This paper discusses a number of likelihood ratio tests on long-run relations and common trends in the I(2) model and provide new results on the test of overidentifying restrictions on beta’xt and the asymptotic variance for the stochastic trends parameters, alpha 1: How to specify...

An algorithm suggested by Hendry (1999) for estimation in a regression with more regressors than observations, is analyzed with the purpose of finding an estimator that is robust to outliers and structural breaks. This estimator is an example of a one-step M-estimator based on Huber's skip...

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which...

We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important...

The purpose of the present paper is to analyse a simple bubble model suggested by Blanchard and Watson. The model is defined by y(t) =s(t)?y(t-1)+e(t), t=1,…,n, where s(t) is an i.i.d. binary variable with p=P(s(t)=1), independent of e(t) i.i.d. with mean zero and finite variance. We take ?1...

This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional...

It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite...

There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the effect of nonstationarity on inference using these methods and compare them to model based inference. Finally we analyse some data on annual mean temperature and...

Iterated one-step Huber-skip M-estimators are considered for regression problems. Each one-step estimator is a reweighted least squares estimators with zero/one weights determined by the initial estimator and the data. The asymptotic theory is given for iteration of such estimators using a...