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on Econometric Time Series |
| By: | Morten Ørregaard Nielsen (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | In this paper a nonparametric variance ratio testing approach is proposed for determining the number of cointegrating relations in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach. |
| Keywords: | Cointegration rank, cointegration space, fractional integration and cointegration, interest rates, long memory, nonparametric, term structure, variance ratio |
| JEL: | C32 |
| Date: | 2009–01–12 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-02&r=ets |
| By: | Giuseppe Cavaliere (Department of Statistical Sciences, University of Bologna); Anders Rahbek (Department of Economics, University of Copenhagen); A. M. Robert Taylor (University of Nottingham) |
| Abstract: | Many key macro-economic and ?nancial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identi?ed inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice. |
| Keywords: | co-integration; non-stationary volatility; trace and maximum eigenvalue tests; wild bootstrap |
| JEL: | C30 C32 |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0834&r=ets |
| By: | Konstantinos Fokianos (Department of Mathematics & Statistics, University of Cyprus); Anders Rahbek (Department of Economics, University of Copenhagen); Dag Tjøstheim (Department of Mathematics, University of Bergen) |
| Abstract: | This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some transaction data. Our approach to verifying geometric ergodicity proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen to be arbitrarily small, the differences between the perturbed and non-perturbed versions vanish as far as the asymptotic distribution of the parameter estimates is concerned. |
| Keywords: | generalized linear models; non-canonical link function; count data; Poisson regression; likelihood; geometric ergodicity; integer GARCH; observation driven models; asymptotic theory |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0835&r=ets |
| By: | Marc Hallin; Ramon van den Akker; Bas Werker |
| Abstract: | We propose a class of simple rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is guaranteed by distribution-freeness, irrespective of the value of the drift and the actual underlying f. When based on a Gaussian reference density g, our tests (of the van der Waerden form) perform uniformly better, in terms of asymptotic relative effciency, than the Dickey and Fuller test --except under Gaussian f, where they are doing equally well. Under Student t3 density f, the effciency gain is as high as 110%, meaning that Dickey-Fuller requires over twice as many observations as we do in order to achieve comparable performance. This gain is even larger in case the underlying f has fatter tails; under Cauchy f, where Dickey and Fuller is no longer valid, it can be considered infinite. The test associated with reference density g is semiparametrically e±cient when f happens to coincide with g, in the ubiquitous case that the model contains a non-zero drift. Finally, with an estimated density f(n) substituted for the reference density g, our tests achieve uniform (with respect to f) semiparametric e±ciency. |
| Keywords: | Dickey-Fuller test, Local Asymptotic Normality |
| JEL: | C12 C22 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2009_001&r=ets |
| By: | Oliver Blaskowitz; Helmut Herwartz |
| Abstract: | Common approaches to test for the economic value of directional forecasts are based on the classical Chi-square test for independence, Fisher’s exact test or the Pesaran and Timmerman (1992) test for market timing. These tests are asymptotically valid for serially independent observations. Yet, in the presence of serial correlation they are markedly oversized as confirmed in a simulation study. We summarize serial correlation robust test procedures and propose a bootstrap approach. By means of a Monte Carlo study we illustrate the relative merits of the latter. Two empirical applications demonstrate the relevance to account for serial correlation in economic time series when testing for the value of directional forecasts. |
| Keywords: | Directional forecasts, directional accuracy, forecast evaluation, testing independence, contingency tables, bootstrap |
| JEL: | C32 C52 C53 E17 E27 E47 F17 F37 F47 G11 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2008-073&r=ets |
| By: | Markku Lanne; Helmut Luetkepohl |
| Abstract: | The role of expectations for economic fluctuations has received considerable attention in recent business cycle analysis. We exploit Markov regime switching models to identify shocks in cointegrated structural vector autoregressions and investigate different identification schemes for bivariate systems comprising U.S. stock prices and total factor productivity. The former variable is viewed as re°ecting expectations of economic agents about future productivity. It is found that some previously used identification schemes can be rejected in our model setup. The results crucially depend on the measure used for total factor productivity. |
| Keywords: | Cointegration, Markov regime switching model, vector error correction model, structural vector autoregression, mixed normal distribution |
| JEL: | C32 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/29&r=ets |
| By: | Jeffrey A. Mills |
| Abstract: | Mills (2008) examines an alternative procedure for testing precise hypotheses based on specifying a set of precise alternative hypotheses. Mills shows that this method resolves several problems with the standard procedure, particularly the Jeffreys-Lindley-Bartlett paradox, and has desirable properties. This paper applies this new testing procedure to the unit root hypothesis for an AR(1) model. A Monte Carlo simulation experiment is conducted to study the performance of the test in terms of robustness to the specification of the prior distribution. The resulting new test is compared with the best alternatives, namely the tests of Conigliani and Spezzaferri (2007) and Elliot, Rothenberg and Stock (1996). |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:cin:ucecwp:2009-02&r=ets |