Show description

Y(τ + tN )] = F[y(s + t1 ), y(s + t2 ), . . 7) where t1 < t2 . . ) is the joint distribution function, (see Appendix 1). 9c) The moments in SS1–SS3 are assumed to exist. The first condition states that the mean is constant, the second that the variance is constant and the third that the k-th order autocovariance is invariant to an arbitrary shift in the time origin. The extension to continuous time is straightforward, replacing yτ by y(τ), and so on. From these three conditions, it is evident that a stochastic process could fail to be weakly stationary because its mean is changing; and/or its variance is changing; and/or the k-th order autocovariances depend on time for some k.

2 Distribution function of visits to the origin. 1 are trajectories or sample paths. Our interest generally lies not in the outcome of a random variable at a single point in time, but in a sample path, or the distribution of sample paths, of a sequence of random variables over an interval of time. To conceptualise how such sample paths arise the idea of a stochastic process involves a sample space Ω, a probability space and time. In the case of the stochastic process defined by the symmetric, binomial random walk then y y Ω = Ωt , with probability measure Pt and t = 1, .

The articles on unit root tests are amongst the most cited in economics and econometrics and have clearly influenced the direction of economic research at a much wider level than simply testing for a unit root. 1. 1). The appropriate prerequisites for this book include some knowledge of econometric theory at an intermediate or graduate level as, for example, in Davidson (2000), Davidson and Mackinnon (2004) or Mittlehammer et al. (2000), and, possibly, with some additional directed study, as in good introductory books such as Gujarati (2006), Dougherty (2007), Ramanathan (2002) and Stock and Watson (2007).