Long memory via networking

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractMany time-series data are known to exhibit "long memory", that is, they have an autocorrelation function that decays very slowly with lag. This behavior has traditionally been attributed to either aggregation of heterogenous processes, nonlinearity, learning dynamics, regime switching, structural breaks, unit roots or fractional Brownian motion. This paper identifies an entirely different mechanism for long memory generation by showing that it can naturally arise when a large number of simple linear homogenous economic subsystems with a short memory are interconnected to form a network such that the outputs of each of the subsystem are fed into the inputs of others. This networking picture yields a type of aggregation that is not merely additive, resulting in a collective behavior that is richer than that of individual subsystems. Interestingly, the long memory behavior is found to be almost entirely determined by the geometry of the network while being relatively insensitive to the specific behavior of individual agents.

Long Memory via Networking

“…A simple "one-lag" autoregressive process (i.e., with r s = 1{s = 1}) is also sufficient to cover a broad range of model economies that include durable capital goods or labor (see Equation (10) and Section V in Foerster, Sarte, and Watson (2011)), after linearization of the model around the equilibrium. More fundamentally, our subsequent analysis actually holds for very general forms of the sequence r s , which is helpful to consider more 3 In particular, finite networks can only generate long memory of a unit-root type; see Theorems 6 and 7 in the working paper version of the present paper (Schennach (2013)). 4 As every agent is already assumed to have the same response function r s , the condition N j=1 W ij = 1 can be seen as a normalization to ensure a unique factorization.…”

“… In particular, finite networks can only generate long memory of a unit‐root type; see Theorems 6 and 7 in the working paper version of the present paper ( Schennach ()). …”

“…We then calculate this parameter for infinite periodic networks in any number of dimensions, before focusing on fractal networks, which enable a richer range of possible long-memory behaviors. The Supplemental Material (Schennach (2018)) provides a simple empirical example to illustrate the theory. FIGURE 1.-General ideas underlying the approach.…”

“… Our approach can easily be adapted to continuous processes, since our proofs rely on a spectral representation—see earlier version of the present paper Schennach (). …”

“…Satisfying this translation-invariance assumption may involve working with some deterministic transformation of the model, for example, discounted present values or logarithms of some variables.2 Our approach can easily be adapted to continuous processes, since our proofs rely on a spectral representation-see earlier version of the present paperSchennach (2013).…”