Statistical Methods in Finance 2025

Change Point Detection in Functional Time Series,

By:Debanjana Datta
ISI, Bangalore

We have devised a novel procedure for change point detection in Functional Time Series (FTS) using a state space representation. Our model features a Functional Autoregressive (FAR) latent variable process driven by Gaussian innovations, naturally accommodating sparse, noisy observations. Crucially, unlike conventional methods, our approach avoids smoothing and Functional Principal Component Analysis (FPCA), thereby mitigating the substantial information loss typically incurred across the functional domain. An efficient Blocked Gibbs sampling algorithm is developed for estimating their locations. The methodology is efficient enough to detect regime shifts in the mean function, volatility and AR-operator. Furthermore, we shall illustrate examples having financial aspects.