Inference for non‐stationary time series regression with or without inequality constraints

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 77; no. 2; pp. 349 - 371
• Main Author: Zhou, Zhou
• Format: Journal Article
• Language: English
• Published: Oxford Royal Statistical Society 01.03.2015; Blackwell Publishing Ltd; John Wiley & Sons Ltd; Oxford University Press
• Subjects: Approximation; Covariance; Estimators; Forecasts; Inequality; Inequality constraints; Inference; International; Least squares; Linear models; Linear regression; Methodology; Piecewise locally stationary time series; Regression analysis; Robust bootstrap; Statistical analysis; Statistics; Structural stability; Studies; Subsampling; Time; Time series; time series analysis; Time series models; United Kingdom > UK
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/rssb.12077

We consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non‐stationary behaviours over time. Meanwhile, the regression parameters may be subject to linear inequality constraints. A simple and unified procedure for structural stability checks and parameter inference is proposed. In the case where the regression parameters are constrained, the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones.