and the stationarity of these variations should be taken into account to analyse price relationships. However, unit root tests at seasonal frequencies are unlikely to have good power properties. Furthermore, movements in actual price series are often not as expected when unit roots are present. Therefore, stationarity tests at seasonal frequencies also need to be applied. In this paper, a procedure to test for the null hypothesis of stationarity at seasonal frequencies was extended to the weekly case. Once critical values were obtained by simulation exercises, unit root and stationarity tests were applied to weekly retail prices of different agricultural commodities in Spain. The most relevant finding was that many unit roots that seasonal unit root tests failed to reject did not seem to be present from the results of seasonal stationarity tests, whereas seasonal unit root tests led to the rejection of some unit roots that seemed to be present according to the results of seasonal stationarity tests. In conclusion, unit root tests should be complemented with stationarity tests before making decisions about the behaviour of seasonal patterns.

Estimating break points in a time series regression with structural changes

Purpose – The purpose of this paper is to examine the time series behavior of Greek labor market series by providing an empirical perspective on trend breaks and unit roots. Trend breaks represent aggregate behavior responses to “infrequent” changes in economic fundamentals, including changes in fiscal or labor market conditions, as have been perceived in Greece during the last years. Unit roots reveal whether “regular” shocks have significant effects on the level of the series over a specified finite horizon. Design/methodology/approach – The authors employ recent procedures that deal with the “circular testing problem” between tests on the parameters of the trend function and unit root tests that often arises in empirical applications. These techniques assess trend function stability and are robust regardless of whether the noise component is stationary or having a unit root. Then, conditional on the presence of breaks, the authors test whether the series can be characterized by a stochastic trend. Findings – The analysis provides evidence of “infrequent” trend breaks that appear to coincide with the recent global economic crisis and the implementation of the counteraction (fiscal) measures to the Greek debt crisis. Allowing for trend breaks does not lead to a rejection of the unit root hypothesis, which might reflect the low flexibility of the country’s labor market operation. Practical implications – The procedures employed can be viewed as new tools that might help empirical researchers to explore more accurately the characteristics of individual time series and to find reasonable approximations to the true processes of the time series examined. Originality/value – The paper provides new information on the presence of structural changes in the Greek labor market, and on whether the “aggressive” and “occasional” nature of fiscal measures can be approximated by infrequent changes in the slope of the trend function.

The efficient market hypothesis explains the random walk hypothesis suggesting that stock prices are independent of each other, hence, it is impossible to earn abnormal profits. The positive effect of a well-functioning and highly efficient stock market on the performance of an economy motivated the Philippine Stock Exchange to pursue massive modernization initiatives. This research provides evidence of the existence of random walk in the Philippine stock market employing the Augmented Dickey-Fuller (1981) and Phillips-Perron (1988) unit root tests, the Lo-MacKinlay's (1988) conventional variance ratio test, and Chow-Denning's (1993) simple multiple variance ratio test. Results of the ADF and PP unit root tests confirm the necessary condition for a random walk. The Chow-Denning (1993) maximum /z/ statistic and the Wald test statistic as in Richardson and Smith (1991) for the joint hypotheses and the Lo and MacKinlay (1988) individual statistics variance ratio test generally accepted the null hypothesis of a random walk. That is, the unit root and variance ratio tests consistently indicate that the null hypothesis of random walk cannot be rejected. The existence of a random walk in weak-form efficiency can be attributed to market liquidity as a result of continuous development and modernization of the Philippine equity market.

Why Frequency Matters for Unit Root Testing

Purchasing Power Parity and the European single currency: Some new evidence

The two types of model introduced in this chapter are linked by the theme of (conditional) heteroscedasticity. The first model relates to the development of AR models to allow for random rather than fixed coefficients, where the particular focus is on a stochastic unit root (StUR) in contrast to the deterministic unit root of the conventional approach. A number of economic models can be viewed as generating a StUR; for example, a model of efficient markets can generate a root that is stochastic and differs from a unit root by the expected return on a financial asset (see LeRoy, 1982, and Leybourne, McCabe and Mills, 1996); another example is based on the permanent income hypothesis, which leads to an equation for consumption with a stochastic root that differs from unity by the ratio of the difference between the rate of inter-temporal time preference and the real rate of interest to the rate of interest (see Granger and Swanson, 1997).

Whether or not a time series is weakly stationary has long been a question of major interest in the field of time series analysis. Stationary time series can be sufficiently described by means of autoregressive moving average (ARMA) processes. When modelling temporal correlations of GNSS observation noise, the applicability of ARMA processes depends on the stationarity of residual time series from GNSS data analysis. According to the property that stationary processes have homogenous variances, statistical inferences on stationarity can be made by testing for homogeneity of variance (HOV). In addition, considering a time series as a realisation of a stochastic process, stationarity can be assessed by testing for stochastic trends using unit root tests. Based on representative data simulations, this paper analyses the empirical size and power of commonly used HOV and unit root tests. The results show that the performance of the HOV test is strongly affected by serial correlations, whereas the unit root test produces high power without significant size distortions.

PurposeIn the Iranian economy, investing in the housing market has been very important and beneficial for investors and households, because of inflationary environment, low real interest rates, underdeveloped financial and tax systems and economic sanctions. Hence, prediction of house prices is the main concern of housing market agents in the economy. The purpose of this paper is to test the stationary properties of Iran's provinces to improve the prediction of future housing prices.Design/methodology/approachIn this paper, the authors have tested the stationary properties of 20 Iran’s province centers over the period from 1993 to 2017 using a novel Fourier quantile unit root test and conventional ordinary/generalized least squares (O/GLS) linear unit root/stationary tests.FindingsAccording to conventional O/GLS linear unit root/stationary tests, most of the house prices series exhibit random walk behavior, whereas by applying the Fourier quantile unit root test, the null hypothesis of unit root is rejected for 15 out of 20 series. Other results indicated that house prices of cities responded differently to positive and negative shocks.Originality/valuePrevious studies only addressed conventional OLS or GLS linear unit root or stationary tests, but novel Fourier quantile unit root test was not used. New results were obtained based on this unit root test, that, as a priori knowledge, will help benefiting from the positive effects, or avoiding being victimized by the negative effects.

Since threshold autoregressive models were discovered, many unit root tests have been developed to test the unit root null hypothesis when considering regime change. On the other hand, Sollis, J Time Ser Anal 25:409–417, 2004, indicates that a threshold unit root test could be combined with some smooth transition logistic functions which are introduced by Leybourne et al., J Time Ser Anal 19:83–97, 1998. This paper investigates whether the Caner and Hansen, Econometrica 69:1555–1596, 2001, unit root test could be expanded with smooth transition functions and demonstrates the performance of this new unit root testing process with Monte Carlo simulations. Simulation results for finite sample properties show reasonable empirical size and power values. Also, the proposed unit root testing procedure is used to test unit root null hypothesis for industrial production indices of United States of America and Turkey.KeywordsThreshold modelSmooth transitionUnit rootMonte Carlo simulations

This paper investigates the impact of crude oil boom on the economy ofNigeria particularly the manufacturing sector. In the study, a descriptive analysis of the three major sectors of the economy is undertaken followed by the formulation of a vector autoregression model depicting the relationship existing among the sectors—resource, manufacturing and service. The model was subsequently estimated using appropriate techniques such as unit root test, cointegration test, causality test, variance decomposition and parametric estimation. The unit root and cointegration tests reveal that the data series employed are reliable and the three sectors are most likely to converge in the long run, which augurs well for policy making. The causality test, variance decomposition and parametric estimation reveal that the oil boom led to significant stagnation in the manufacturing sector and a marginal decline in the service sector. The growth of manufacturing sector ofNigeria has thus been severely impaired by the oil boom. In light of this, adequate policy measures need to be taken to resuscitate the manufacturing sector. These measures may include attracting more foreign investment, reducing operating cost in the sector, developing local sources of raw materials, and allocation of more funds from the crude oil revenue to assist the sector. These policy measures may not only resuscitate the manufacturing sector, they would also accelerate growth of the economy as a whole.

The need to understand the stationarity property of inflation of any country is paramount in the design of monetary targeting policy. In this paper, unit root hypotheses of inflation rates in 21 OECD countries are investigated using the newly proposed GARCH-based unit root tests with structural break and trend specifications. The results show that classical tests over-accept unit roots in inflation rates, whereas these tests are not robust to heteroscedasticity. As it is observed from the pre-tests, those tests with structural break reject more null hypotheses of unit roots of most inflation series than those without structural breaks. By applying variants of GARCH-based unit root tests, which include those with structural breaks and time trend regression specifications, we find that unit root tests without time trend give most rejections of the conventional unit roots. Thus, care should be taken while applying variants of the new unit root tests on weak trending time series as indicated in this work. Batteries of unit root tests for discriminating between stationarity and nonstationarity of inflation rates are recommended, since in the case of over-differenced series, wrong policy decision will be made, particularly when inflation series is considered in a cointegrating relationship with other variables.

We extend the Range Unit Root test in two directions. First, we consider the process with time trend and prove that the modified standardized number of new records converges to a sum of two Rayleigh distributions. Second, more general structures of autocorrelated disturbances are also taken into account. Monte Carlo experiments show the good sample properties of this nonparametric unit root test.

This paper studies the effect of macroeconomic fundamentals and demographic change on housing price in Korea. A housing price model is specified as the function of GDP, interest rate, housing construction permit, and working age population to examine the effect. Based on the observation that the variables are non-stationary, unit root and cointegration tests are performed. Unit root test indicates that the variables are non-stationary and first-order integrated. Cointegration test, however, shows that the variables are co-integrated, implying that a stable long-run relationship exists among the variables. Based on the cointegration test result, a vector error correction model is constructed and estimated. The VECM estimation result shows that while GDP and interest rate significantly affect housing price, the effects of housing construction permit and working age population are statistically insignificant. Empirical result of this paper suggests that the macroeconomic fundamentals that affect the demand side of the housing market are important determinants of housing price in Korea.