Comparing two multivariate unit root tests

In this essay, a method for comparing the asymptotic power of the multivariate unit root tests proposed in Phillips & Durlauf (1986) and Flˆores, Preumont & Szafarz (1996) is proposed. In order to determine the asymptotic power of the tests the asymptotic distributions under the null hypothesis and under the set of alternative hypotheses described in Phillips (1988) are determined. In addition, a test which combines characteristics of both tests is proposed and its distributions under the null hypothesis and the same set of alternative hypotheses are determined. This allows us to determine what causes any difference in the asymptotic power of the two tests against the set of alternative hypotheses considered

Multivariate unit root tests

A new multivariate test for the detection ofunit roots is proposed. Use is made ofthe possible correlations between the disturbances of difIerent series, and constrained and unconstrained SURE estimators are employed. The corresponding asymptotic distributions, for the case oftwo series, are obtained and a table with criticai vaIues is generated. Some simulations indivate that the procedure performs better than the existing alternatives.

Mean reversion in stock prices: new evidence from panel unit root tests

Purpose – There are several studies that investigate evidence for mean reversion in stock prices. However, there is no consensus as to whether stock prices are mean reverting or random walk (unit root) processes. The goal of this paper is to re-examine mean reversion in stock prices.
Design/methodology/approach – The authors use five different panel unit root tests, namely the Im, Pesaran and Shin t-bar test statistic, the Levin and Lin test, the Im, Lee, and Tieslau Lagrangian multiplier test statistic, the seemingly unrelated regression test, and the multivariate augmented Dickey Fuller test advocated by Taylor and Sarno.
Findings – The main finding is that there is no mean reversion of stock prices, consistent with the efficient market hypothesis.
Research limitations/implications – One issue not considered by this study is the role of structural breaks. It may be the case that the efficient market hypothesis is contingent on structural breaks in stock prices. Future studies should model structural breaks.
Practical implications – The findings have implications for econometric modelling, in particular forecasting.
Originality/value – This paper adds to the scarce literature on the mean reverting property of stock prices based on panel data; thus, it should be useful for researchers.

Panel unit root tests in the presence of cross-sectional dependence: finite sample performance and an application

This paper examines the finite sample properties of three testing regimes for the null hypothesis of a panel unit root against stationary alternatives in the presence of cross-sectional correlation. The regimes of Bai and Ng (2004), Moon and Perron (2004) and Pesaran (2007) are assessed in the presence of multiple factors and also other non-standard situations. The behaviour of some information criteria used to determine the number of factors in a panel is examined and new information criteria with improved properties in small-N panels proposed. An application to the efficient markets hypothesis is also provided. The null hypothesis of a panel random walk is not rejected by any of the tests, supporting the efficient markets hypothesis in the financial services sector of the Australian Stock Exchange.

Synergy Between an Improved Covariate Unit Root Test and Cross-sectionally Dependent Panel Data Unit Root Tests, with two Applications

This paper proposes the use of an improved covariate unit root test which exploits the cross-sectional dependence information when the panel data null hypothesis of a unit root is rejected. More explicitly, to increase the power of the test, we suggest the utilization of more than one covariate and offer several ways to select the ‘best’ covariates from the set of potential covariates represented by the individuals in the panel. Employing our methods, we investigate the Prebish-Singer hypothesis for nine commodity prices. Our results show that this hypothesis holds for all but the price of petroleum.

GLS Detrending, Efficient Unit Root Tests and Structural Change

We extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models : one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests are tabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. An extensive simulation study analyzes the size and power in finite samples under various methods to select the truncation lag for the autoregressive spectral density estimator. An empirical application is also provided.

Beyond Panel Unit Root Tests: Using Multiple Testing to Determine the Non Stationarity Properties of Individual Series in a Panel

Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of n individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we demonstrate how to use the false discovery rate (FDR) in evaluating I(1)=I(0) classifications based on individual unit root tests when the size of the cross section (n) and time series (T) dimensions are large. We report results from a simulation experiment and illustrate the methods on two data sets.

Do shocks to G7 stock prices have a permanent effect? : evidence from panel unit root tests with structural change

There is a plethora of studies that investigate evidence for the behaviour of stock prices using univariate techniques for unit roots. Whether or not stock prices are characterised by a unit root have implications for the efficient market hypothesis, which asserts that returns of a stock market are unpredictable from previous price changes. The extant literature has found mixed evidence on the integrational properties of stock prices. In this paper, for the first time, we provide evidence on the unit root hypothesis for G7 stock price indices using the Lagrangian multiplier panel unit root test that allows for structural breaks. Our main finding is that stock prices are stationary processes, inconsistent with the efficient market hypothesis.

Examining the behaviour of visitor arrivals to Australia from twenty different countries : an application of panel unit root tests

Testing for the behaviour of visitor arrivals has important implications for policy, for if visitor arrivals are stationary processes then it implies that shocks to visitor arrivals are transitory. However, if visitor arrivals are found to be characterised by a unit root then this implies that shocks to visitor arrivals are permanent. In this paper we provide the first evidence on the unit root hypothesis for visitor arrivals to Australia using a suite of recently developed panel unit root tests. Our main finding is that visitor arrivals to Australia from twenty tourist source markets and from the G7 markets are mean reverting. implying that any shocks will have only a transitory effect. However; visitor arrivals from eight Asian countries are characterised by a unit root. implying that shocks will have a permanent effect on this market.

Are bilateral real exchange rates stationary? Evidence from Lagrange multiplier unit root tests for India

The paper examines the stationarity of India’s real exchange rate vis-a` -vis 16 of its major trading partner countries for the period 1960–2000. Application of the conventional ADF unit root test, the Lagrange multiplier (LM) unit root test with one structural break, and the LM unit root test with two structural breaks provides evidence that India’s exchange rate vis-a` -vis 15 out of 16 countries is stationary, implying support for purchasing power parity.

The purchasing power parity revisited : new evidence for 16 OECD countries from panel unit root tests with structural breaks

In this paper, we apply a range of univariate unit root tests including the Lagrangian multiplier (LM) univariate and panel unit root tests to examine PPP for 16 OECD countries. In addition to incorporating structural breaks in the univariate exchange rate series, we also incorporate structural breaks in the panel exchange rate models. Our main finding from univariate tests, with and without structural breaks and panel LM test with one break, is that real exchange rates are not stationary, inconsistent with PPP hypothesis. However, when we incorporate two structural breaks in the univariate LM test, for most countries we find that real exchange rates are stationary. Moreover, we obtain overwhelming support for PPP when we apply panel LM unit root tests with two structural breaks.

Mean reversion versus random walk in G7 stock prices evidence from multiple trend break unit root tests

This paper provides evidence on the random walk hypothesis in G7 stock price indices using unit root tests which allow for one and two structural breaks in the trend. Of the seven countries we find, at best, evidence of mean reversion in the stock price index of Japan. Thus, overall, our results support the random walk hypothesis. We also consider the implications of the identified structural breaks for movement in stock prices over time. Our main conclusion from this exercise is that the second break in stock prices has had a detrimental effect on movements in stock prices in the G7 countries.

Comparing the small sample properties of two break Lagrange Multiplier unit root tests

In this note, we examine the size and power properties and the break date estimation accuracy of the Lee and Strazicich (LS, 2003) two break endogenous unit root test, based on two different break date selection methods: minimising the test statistic and minimising the sum of squared residuals (SSR). Our results show that the performance of both Models A and C of the LS test are superior when one uses the minimising SSR procedure.