Augmented Dickey-Fuller Regression Research Articles

NONSTATIONARY LINEAR PROCESSES WITH INFINITE VARIANCE GARCH ERRORS

Recently, Cavaliere, Georgiev, and Taylor (2018, Econometric Theory 34, 302–348) (CGT) considered the augmented Dickey–Fuller (ADF) test for a unit-root model with linear noise driven by i.i.d. infinite variance innovations and showed that ordinary least squares (OLS)-based ADF statistics have the same distribution as in Chan and Tran (1989, Econometric Theory 5, 354–362) for i.i.d. infinite variance noise. They also proposed an interesting question to extend their results to the case with infinite variance GARCH innovations as considered in Zhang, Sin, and Ling (2015, Stochastic Processes and their Applications 125, 482–512). This paper addresses this question. In particular, the limit distributions of the ADF for random walk models with short-memory linear noise driven by infinite variance GARCH innovations are studied. We show that when the tail index $\alpha <2$ , the limit distributions are completely different from that of CGT and the estimator of the parameters of the lag terms used in the ADF regression is not consistent. This paper provides a broad treatment of unit-root models with linear GARCH noises, which encompasses the commonly entertained unit-root IGARCH model as a special case.

Semi-parametric real exchange rates dynamics

A flexible semi-parametric augmented Dickey Fuller (ADF) regression is proposed to explore real exchange rate dynamics for 16 countries over the twentieth century, and to estimate half-lives. Departing from existing literature, the present approach does not impose a functional form of the ADF regression and encompasses parametric extensions. Significant impediments to real exchange rates adjustment are found, and estimated half-lives are longer than those reported by earlier studies. These findings reveal a dismal PPP performance, difficulties in designing profitable strategies based on mean-reversion, complexities in production relocation policies by firms to reduce exchange rate risk, and carry implications for foreign subsidiary ownership structure.

A Speedy and Seamless Stationarity Analysis via causfinder Package in R

Stationarity analysis is a must for various studies in many fields that employ time series analysis. adfcs function in causfinder package in R performs Augmented Dickey-Fuller (ADF) test that takes into account the usage of same (i.e., common) sub-sample for all of the lag orders for the autoregressive process when stationarity is investigated. As is known, in all of the lag selection procedures in econometrics, same sub-sample must be used to determine the correct optimal minimum lag. We bouqoueted adfcs functions in adfcstable function whose functional value is a table that reveals all of the needed stationarity analysis of all the variables in a given system in a couple of seconds. In the returned ADF table, the results of all of the three standard cases (“both drift and time trend”, “drift without time trend” and “no drift, no time trend”) are presented for all of the variables in question. Whether the drift and time trend coefficients in the ADF regressions is significant is specified. adfcstable reveals the inconclusivities of ADF tests (the coefficient of the 1st lag of the dependent variable in the right of ADF regression is not “<0”; in the left, the dependent variable appear with the differenced form) whenever there appears such cases. It also presents optimal minimum lag order for the ADF regressions. We used three datasets from various fields: a dataset of functional integration of brain, a dataset for the determinants of foreign direct investment in Turkey, and a dataset for the determinants of current account deficit of Turkey.

THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS

In this paper we investigate the impact of persistent (nonstationary or near nonstationary) cycles on the asymptotic and finite-sample properties of standard unit root tests. Results are presented for the augmented Dickey–Fuller (ADF) normalized bias andt-ratio-based tests (Dickey and Fuller, 1979,Journal of the American Statistical Association745, 427–431; Said and Dickey, 1984;Biometrika71, 599–607). the variance ratio unit root test of Breitung (2002,Journal of Econometrics108, 343–363), and theMclass of unit-root tests introduced by Stock (1999, in Engle and White (eds.),A Festschrift in Honour of Clive W.J. Granger) and Perron and Ng (1996,Review of Economic Studies63, 435–463). We show that although the ADF statistics remain asymptotically pivotal (provided the test regression is properly augmented) in the presence of persistent cycles, this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that thet-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994,Journal of Business &amp; Economic Statistics17, 461–470; Ng and Perron, 1995,Journal of the American Statistical Association90, 268–281) used to determine the order of augmentation in the ADF regression remain valid in the presence of persistent cycles.

Modified fast double sieve bootstraps for ADF tests

This paper studies the finite sample performance of the sieve bootstrap augmented Dickey-Fuller (ADF) unit root test. It is well known that this test’s accuracy in terms of rejection probability under the null depends greatly on the underlying DGP. Through extensive simulations, we find that it also depends on the number of lags employed in the bootstrap DGP and in the bootstrap ADF regression. Based on this finding and using some well established theoretical results, we propose a simple modification that significantly improves the test’s accuracy. We also introduce different versions of the fast double bootstrap, each modified according to the same theoretical basis. According to our simulations, these new testing procedures have lower error in rejection probability under the null while retaining good power.

Real Exchange Rate Dynamics Under The Current Float: A Re–Examination

Augmented Dickey–Fuller regressions on pooled (but not individual) real exchange rates for the post–1973 period consistently reject the unit root null, even after accounting for cross–sectional dependence. The inference that the series is stationary, however, is not necessarily correct, because these tests strongly over–reject the null in certain circumstances, particularly when the series has a stochastic unit root. We find that bilateral real exchange rates against the US dollar have a stochastic unit root. Out–of–sample prediction exercises for an autoregressive model confirm these findings.

F-tests for lag length selection in augmented Dickey–Fuller regressions: some Monte Carlo evidence

This paper investigates the empirical performance of sequential f-tests as a criterion for selecting the lag length in Augmented Dickey-Fuller regressions. This criterion performs approximately as well as the AIC and a criterion based on eliminating residual autocorrelation. However, no single criterion is clearly superior to the other two.

Testing for Unit Roots and Non‐linear Transformations

It is well known that the augmented Dickey–Fuller (ADF) test of unit roots in univariate time series is sensitive to non‐linear transformations: a common example is when variables expressed in logarithms are found to be stationary, whereas the same variables in levels are found to be non‐stationary. In this paper, the effects of non‐linear transformations on the ADF auxiliary regression are investigated within the class of the Box–Cox model, and a test of non‐linear transformation is developed to assess the adequacy of the ADF regression. The proposed test is computationally simple and is calculated as thet ratio of an added variable in the ADF regression. Cointegration among series which are subject to non‐linear transformations is also analysed, and a simple procedure is developed to test the non‐linear transformation used in cointegration analysis. Several empirical examples taken from the Nelson–Plosser data set illustrate the practical relevance of the proposed test for univariate series, and a second empirical example is used to illustrate the test of non‐linear transformation for cointegrated series

Alternative stratetgies for ‘augmenting’ the dickey-fuller test: size-robustness in the face of pre-testing

The outcome of the ‘augmented’ Dickey-Fuller test for unit roots can be sensitive to the chosen degree of augmentation in the Dickey-Fuller regression. Researchers use a variety of pre-testing techniques to choose this augmentation level, with commensurate implications for the properties of the test. We consider six broad selection strategies which match or mimic some of the procedures encountered in practice, and focus on the true (as opposed to nominal) size of the test in the face of such pre-testing. On balance, our results favour the strategy incorporated into the SHAZAM package in relatively small samples; and favour determining the augmentation level on the basis of the autocorrelation and partial autocorrelation functions of the residuals of the augmented Dickey-Fuller regression when the sample is larger.