Detecting parameter shift in garch models
将参数恒定性检验的最新理论应用于GARCH模型的条件方差，提出了上确界拉格朗日乘子检验及其稳健版本，蒙特卡洛模拟和S&P 500数据应用表明条件方差参数稳定的假设可被拒绝。
This paper applies recent theories of testing for parameter constancy to the conditional variance in a GARCH model. The supremum Lagrange multiplier test for conditional Gaussian GARCH models and its robustified variants are discussed. The asymptotic null distribution of the test statistics are derived from the weak convergence of the scores, and the critical values from the hitting probability of squared Bessel process. Monte Carlo studies on the finite sample size and power performance of the supremum LM tests are conducted. Applications of these tests to S&P 500 indicate that the hypothesis of stable conditional variance parameters can be rejected.