We modeled long memory with just one lag!✩

Two recent contributions have found conditions for large dimensional networks or systems to generate long memory in their individual components. We build on these and provide a multivariate methodology for modeling and forecasting series displaying long range dependence. We model long memory properties within a vector autoregressive system of order 1 and consider Bayesian estimation or ridge regression. For these, we derive a theory-driven parametric setting that informs a prior distribution or a shrinkage target. Our 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.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

Two recent studies have found conditions for large dimensional networks or systems to generate long memory. Building on these findings, we propose a multivariate methodology for modeling and forecasting series with long range dependence. By incorporating long memory properties in a vector autoregressive system of order 1, and applying Bayesian estimation or ridge regression, we outperform univariate time series long memory models in forecasting daily volatility for 250 U.S. company stocks over twelve years. This empirical validation supports the theoretical results that long memory can be sourced from marginalization within a large dimensional system.