Pre and post break parameter inference

Abstract

JEL classification: C32 C12Keywords: Structural breaks Time varying parameters Convergence of experiments Asymptotic efficiency of tests a b s t r a c t Consider inference about the pre and post break value of a scalar parameter in a time series model with a single break at an unknown date. Unless the break is large, treating the break date estimated by least squares as the true break date leads to substantially oversized tests and confidence intervals. To develop a suitable alternative, we first establish convergence to a Gaussian process limit experiment. We then determine a nearly weighted average power maximizing test in this limit experiment, and show how to implement a small sample analogue in GMM time series models.

Inference on winners

“…where the residuals U t are orthogonal to C t . Similarly to Elliott and Müller (2014) the function ϕ T : [0, 1] → R k determines the value of the time-varying coefficient β +ϕ T (t/T ). This model nests the traditional structural break model (see e.g.…”

“…To allow the possibility of misspecification, however, we assume only that the data is generated by (10). To provide a good asymptotic approximation to finite sample behavior, we follow Elliott and Müller (2007) and Elliott and Müller (2014) and model parameter instability as on the same order as sampling uncertainty, with ϕ T (t/T ) = 1 √ T g(t/T ) for a fixed function g. We further assume that 1 T…”

“…Even if we only desire coverage of δ(θ) on average over the distribution ofθ, and so prefer to consider unconditional confidence sets, accounting for the randomness ofθ remains important. If on the other hand we are confident that the break model is correctly specified, so (11) holds, it will typically be more appealing to focus on inference for the "true" parameters as in Elliott and Müller (2014).…”

Forecasting With Model Uncertainty: Representations and Risk Reduction

“…A variant of our basic regression model specifies that y t = β t x t + u t , where T 1/2 β [T r] = W (r), where W (r) may be either a stochastic or nonstochastic process. This allows various forms of structural breaks, and is similar to specifications used by Andrews (1993) and Elliott and Müller (2014) Suppose that the researcher ignores the possibility of structural change, and simply uses the available estimators for forecasting. The limiting distributions of the estimators will be as in Proposition 3.5, with Y (r) replaced by Z(r) everywhere.…”

Inference after estimation of breaks

“…Elliott and Müller (2014) employ a switching scheme such that their approach nearly reduces to standard inference, but they use a slightly larger critical value to account for the switch.10 While direct application of this approach fails in structural break settings since the data may be non-stationary, an analogous effect can be achieved by adding normal noise: see Section 5 below for details.11 In a manuscript circulated after the initial public version of this paper,Hyun et al (2018) consider the related problem of conditional inference for changepoint detection, but the changepoint estimation methods they consider cannot be cast as norm-maximization, so their results do not overlap with ours.…”