Specification tests for nonlinear dynamic models
提出一种新的非线性动态模型充分性检验和图形评估工具，基于概率积分变换的多变量经验过程，适用于条件波动率、分位数、VaR等模型，蒙特卡洛实验显示良好有限样本性质，并用于检验股票指数数据的异方差模型。
We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any set‐up where parametric conditional distribution of the data is specified and, in particular, to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behaviour in conditional distribution and does not rely on smoothing techniques that require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous and lagged probability integral transforms. We establish weak convergence of the process under parameter uncertainty and local alternatives. We justify a parametric bootstrap approximation that accounts for parameter estimation effects often ignored in practice. Monte Carlo experiments show that the test has good finite‐sample size and power properties. Using the new test and graphical tools, we check the adequacy of various popular heteroscedastic models for stock exchange index data.