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Title: Modelling long memory with just one lag Authors:  Luc Bauwens - Universite catholique de Louvain (Belgium)
Guillaume Chevillon - ESSEC Business School (France) [presenting]
Sebastien Laurent - AMU (France)
Abstract: A large dimensional network or system can generate long memory in its components. Conditions have been derived 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 modelling and inference regarding series with long-range dependence that belongs to 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 previous work. The proposal significantly outperforms ARFIMA and HAR models when forecasting a nonparametric 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 localisations of the Columbia river basin.