An analysis of some identification problems in the cointegrated VAR is given. We give a new criteria for identification by linear restrictions on individual relations which is equivalent to the rank condition. We compare the asymptotic distribution of the estimators of alpha and beta when they...

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 deterministic...

In a linear state space model Y(t)=BT(t) e(t), we investigate if the unobserved trend, T(t), cointegrates with the predicted trend, E(t), and with the estimated predicted trend, in the sense that the spreads are stationary. We find that this result holds for the spread B(T(t)-E(t)) and the...

We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness...

A multivariate CVAR(1) model for some observed variables and some unobserved variables is analysed using its infinite order CVAR representation of the observations. Cointegration and adjustment coefficients in the infinite order CVAR are found as functions of the parameters in the CVAR(1) model....

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their consistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that...

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...

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=Δ^(-d)u(t), where d ∈ (-1/2,1/2) is the fractional integration parameter and u(t) is weakly dependent. The classical condition is existence of qmax(2,(d 1/2)⁻¹) moments of...

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)ρy(t-1) ε(t), t=1,…,n, where s(t) is an i.i.d. binary variable with p=P(s(t)=1), independent of ε(t) i.i.d. with mean zero and finite variance. We take...

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 using the cointegrated vector autoregressive model. Finally...