The empirical process of the residuals from general autoregressions is investigated. If an intercept is included in the regression, the empirical process is asymptotically Caussian and free of nuissance parameters. This contrasts the known result that in the unit root case without intercept the...

A vector autoregression with deterministic terms and with no restrictions to its characteristic roots is considered. Strong consistency results for the least squares statistics are presented. This extends earlier results where deterministic terms have not been considered. In addition the...

This paper addresses the question of whether a conventional approach to cointegration is applicaple to the case where changes are allowed in the parameters for the short term dynamics. We reparametrise a vector autoregressive model such that the short-run parameters exhibiting changes at known...

A vector autoregression with deterministic terms and with no restrictions to its characteristic roots is considered. Strong consistency results and also some weak convergence results are given for a number of least squares statistics. These statistics are related to the denominator matrix of the...

Dickey and Fuller (1981) suggested unit root tests for an autoregressive model with a linear trend and a fixed initial value. This model has nuisance parameters so later authors have often worked with a slightly different model with a random initial value in which nuisance parameters can be...

When analysing macroeconomic data it is often of relevance to allow for structural breaks in the statistical analysis. In particular, cointegration analysis in the presence of structural breaks could be of interest. We propose a cointegration model with piecewise linear trend and known break...

This paper derives the exact distribution of the maximum likelihood estimator of a first order linear autoregression with exponential innovations. We show that even if the process is stationary, the estimator is T-consistent, where T is the sample size. In the unit root case the estimate is...

In this paper we present a general result concerning the convergence to stochastic integrals with non-linear integrands. The key finding represents a generalization of Chan and Wei`s (1988) Theorem 2.4. and that of Ibragimov and Phillips` (2004) Theorem 8.2. This result is necessary for...

Empirical analyses of Cagan`s money demand schedule have broadly speaking suffered from the following problems: (i) Inability to model the data to the end of the hyperinflation. (ii) Difficulties in making congruent models for systems of variables. (iii) Discrepancies between estimated and...

We use high frequency financial data to proxy, via the realised variance, each days financial variability. Based on a semiparametric stochastic volatility process, a limit theory shows you can represent the proxy as a true underlying variability plus some measurement noise with known...