Residual-based Tests For Cointegration Research Articles

Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics

A Lagrange multiplier test of the null hypothesis of cointegration in fractionally cointegrated models is proposed. The test statistic uses fully modified residuals to cancel the endogeneity and serial correlation biases, and standard asymptotic properties apply under the null and under local alternatives. With iid Gaussian errors, the asymptotic Gaussian power envelope of all (unbiased) tests is achieved by the one-sided (two-sided) test. The finite-sample properties are illustrated by a Monte Carlo study. In an application to the dynamics among exchange rates for seven major currencies against the U.S. dollar, mixed evidence of the existence of a cointegrating relation is found.

The power of residual-based tests for cointegration when residuals are fractionally integrated

We establish divergence rates of various residual-based cointegration tests under fractional cointegration, and show that the power of these tests is rather poor.

A Reassessment Of Balance Of Payments Constrained Growth: Results From Panel Unit Root And Panel Cointegration Tests

The paper reassesses the empirical evidence for Thirlwall's law in seven industrial countries by using panel unit root and panel cointegration tests including Johansen maximum likelihood cointegration tests. Current practice restricts attention to time series residual based cointegration tests, which are known to have low power and are subject to normalization problems. Since economic time series are typically short, it is desirable to exploit panel data in order to draw sharper inferences. The empirical results reveal that imports are cointegrated with terms of trade and income (although residual-based tests indicate the opposite). We find that, with the exception of Australia, Thirlwall's law holds. [C22, C23, O40, O57]

Testing for long-run stability - an application to money multiplier in India

In testing for a stable long-run relation between monetary aggregates and reserve money most previous studies have used the conventional tests for cointegration. Using the recently developped residual-based cointegration tests of Gregory and Hansen that explicitly allow for regime shifts, the present paper, contrary to the findings of previous studies, finds that there exists a stable, but time-varying, longrun relation between measures of money stock and reserve money in the Indian context. It also finds that the observed variation in cointegrating relations is better characterized by a discrete one-time shift, rather than a gradually evolving random walk process, attributable, probably, to discrete changes in monetary policy.

Residual-based tests for fractional cointegration

This paper reports an extensive Monte Carlo study of six residual-based tests of the hypothesis of no cointegration against the alternative of fractional cointegration. Critical values, power and size are simulated and compared. It turns out that the Lobato–Robinson LM test, the Geweke–Porter-Hudak test and the two Phillips–Perron tests exhibit severe size distortions. On the other hand, the augmented Dickey–Fuller test and the modified rescaled range test show only moderate size distortions but are generally less powerful. In addition, the impact and possible treatment of trends in the individual series, and in the cointegration equilibrium, are discussed.

Spurious regression and residual-based tests for cointegration in panel data

In the first half of the paper I study spurious regressions in panel data. Asymptotic properties of the least-squares dummy variable (LSDV) estimator and other conventional statistics are examined. The asymptotics of LSDV estimator are different from those of the spurious regression in the pure time-series. This has an important consequence for residual-based cointegration tests in panel data, because the null distribution of residual-based cointegration tests depends on the asymptotics of LSDV estimator. In the second half of the paper I study residual-based tests for cointegration regression in panel data. I study Dickey–Fuller (DF) tests and an augmented Dickey–Fuller (ADF) test to test the null of no cointegration. Asymptotic distributions of the tests are derived and Monte Carlo experiments are conducted to evaluate finite sample properties of the proposed tests.

Weighted symmetric tests for cointegration based on residual

Weighted symmetric estimation of Fantuia et al. (1994) and Shin and So(1997) is employed to improve powers of residual-based tests for cointegration. The augmented Dickey-Fuller tests and the semiparametnc tests are considered. A Monte Carlo investigation reveals that tests based on the weighted symmetric estimator have better powers than those based on the ordinarv least souares estimator.Limiting distributions of the weighted symmetric tests are derived.

Are the Greek budget deficits too large?

We use a residual-based cointegration test suggested by Gregory and Hansen that allows for the determination of a structural break in the cointegration vector to test for the sustainability of Greek fiscal deficits over the 1958–92 period. This relatively recent test leads to a different result from that derived from standard Engle–Granger cointegration tests. The use of the conventional Engle–Granger test implies no cointegration between tax revenues and interest-inclusive government expenditures. On the other hand, using the Gregory–Hansen test we conclude that tax revenues and interest-inclusive government expenditures are cointegrated and a structural break in the cointegrating vector took place in either 1981 or 1983. Our result of cointegration with a structural break is consistent with a strict interpretation of the government's intertemporal budget constraint since it implies a zero discounted value of the public debt. However, since the cointegration-regression slope parameter is significantly le...

Residual-based tests for cointegration in models with regime shifts

In this paper we examine tests for cointegration which allow for the possibility of regime shifts. We propose ADF-, Z α-, and Z t -type tests designed to test the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift. In particular we consider cases where the intercept and/or slope coefficients have a single break of unknown timing. A formal proof is provided for the limiting distributions of the various tests for the regime shift model (both a level and slope change). Critical values are calculated for the tests by simulation methods and a simple Monte Carlo experiment is conducted to evaluate finite-sample performance. In the limited set of experiments, we find that the tests can detect cointegrating relations when there is a break in the intercept and/or slope coefficient. For these same experiments, the power of the conventional ADF test with no allowance for regime shifts falls sharply. As an illustration we test for structural breaks in the U.S. long-run money-demand equation using annual and quarterly data.

PREDICTIVE POWER OF THE TERM STRUCTURE IN AUSTRALIA IN THE LATE 1980'S: A NOTE

Abstract:The Market Expectations Theory of the Term Structure of Interest Rates is tested using Wednesday yields on 13 week and 26 week treasury notes and 90 and 180 day bank accepted bills for the period 3 December 1986 to 13 March 1991 obtained from the Reserve Bank of Australia. In ordinary least squares regression based tests the Market Expectations Theory of the Term Structure of Interest Rates is accepted for bank accepted bills but rejected for treasury notes. Augmented Dickey Fuller unit root tests provide evidence of non‐stationarity in the variables; a possibility often ignored in Australian studies. Although the unit root tests are generally consistent with the existence of one unit root, residual based cointegration tests between the forward rate and spot rate are not consistent with cointegration. This suggests that the prior expectations theory results may be a result of spurious regression. Perhaps a more complex model is required, coupled with tests which take account of non‐stationary time series.

Durbin-Hausman tests for cointegration

We develop Durbin-Hausman tests for cointegration which use regression residuals. The asymptotic distributions of the Durbin-Hausman tests are derived under the null and the rates of divergence under the alternative are obtained. The asymptotic distributions are tabulated by simulation. We also show by simulation that the Durbin-Hausman tests are more powerful in finite samples than the other existing residual-based tests for cointegration.

Spurious regressions and residual-based tests for cointegration when regressors are cointegrated

We study a spurious regression with cointegrated regressors. Asymptotic properties of the OLS estimates and other conventional statistics are reported. Using these results, we analyze the asymptotic null distributions of such residual-based cointegration tests as Phillips' Ž ∝ and the augmented Dickey–Fuller (ADF) tests, when regressors are cointegrated.

Residual based tests for cointegration: A Monte Carlo study of size distortions

This paper compares seven residual based tests for cointegration with the Monte Carlo method. First-order moving average components lead to substantial size distortions for all tests. Among the tests considered, Engle and Granger's ( Econometrica, 1987, 55, 251–276) augmented Dickey-Fuller (ADF) test show the least size distortions.

Is there trend reversion in purchasing power parity?

This study presents some empirical evidence on purchasing power parity (PPP) using residualbased co-integration tests. Engle and Granger's (1987) tests and the ratio of the variance of higher-order differences to the variance of the first difference of the residuals of the cointegrating regression are used. Monthly data, over a span of 30 years, do not provide any empirical support to the theory. Conversely, in the annual data long-run equilibrium tendencies are evident. Since PPP has been widely used to provide an anchor for the equilibrium exchange rate, our results indicate that such an assumption is not completely inadequate.

Asymptotic Properties of Residual Based Tests for Cointegration

This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript alpha) and Z(subscript t) unit root tests. Two new tests are also introduced. The tests are shown to be asymptotically similar, and simple representations of their limiting distributions are given and asymptotic critical values are tabulated. The ADF and Z(subscript t) tests are asymptotically equivalent. Power properties of the test are also studied. The tests are consistent if suitably constructed, but the ADF and Z(subscript t) tests have slower rates of divergence under cointegration than the other tests. Copyright 1990 by The Econometric Society.