Difference-based covariance matrix estimation in time series nonparametric regression with application to specification tests
提出一种新的基于差分的去偏长程协方差矩阵估计量，适用于时变回归系数的函数线性模型，能处理非平稳、长记忆和异方差，并用于结构稳定性检验和长记忆检验，克服了传统方法的偏差和非单调功效问题。
Summary Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt structural breaks and its competitive finite sample performance. However, existing methods mainly focus on estimators for the univariate process, while their direct and multivariate extensions for most linear models are asymptotically biased. We propose a novel difference-based and debiased long-run covariance matrix estimator for functional linear models with time-varying regression coefficients, allowing time series nonstationarity, long-range dependence, state heteroscedasticity and combinations thereof. We apply the new estimator to (i) the structural stability test, overcoming the notorious nonmonotonic power phenomena caused by piecewise smooth alternatives for regression coefficients, and (ii) the nonparametric residual-based tests for long memory, improving the performance via the residual-free formula of the proposed estimator. The effectiveness of the proposed method is justified theoretically and demonstrated by superior performance in simulation studies, while its usefulness is elaborated via real data analysis. Our method is implemented in the R package mlrv.