On the properties of the Dickey-Pantula test against fractional alternatives

The limit properties of the testing sequence underlying the Dickey-Pantula test for a double unit root in a time series are derived when the true data generating process is assumed to be nonstationary fractionally integrated.Publicad

Asymptotic inference results for multivariate long-memory processes

In this paper, we extend the well-known Sims, Stock and Watson (SSW)(Sims et al. 1990; Econometrica 56, 113?44), analysis on estimation and testing in vector autoregressive process (VARs) with integer unit roots and deterministic components to a more general set-up where non-stationary fractionally integrated (NFI) processes are considered. In particular, we focus on partial VAR models where the conditioning variables are NFI since this is the only finite-lag VAR model compatible with such processes. We show how SSW?s conclusions remain valid. This means that whenever a block of coefficients in the partial VAR can be written as coefficients on zero-mean I(0) regressors in models including a constant term, they will have a joint asymptotic normal distribution. Monte Carlo simulations and an empirical application of our theoretical results are also provided.Publicad

Instrumental Variable Interpretation of Cointegration with Inference Results for Fractional Cointegration

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that, in the I(1) case, with a semiparametric correction simpler than the one required for the fully modified ordinary least squares (FM-OLS), our fully modified instrumental variables (FM-IV) estimator is median-unbiased, a mixture of normals, and asymptotically efficient. As a consequence, standard inference can be conducted with this new FM-IV estimator of the cointegrating parameter. We show by the use of Monte Carlo simulations that the small sample gains with the new IV estimator over OLS are remarkable.Publicad

How spurious features arise in case of fractional cointegration

It is well-known that a linear regression among the levels of independent highly persistent processes yields high values of the corresponding coefficient of determination along with divergent I-ratios and low values of the Durbin-Watson statistic. In fact, such a behaviour of the customary OLS statistics has become a sort of definition of the so-called spurious regressions in econometrics. In this paper, however, we show how these spurious stylized facts also arise among nonstationary (fractionally) cointegrated processes

Effects of Applying Linear and Nonlinear Filters on Tests for Unit Roots with Additive Outliers

Conventional univariate Dickey-Fuller tests tend to produce spurious stationarity when there exist additive outlying observations in the time series. Correct critical values are usually obtained by adding dummy variables to the Dickey-Fuller regression. This is a nice theoretical result but not attractive from the empirical point of view since almost any result can be obtained just by a convenient selection of dummy variables. In this paper we suggest a robust procedure based on running Dickey-Fuller tests on the trend component instead of the original series. We provide both finite-sample and large-sample justifications. Practical implementation is illustrated through an empirical example based on the US/Finland real exchange rate series.Additive outliers, Dickey-Fuller test, Linear and nonlinear filtering, Bootstrap

Instrumental Variable Interpretation of Cointegration with Inference Results for Fractional Cointegration.

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that, in the I(1) case, with a semiparametric correction simpler than the one required for the fully modified ordinary least squares (FM-OLS), our fully modified instrumental variables (FM-IV) estimator is median-unbiased, a mixture of normals, and asymptotically efficient. As a consequence, standard inference can be conducted with this new FM-IV estimator of the cointegrating parameter. We show by the use of Monte Carlo simulations that the small sample gains with the new IV estimator over OLS are remarkable.

Bargaining Multiple Issues with Leximin Preferences

Global bargaining problems over a finite number of different issues, are formalized as cartesian products of classical bargaining problems. For maximin and leximin bargainers we characterize global bargaining solutions that are efficient and satisfy the requirement that bargaining separately or globally leads to equivalent outcomes. Global solutions in this class are constructed from the family of monotone path solutions for classical bargaining problems.Global bargaining, maximin preferences, leximin preferences