Asymptotic inference for change-points in time time series under various break-sizes

Thomas M. Menino Convention & Exhibition Center 

In this paper, we investigate the asymptotic distribution of a change-point
estimator for piecewise stationary time series across different magnitudes of
break sizes. Specifically, we examine break sizes of order O(1/n^α) for 0 <
α < 1/2, α = 1/2, and α > 1/2, corresponding to large, moderate, and small
break sizes, respectively, where n denotes the sample size. Our results reveal
that the asymptotic distributions in these three regimes differ but are all linked
to the maximizer of certain functions of a two-sided drifted Brownian motion.
To address the practical challenge of unknown break sizes, we introduce an
asymptotically pivotal statistic that is robust across the whole range of break
size regimes on α ∈ [0,∞). This statistic provides a unified approach for
constructing confidence intervals for the change-point without requiring prior
knowledge of the break size. Simulation studies show that the asymptotic
inference performs well under different break sizes, while the pivotal statistic
demonstrates better performance in most scenarios. Applications to financial
time series further highlight the practical relevance of the proposed inference
methods.

piecewise stationary time series models

structural break

pivotal statistic 

Business and Economic Statistics Section