We consider a streaming time series data, which is assumed to come from a non-explosive p-th order autoregressive (AR(p)) model with p ≥ 1. Our goal is to estimate the parameters of this model using a subsample of random size drawn sequentially from the streaming data based on a stopping rule. Traditionally, sequential sampling is carried out after observing an initial sample of fixed size. However, our sampling starting point is chosen according to statistical leverage scores of the data and the subsample size is decided by a sequential sampling rule. We show that the least squares estimator of the model parameters based on the leverage-based sequential subsample is uniformly asymptotically normally distributed. We also support the theory by simulations and data analysis.
This is joint work with Rui Xie, Ping Ma, Wei Biao Wu, and Ray Bai