Confidence sets for the date of a break in level and trend when the order of integration is unknown

David I. Harvey and Stephen J. Leybourne

Structural change in the time series properties of macroeconomic and financial time series is relatively common, and the primary issues to be resolved when considering the possibility of structural change are whether a break is present, and, if so, when the break occurred. 

The focus of this Nottingham School of Economics working paper, forthcoming in the Journal of Econometrics concerns the latter issue regarding the timing of the break, and is therefore complementary to procedures that focus on break detection. A proper understanding of the likely timing of a break in the trend function is crucial for modelling and forecasting efforts, and is also of clear importance when attempting to gain economic insight into the cause and impact of a break. While a number of procedures exist to determine a point estimate of a break in level and/or trend, this paper concentrates on ascertaining the degree of uncertainty surrounding break date estimation by developing procedures for calculating a confidence set for the break date, allowing practitioners to identify a valid set of possible break points with a specified degree of confidence.

When attempting to specify the deterministic component of an economic time series in practice, a critical consideration is the order of integration of the stochastic element of the process. Given the prevalence of integrated data, it is important to develop methods that are valid in the presence of I(1) shocks. Moreover, since there is very often a large degree of uncertainty regarding the order of integration in any given series, it is extremely useful to have available techniques that are robust to the order of integration, dealing with the potential for either stationary or unit root behaviour at the same time as specifying the deterministic component. In this paper David I. Harvey and Stephen J. Leybourne propose methods for constructing confidence sets for the timing of a break in level and/or trend that have asymptotically correct coverage for both I(0) and I(1) processes. These are based on inverting a sequence of tests for the break location, evaluated across all possible break dates. The authors separately derive locally best invariant tests for the I(0) and I(1) cases; under their respective assumptions, the resulting confidence sets provide correct asymptotic coverage regardless of the magnitude of the break. The article suggests use of a pre-test procedure to select between the I(0)- and I(1)-based confidence sets, and Monte Carlo evidence demonstrates that our recommended procedure achieves good finite sample properties in terms of coverage and length across both I(0) and I(1) environments. An application using US macroeconomic data is provided which further evinces the value of these procedures.

Journal of Econometrics, “Confidence sets for the date of a break in level and trend when the order of integration is unknown” by David I. Harvey and Stephen J. Leybourne.

http://dx.doi.org/10.1016/j.jeconom.2014.09.004

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