Statistical Methods in Finance 2021

June 27 to July 1, 2021, 2-8pm IST


Bootstrap prediction bands for functional time series

By Hanlin Shang
Macquarie University, Sydney, Australia

A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing in the Karhunen-Loève representation of the functional process. It generates backwards-in-time, functional replicates that adequately mimic the dependence structure of the underlying process in a model-free way and have the same conditionally fixed curves at the end of each functional pseudo-time series. The bootstrap prediction error distribution is then calculated as the difference between the model-free, bootstrap-generated future functional observations and the functional forecasts obtained from the model used for prediction. This allows the estimated prediction error distribution to account for not only the innovation and estimation errors associated with prediction but also for the possible errors due to model misspecification. We establish asymptotic validity of the bootstrap procedure in estimating the conditional prediction error distribution of interest and we also show that the procedure enables the construction of prediction bands that achieve (asymptotically) the desired coverage. Such prediction bands also can be based on a consistent estimation of the conditional distribution of the studentized prediction error process. Through a simulation study and the analysis of two data sets, we demonstrate the capabilities and the good finite-sample performance of the proposed method.

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Call for Papers in Sankhya B: Special Issue on Recent Advances in Statistical Finance

The aim of this special issue is to feature research papers on theory, methodology, and applications of models and methods for recent advances in statistical finance. We encourage submissions presenting original works on statistical, computational, and mathematical approaches to modelling and analysis of financial data. Innovative applications and case studies in financial statistics are welcome, especially related to novel methodological challenges in the treatment of big data and high-frequency data.

This special issue will bring together contributions from practitioners and researchers working on different aspects of statistical methods in finance, with methodological interests encompassing, but not limited to, the following domains:

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