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...

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 studies cointegration in non-linear error correction models characterized by discontinuous and regime-dependent error correction and variance specifications. In addition the models allow for autoregressive conditional heteroscedasticity (ARCH) type specifications of the variance. The...

We address the IGARCH puzzle by which we understand the fact that a GARCH(1,1) model fitted by quasi maximum likelihood estimation to virtually any financial dataset exhibit the property that alpha^hat + beta^hat is close to one. We prove that if data is generated by certain types of continuous...

This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of...

We analyze vector autoregressive processes using the matrix valued characteristic polynomial. The purpose of this article is to give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes. The new...

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

Asset prices undergo long swings that revolve around benchmark levels. In currency markets, fluctuations involve real exchange rates that are highly persistent and that move in near-parallel fashion with nominal rates. The inability to explain these two regularities with one model has been...

Yule (1926) introduced the concept of spurious or nonsense correlation, and showed by simulation that for some nonstationary processes, that the empirical correlations seem not to converge in probability even if the processes were inde- pendent. This was later discussed by Granger and Newbold...

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...