Inference on a Structural Break in Trend with Fractionally Integrated Errors

Perron and Zhu (2005) established the consistency, rate of convergence and the limiting distributions of parameter estimates in a linear time trend with a change in slope with or without a concurrent change in level. They considered the dichotomous cases whereby the errors are shortmemory stationary, I(0), or have an autoregressive unit root, I(1). We extend their analysis to cover the more general case of fractionally integrated errors for values of d in the interval (0:5, 1:5) excluding the boundary case 0:5. Our theoretical results uncover some interesting features. For example, when a concurrent level shift is allowed, the rate of convergence of the estimate of the break date is the same for all values of d in the interval (0:5;0:5). This feature is linked to the contamination induced by allowing a level shift, previously discussed by Perron and Zhu (2005). In all other cases, the rate of convergence is monotonically decreasing as d increases. We also provide results about the so-called spurious break issue. Simulation experiments are provided to illustrate some of the theoretical results.