Specification testing in nonparametric AR-ARCH models
  In this paper an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. A test for the model assumption of independence of innovations from past time series values is suggested. The test is based on an weighted $L^2$-distance of empirical characteristic functions. The asymptotic distribution under the null hypothesis of independence is derived and consistency against fixed alternatives is shown. A smooth autoregressive residual bootstrap procedure is suggested and its performance is shown in a simulation study. 
Marie Hu\v{s}kov\'a, Natalie Neumeyer, Tobias Niebuhr, Leonie Selk
math.ST stat.TH