運用 Karhunen-Loeve展開式 建構資料驅動的尼曼平滑檢定

Abstract

New data-driven smooth tests are proposed in this thesis. The new tests are proposed to eschew the downward weighting problem of the traditional omnibus tests, and the new tests are constructed based on the components of Karhunen-Lo′eve expansion of limiting process. As examples, we construct tests for the null hypothesis of stationarity, coefficient stability, symmetric dynamics of quantile autoregressive model, and bivariate independence. Simulation results show that, new tests have moderate size control and nice power performance for a wide range of alternatives. In contrast to traditional omnibus tests, new tests are more robust to complex models and perform well under high-frequency alternatives.