Jingcheng Yu
PhD Candidate, University of Waterloo
Room: M3 3127
Rank-based E-processes for ARMA–GARCH Type Models
We develop rank-based e-processes for testing whether a prespecified time series model class remains compatible with incoming observations. The framework covers ARMA–GARCH type models. The null hypothesis is that the data follow a model in this class with constant parameters and iid innovations. Both the parameters and the innovation distribution are unknown. Under this null hypothesis, our construction yields anytime-valid e-processes within the calibrated monitoring horizon. For each candidate parameter, we filter the observations and combine rank statistics for residual scale, serial dependence and distributional shape. Using residual ranks avoids specifying the innovation distribution. We account for parameter uncertainty by rejecting the model class only when every candidate parameter value in the prespecified domain has been rejected. We establish convergence of a finite-grid approximation to the theoretical e-process as the grid is refined at a fixed monitoring horizon. Simulation studies show that the proposed method has good power against changes in parameters and innovation distributions. We also discuss an application to daily stock returns for monitoring potential regime changes relative to a prespecified AR–GARCH model class.