Georgia Institute of Technology College of Sciences

The functional autoregressive process has become a useful tool in the analysis of functional time series data. In this model, the observations and the errors are curves, and the role of the autoregressive coefficient is played by an integral operator. To ensure meaningful inference and prediction, it is important to verify that this operator does not change with time. We propose a method for testing its constancy which uses the functional principal component analysis. The test statistic is constructed to have a Kiefer type asymptotic distribution. The asymptotic justification of the procedure is very delicate and touches upon central notions of functional data analysis. The test is implemented using the R package fda. Its finite sample performance is illustrated by an application to credit card transaction data.