Dickey and fuller 1979 developed a procedure for testing whether a. Dickey fuller tests if a constant or trend belong in the equation we must also use df test stats that adjust for the impact on the distribution of the test statistic see problem set 3 where we included the driftlinear trend in the augmented df test. The occurrence of unit roots in economic time series has far reaching consequences for univariate as well as multivariate econometric modelling. In its most basic form, the dickeyfuller test compares the null hypothesis. Hamilton 1994, 528529 describes the four different cases to which the augmented dickeyfuller test can be applied. Therefore, this study uses the augmented dickey fuller test 1981, which is a modified version of the pioneer work of dickey and fuller 1979 and the phillips and perron 1988 non. This paper was cited in the support documentation for the 2003 nobel prize in economics. Testing the null hypothesis of stationarity against the alternative of a. The composite null hypothesis is that of dd0 against d d0 against d d0, using the generalization of sowells results 1990, we propose a test based on the least favorable case dd0, to control type.
The dickey fuller test 1979 1981 1819 is employed to. Therefore, this study uses the augmented dickeyfuller test 1981, which is a modified version of the pioneer work of dickey and fuller 1979 and the phillips and perron 1988 non. Augmented dickeyfuller table real statistics using excel. Hamilton1994, 528529 describes the four different cases to which the augmented dickeyfuller test can be. The augmented englegranger cointegration test result. Differencing and unit root tests new york university. Nonstationary time series andunitroottests heino bohn nielsen 1of25 introduction many economic time series are trending. It was the paper by nelson and plosser 1982 that sparked the huge surge in interest for unit root models among economists. In statistics, the dickeyfuller test tests the null hypothesis that a unit root is present in an autoregressive model. Stationary ar1 y d a test involving much more narrowlyspeci. Dickey fuller test, augmented dickey fuller test, stationarity, nonstationary.
Dickey and fuller 1979 and dickey and fuller 1981 derived this distribution under the assumption that the order of the underlying autoregressive process is. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trendstationarity. Dickey and fuller 1979 show that under the null hypothesis of a unit root, this statistic does not follow the conventional students tdistribution, and they derive asymptotic results and simulate critical values for various test and sample sizes. Augmented dickeyfuller test performed regression in package urca. Distribution of the estimators for autoregressive time series with a unit root, j.
Fullerdistribution of the estimators for autoregressive time series with a unit root. Unit root test, augmented dickeyfuller test, phillipsperron test, kpss test, adfgls test. The role of the initial condition steven cook university of wales swansea abstract the relationship between the initial condition of time series data and the power of the dickey. It is named after the statisticians david dickey and wayne fuller, who developed the test in 1979. Dftest and adf test dickey and fuller, 1979, phillipsperron test phillips and. Dickeyfuller type of tests against nonlinear dynamic models. In section 4 the monte carlo method is used to compare the power of the statistics t and a with that of qk. Journal of the american statistical association, june 1979.
Augmented dickey fuller test by rizwan mushtaq ssrn. Article pdf available in journal of the american statistical association 74366 june 1979 with 5,776 reads. When using dickeyfuller unit root tests dickey and fuller 1979 practitioners typically employ lefttailed versions of the tests with the alternative hypothesis of level stationarity or trend stationarity. Selection of unit root test on the basis of length of. This chapter is concerned with some of the basic issues underlying testing for a unit root using least squares ls and related estimation methods. Determinants of stock market performance in nigeria. The authoritative paper by phillips 1987 sums up most of the theory. Bartlett type correction, unit root test, monte carlo simulation, bootstrap 1. However, their representation did not utilize functions of.
In statistics, the dickeyfuller test tests the null hypothesis that a unit root is present in an. Seeq53 dickey fuller test the df test for unit root is actually based on the ar. Reviewing this test and variants thereof we focus on the importance of. As we cannot do this based solely on the visual analysis of the series, as this is an informal test for stationarity, some formal tests should apply. Distribution of the estimators for autoregressive time. For example, dickey and fuller 1979, phillips and perron 1988. Finitesample properties of the glsbased dickeyfuller. The oldest and most widely used test is due to dickey and fuller 1979. Dickey, hasza, and fuller, 1984, the probdf function can be expected to produce results that are substantially more accurate than the critical values reported in. June 1979 are also generalized to models containing intercept and time terms. The properties of the time series variables are examined using the augmented dickeyfuller adf unit root test and most of the incorporated variables in the study was found to have a unit root at level. Using localtounity detrending, the glsbased dickeyfuller test has been shown to possess higher power than other available unit root tests. Representations for the limit distributions of the estimator of p and of the. Following dickey and fuller, 1979, dickey and fuller, 1981, the t statistic will be recorded as.
Pdf distribution of the estimators for autoregressive. The null hypothesis is always that the variable has a unit root. Because the number of simulation replications used to produce the probdf function is much greater than the 60,000 replications used by dickey and colleagues dickey and fuller, 1979. Pour pallier a cela, des auteurs comme dickey et fuller 1979, 1981 vont. An understanding of these issues is necessary to interpret developments subsequent to the seminal work of dickey 1976. More recently, mackinnon 1991, 1996 implements a much larger set of simulations than those. This paper proposes a new testing procedure for the degree of fractional integration of a time series inspired on the unit root test of dickeyfuller 1979. Properties of the regression estimator of p are obtained under the assumption that p 1. Therefore, unit root tests are nowadays the starting point of most empirical time series studies. To determine the number of lags, k, we can use the normal procedures. Fuller 1976, dickey and fuller 1979,1981, and evans and savin 1981,1984.
Dickeyfuller tests if a constant or trend belong in the equation we must also use df test stats that adjust for the impact on the distribution of the test statistic see problem set 3 where we included the driftlinear trend in the augmented df test. Distribution of the estimators for autoregressive time series with a unit root. The asymptotic size and power of the augmented dickey. Bootstrap versus bartlett type correction of the dickey. Lecture 6 stationarity and cointegration stationary. This study examines critically the longrun macroeconomic determinants of stock market performance in nigeria between 1984 and 2007. The df is generalized into the augmented df test to accommodate the general. The basic objective of the test is to test the null hypypothesis that. Introduction more than 30 years after the seminal work of fuller 1976 and dickey and fuller 1979, 1981, the issue of whether a time series is generated by a unit root process or not is still an area of great interest. A strategic study on foreign fund utilization in chinese. Finitesample properties of the glsbased dickeyfuller test in the presence of breaks in innovation variance steven cook university of wales swansea abstract. In these gures it is also seen that a random walk is a relevant null hypothesis in lstar type of models, i. This note shows that the augmented dickeyfuller test is consi stent against. Let n observations y 1, y 2, y n be generated by the model y t py t.
Dickey and fuller 1979, 1981 and said and dickey 1984, usually referred as df and adf tests respectively, testing unit root has become routine in empirical. The basic objective of the test is to test the null hypothesis that. A computer program to run a monte carlo experiment. Dickey fuller test the earlyyp g g and pioneering work on testing for a unit root in time series was done by dickey and fuller dickey and fuller 1979, fuller 1976. Distribution of estimators for autoregressive time series. Fractional integration and the augmented dickeyfuller test1. Said and dickey 1984 extended this result for the case where the. Dickeyfuller test the earlyyp g g and pioneering work on testing for a unit root in time series was done by dickey and fuller dickey and fuller 1979, fuller 1976.
Augmented dickeyfuller table if the calculated tau value is less than the critical value in the table above, then we have a significant result. Simple fractional dickey fuller test munich personal. Dickey and fuller 1979 developed a procedure for testing whether a variable has a unit root or, equivalently, that the variable follows a random walk. Dickeyfuller test an overview sciencedirect topics. Stationarity and unit root testing why do we need to test for nonstationarity. The dickey fuller test 1979 1981 1819 is employed to examining the stationarity from economic 214 at stellenbosch universitysouth africa.
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