Oscillating systems with cointegrated phase processes

Oscillating systems with cointegrated phase processes

We present cointegration analysis as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we pres...

Phase Tuning in Synchronization of Nonlinear Master-slave Oscillating Systems Using Decomposition Method

Cointegrated linear processes in Hilbert space

Consider a sequence X = (X0,X1, . . .) of random elements of a real separable Hilbert space H , whose €rst di‚erence is a standard linear process with long run covariance operator Λ. We show that, under a mild summability condition, the set of vectors x ∈ H for which 〈Xt ,x〉 is stationary given a suitable initialization X0 is the kernel of Λ. We call this space the cointegrating space, and its ...

OPTIMAL ESTIMATION OF COINTEGRATED SYSTEMS WITH IRRELEVANT INSTRUMENTS By

It has been known since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such ‘‘irrelevant’’ deterministic trend instruments may be systematically used to produce asymptotically eff...

Short Run Dynamics in Cointegrated Systems