Abstract Mediation analysis is widely adopted to infer causal mechanism by disentangling indirect or mediated effects of an exposure on an outcome through given intermediaries, from the remaining direct effect. Traditional approaches build on standard regression models for the outcome and...

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...

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...

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...

It is well known that if Xt is a nonstationary process and Yt is a linear function of Xt, then cointegration of Yt implies cointegration of Xt. We want to find an analogous result for common trends if Xt is generated by a finite order VAR with i.i.d. (0,Ωx) errors εxt. We first show that Yt...