Michel Lubrano : michel.lubrano[at]univ-amu.fr
Pierre Michel : pierre.michel[at]univ-amu.fr
A large dimensional network or system can generate long memory in its components, as shown by Chevillon, Hecq and Laurent (2018, CHL) and Schennach (2018). These authors derive conditions under which the variables generated by an infinite dimensional vector autoregressive model of order 1, a VAR(1), exhibit long memory. We go one step further and show how these asymptotic results can be put to practice for finite sample modeling and inference regarding series with long range dependence that belong a network or a large system. We propose to use a VAR(1), or an AR(1)-X when the VAR(1) model is estimated equation by equation, whose parameters we shrink to generic conditions matching those of CHL and Schennach. Our proposal significantly outperforms ARFIMA and HAR models when forecasting a non-parametric estimate of the log of the integrated variance (i.e., log(MedRV)) of 250 assets, the annual productivity growth recorded in 100 industrial sectors in the U.S., as well as seasonally adjusted historic monthly streamflow series recorded in 97 localizations of the Columbia river basin.