The importance of window size: a study on the required window size for optimal-quality market risk models

Mateusz Buczyński and Marcin Chlebus

Abstract

When it comes to market risk models, should we use the full data set that we possess or rather find a sufficient subsample? We conduct a study of different fixed moving-window lengths: moving-window sizes varying from 300 to 2000 are considered for each of the 250 combinations of data and a value-at-risk evaluation method. Three value-at-risk models (historical simulation, a generalized autoregressive conditional heteroscedasticity (GARCH) model and a conditional autoregressive value-at-risk (CAViaR) model) are used for three different indexes (the Warsaw Stock Exchange 20, the Standard & Poor’s 500 and the Financial Times Stock Exchange 100) for the period 2015–19. We also address subjectivity in choosing the window size by testing change point detection algorithms (binary segmentation and pruned exact linear time) to find the best matching cutoff point. Results indicate that a training sample size greater than 900–1000 observations does not increase the quality of the model, while lengths lower than this cutoff provide unsatisfactory results and decrease the model’s predictive power. Change point detection methods provide more accurate models: applying the algorithms to each model’s recalculation on average provides results better by one exceedance. Our recommendation is to use GARCH or CAViaR models with recalculated window sizes.