For non-stationary high-dimensional time series with short memory and light tails, normalized sums can be approximated by Gaussian vectors in Wasserstein distance and on all convex sets at nearly optimal rates.
Simultaneous Inference for Time Series Functional Linear Regression
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abstract
We consider the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by roughness penalization approach with flexible choices of orthonormal basis functions. A simple and unified multiplier bootstrap methodology is proposed for the JSCB construction which is shown to achieve the correct coverage probability asymptotically. Furthermore, the JSCB is asymptotically robust to inconsistently estimated standard deviations of the model. The proposed methodology is applied to a time series data set of electricity market to visually investigate and formally test the overall regression relationship as well as perform model validation.
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Wasserstein and Convex Gaussian Approximations for Non-stationary Time Series of Diverging Dimensionality
For non-stationary high-dimensional time series with short memory and light tails, normalized sums can be approximated by Gaussian vectors in Wasserstein distance and on all convex sets at nearly optimal rates.