Research on Regularized Trend Filtering Generalized Least Squares Method and Spurious Regression Problem

The presence of trend components or random disturbance in a sequence with autocorrelation or unit root processes can cause spurious regression. To solve this problem, this paper proposes a regularized trend filtering generalized least squares method. This method does not require prior knowledge of the specific forms of trend components and random disturbance autocorrelation, and does not require the introduction of new estimate method or test statistics. It can draw on existing traditional regression analysis methods for statistical inference and has universality and important practical application value. Numerical simulations have verified the robustness and effectiveness of this method in various situations and actual data. The results show that the regularized trend filtering generalized least squares method proposed in this paper can effectively solve the spurious regression problem caused by trends or autocorrelation of random disturbance, as well as unit root processes, and effectively improve the reliability of regression estimators.