We modeled long memory with just one lag!
Author: Prof Sebastien Laurent
Many series like the realized variance of Apple stock plotted in the top panel of the figure below (computed from 5-minute log-returns in %) display long-memory. Long-memory is characterised by a very slowly decreasing autocorrelation function as illustrated in the bottom panel of the figure. This figure suggests that today’s realized variance has a correlation of about 15% with the realized variance 500 days ago (approximately 2 years).
Many economic, financial and also hydrological series share this property. Looking at the above graph, it seems natural to use a time series model that uses the very distant past to predict the future values of this type of series (such as an ARFIMA model). But is it rational to use such distant observations to predict tomorrow's risk when financial markets react very quickly to new information? Is this long memory not hiding something else?
In the article “We modeled long memory with just one lag!”, forthcoming in Journal of Econometrics, Bauwens, Chevillon and Laurent (2023) provide a novel multivariate methodology for modeling and forecasting series displaying long range dependence but using just one lag instead of an infinite history. They model long memory properties within a vector autoregressive system of order 1 and consider Bayesian estimation or ridge regression. For these, they derive a theory-driven parametric setting that informs a prior distribution or a shrinkage target. Their proposal significantly outperforms univariate time series long-memory models when forecasting a daily volatility measure for 250 U.S. company stocks over twelve years. This provides an empirical validation of the theoretical results showing long memory can be sourced to marginalization within a large dimensional system. All estimations have been performed using OxMetrics.
by Luc Bauwens (1), Guillaume Chevillon (2), and Sebastien Laurent (3)
- LIDAM/CORE, UCLouvain, Voie du Roman Pays 34, 1348 Louvain-La-Neuve, Belgium
- ESSEC Business School
- Aix-Marseille University (Aix-Marseille School of Economics), CNRS, EHESS, Aix-Marseille Graduate School of Management – IAE
If you're interested in reading more the full paper can be accessed here for free until the 9th August 2023.
