Anders Rygh Swensen

Testing exact rational expectations in cointegrated vector autoregressive models

Abstract This paper considers the testing of restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I (1) variables. If the rational expectations involve one-step-ahead observations only and the coefficients are known, an explicit parameterization of the restrictions is found, and the maximum-likelihood estimator is derived by regression and reduced rank regression. An application is given to a present value model.

Bootstrapping unit root tests for integrated processes

In this paper, we consider two bootstrap algorithms for testing unit roots under the condition that the observed process is unit root integrated. The first method consists of generating the resampled data after fitting an autoregressive model to the first differences of the observations. The second method consists of applying the stationary bootstrap to the first differences. Both procedures are shown to give methods that approach the correct asymptotic distribution under the null hypothesis of a unit root. We also present a Monte-Carlo study comparing the two methods for some ARIMA models. Copyright 2003 Blackwell Publishing Ltd.

A NOTE ON THE POWER OF BOOTSTRAP UNIT ROOT TESTS

In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the differences of the observations, i.e., the so-called restricted residuals, or the ordinary least squares residuals are used to construct the resampled observations. We also consider models containing a constant and a linear trend and the DF-GLS tests proposed by Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836). A small Monte Carlo experiment is included.I thank the associate editor, Bruce E. Hansen, and three anonymous referees for very constructive comments on the previous versions of the manuscript.

On a GI/M/c Queue with Bounded Waiting Times

We derive the asymptotic distribution of the remaining load, virtual waiting time and actual waiting time for a multiserver queueing system with exponentially distributed service times and bounded waiting times. Interarrival distributions are Coxian, with m stages. This model has application to telephone exchange operations and to perishable inventory. The explicit derivation of the distributions involves determining the eigenvalues of m-dimensional matrices and solving linear equations in m unknowns. We give a few numerical illustrations.

On a Numerical and Graphical Technique for Evaluating Some Models Involving Rational Expectations

Campbell and Shiller (1987) proposed a graphical technique for the present value model which consists of plotting the spread and theoretical spread as calculated from the cointegrated vector autoregressive model. We extend these techniques to a number of rational expectation models and give a general definition of spread and theoretical spread. The main results are the asymptotic distributions of the variance ratio, noise ratio, and correlation between the estimated spread and theoretical spreads. We derive sup tests for the recursively calculated quantities. Finally we apply the methods to two previous studies by Campbell and Shiller (1987) and Engsted (2002).

On maximum likelihood estimation in the moverstayer model

We derive the profile likelihood function of the mixing parameters in the discrete time mover-stayer model This result is used to find a simple necessary and sufficient condition for the maximum Ekelihood estimator to take values in the interior of the parameter space, We point out the relevance of this result for the convergence properties of the EM algorithm, Furthermore, the likelihood-ratio test for the hypothesis that there are equality constraints among the mixing parameters is developed. Finally an illustration of the use of the results is given.

A note on asymptotic inference in a class of non-stationary processes

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.

Contiguity in Nonstationary Time Series

We show how a result of Cox & Llatas (1991) can be derived using contiguity arguments. Also we compare the asymptotic power functions of three tests of the characteristic polynomial of an AR(1) process having a root at unity.

A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

Inflation Dynamics in a Small Open Economy

We evaluate the empirical performance of forward‐looking models for inflation dynamics in a small open economy. Using likelihood‐based testing procedures, we find that the exact formulation is at odds with Norwegian data. Moreover, some of the parameters in the model are not well identified. We also find that the inexact formulation is not rejected statistically using a test based on a minimum distance method. However, confidence regions also reveal an identification problem with this model. Instead, we find a well‐specified backward‐looking model with imperfect competition underlying the price setting, which is a model that outperforms an alternative forward‐looking model in‐sample. The backward‐looking model also forecasts somewhat better than the alternative forward‐looking model, during and after the recent financial crisis.