Wavelet estimation in time-varying coefficient time series models with measurement errors

ABSTRACT

The article studies a time-varying coefficient time series model in which some of the covariates are measured with additive errors. In order to overcome the bias of estimator of the coefficient functions when measurement errors are ignored, we propose a modified least squares estimator based on wavelet procedures. The advantage of the wavelet method is to avoid the restrictive smoothness requirement for varying-coefficient functions of the traditional smoothing approaches, such as kernel and local polynomial methods. The asymptotic properties of the proposed wavelet estimators are established under the α-mixing conditions and without specifying the error distribution. These results can be used to make asymptotically valid statistical inference.

KEYWORDS:

• Measurement errors
• time series models
• time-varying coefficient
• Wavelet estimation.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05

Additional information

Funding

This work is partially supported by Anhui Provincial Natural Science Foundation of China (Nos. 1408085MA03, 1708085MA04), NSFC (No. 11571073), and China Postdoctoral Science Foundation (No. 2016M590396).