REGRESSION THEORY FOR NEARLY COINTEGRATED TIME SERIES

2002 ◽  
Vol 18 (6) ◽  
pp. 1309-1335 ◽  
Author(s):  
Michael Jansson ◽  
Niels Haldrup
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Power Functions ◽  
Asymptotic Power ◽  
Cointegration Tests ◽  
Local Asymptotic Power ◽  
Regression Theory

This paper proposes a notion of near cointegration and generalizes several existing results from the cointegration literature to the case of near cointegration. In particular, the properties of conventional cointegration methods under near cointegration are characterized, thereby investigating the robustness of cointegration methods. In addition, we obtain local asymptotic power functions of five cointegration tests that take cointegration as the null hypothesis.

Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power

1995 ◽  
Vol 11 (5) ◽  
pp. 1148-1171 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Unit Root ◽  
Convex Combination ◽  
Ordinary Least Squares ◽  
Power Functions ◽  
Large Power ◽  
Unit Root Testing ◽  
Local Asymptotic Power ◽  
Fuller Distribution

In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation.The paper derives the asymptotic distribution of ordinary least-squares estimates of the largest autoregressive root and its t-statistic. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a convex combination of the Dickey-Fuller distribution and the standard normal, the mixture depending on the correlation between the equation error and the regression covariates. The local asymptotic power functions associated with these test statistics suggest enormous gains over the conventional unit root tests. A simulation study and empirical application illustrate the potential of the new approach.

THE LOCAL ASYMPTOTIC POWER OF CERTAIN TESTS FOR FRACTIONAL INTEGRATION

1999 ◽  
Vol 15 (5) ◽  
pp. 704-709 ◽  
Author(s):  
Jonathan H. Wright
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Fractional Integration ◽  
Empirical Work ◽  
Local Alternatives ◽  
Asymptotic Power ◽  
Rescaled Range ◽  
Partial Sum Process ◽  
Local Asymptotic Power ◽  
Range Test

It is possible to construct a test of the null of no fractional integration that has nontrivial asymptotic power against a sequence of alternatives specifying that the series is I(d) with d = O(T−1/2), where T is the sample size. In this paper, I show that tests for fractional integration that are based on the partial sum process of the time series have only trivial asymptotic power (i.e., equal to the size) against this sequence of local alternatives. These tests include the rescaled-range test. In this sense, despite its widespread use in empirical work, the rescaled-range test is a poor test for fractional integration.

scholarly journals Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown

1994 ◽  
Vol 10 (3-4) ◽  
pp. 672-700 ◽  
Author(s):  
Graham Elliott ◽  
James H. Stock
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Critical Values ◽  
Asymptotic Power ◽  
Time Series Regression ◽  
Second Stage ◽  
Alternative Approach ◽  
Local Asymptotic Power ◽  
Size Distortions ◽  
Correct Size

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible situations. We then propose an alternative approach in which the second-stage critical values depend continuously on a first-stage statistic that is informative about the order of integration of the regressor. This procedure has the correct size asymptotically and good local asymptotic power.

ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

2014 ◽  
Vol 31 (3) ◽  
pp. 539-559 ◽  
Author(s):  
I. Gaia Becheri ◽  
Feike C. Drost ◽  
Ramon van den Akker
Keyword(s):  
Unit Root ◽  
Generalized Least Squares ◽  
Applied Economics ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Optimal Tests ◽  
Independent Panel ◽  
Local Asymptotic Power ◽  
Uniformly Most Powerful

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

TESTING TIME-SERIES STATIONARITY AGAINST AN ALTERNATIVE WHOSE MEAN IS PERIODIC

2001 ◽  
Vol 5 (3) ◽  
pp. 380-412 ◽  
Author(s):  
Melvin A. Hinich ◽  
Phillip Wild
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Real World ◽  
Null Hypothesis ◽  
Data Sets ◽  
Testing Time ◽  
Economic Data ◽  
The Mean ◽  
Important Form ◽  
Real World Problems

We develop a test of the null hypothesis that an observed time series is a realization of a strictly stationary random process. Our test is based on the result that the kth value of the discrete Fourier transform of a sample frame has a zero mean under the null hypothesis. The test that we develop will have considerable power against an important form of nonstationarity hitherto not considered in the mainstream econometric time-series literature, that is, where the mean of a time series is periodic with random variation in its periodic structure. The size and power properties of the test are investigated and its applicability to real-world problems is demonstrated by application to three economic data sets.

Determinants of international tourism demand: Evidence from Australian states and territories

2018 ◽  
Vol 25 (2) ◽  
pp. 274-296 ◽  
Author(s):  
Muhammad Shafiullah ◽  
Luke Emeka Okafor ◽  
Usman Khalid
Keyword(s):  
Time Series ◽  
State Level ◽  
International Tourism ◽  
Tourism Demand ◽  
Causality Analysis ◽  
Foreign Born ◽  
Demand Model ◽  
Explanatory Variables ◽  
Cointegration Tests ◽  
World Income

This article explores whether the determinants of international tourism demand differ by states and territories in Australia. This is the first attempt at econometric modelling of international tourism demand in the states and territories of Australia. A demand model is specified where international visits to states and territories is a function of world income, state-level transportation costs, stock of foreign-born residents, the Australian real exchange rate and the price levels of international and domestic substitutes. Panel and time series econometric techniques are employed to test the model variables for stationarity, cointegration and direction of causality. Panel and time series cointegration tests show that the model is cointegrated. The causality analysis indicates that all explanatory variables Granger cause international visits to the Australian states and territories. Further, we show that the impacts of the determinants of international tourism vary by states and territories. The results underscore the importance of targeted policymaking that takes into account the economic and social structure of each state and territory instead of designing tourism policies on the basis of one-size-fits-all approach.

How Smart Is my Dummy? Time Series Tests for the Influence of Politics

2005 ◽  
Vol 13 (1) ◽  
pp. 77-94 ◽  
Author(s):  
Tony Caporale ◽  
Kevin Grier
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Potential Problem ◽  
Time Series Data ◽  
Political Influence ◽  
Single Equation ◽  
Series Data ◽  
The Political ◽  
Dummy Variables ◽  
Inference Problems

Of necessity, many tests for political influence on policies or outcomes involve the use of dummy variables. However, it is often the case that the hypothesis against which the political dummies are tested is the null hypothesis that the intercept is otherwise constant throughout the sample. This simple null can cause inference problems if there are (nonpolitical) intercept shifts in the data and the political dummies are correlated with these unmodeled shifts. Here we present a method for more rigorously testing the significance of political dummy variables in single equation models estimated with time series data. Our method is based on recent work on detecting multiple regime shifts by Bai and Perron. The article illustrates the potential problem caused by an overly simple null hypothesis, exposits the Bai and Perron model, gives a proposed methodology for testing the significance of political dummy variables, and illustrates the method with two examples. Before the curse of statistics fell upon mankind we lived a happy, innocent life—Hilaire Belloc, On Statistics

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