I'm new to working with neural networks and have recently began implementing neural networks for time series forecasting in some of my work. I've been particularly using Echo State Networks and have been doing some reading to understand how they work. For the most part things seem pretty straight forward but I'm confused as to why we use a 'delay' when feeding our input data (the delay concept mentioned in this paper: https://science.sciencemag.org/content/304/5667/78)?

I'm looking at some source code on github (https://github.com/stefanonardo/echo-state-network) and they implement this delay as well (they feed two arrays inputData & targetData, into the network where one is delayed by one element relative to the other). I am noticing that the larger the delay, the worse the fit.

Why is this done? My interest is eventually to forecast past sample data. Anything helps thanks!

I'm new to working with neural networks and have recently began implementing neural networks for time series forecasting in some of my work. I've been particularly using Echo State Networks and have been doing some reading to understand how they work. For the most part, things seem pretty straight forward, but I'm confused as to why we use a 'delay' when feeding our input data (the delay concept mentioned in the paper Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication)?

I'm looking at some source code on Github, and they implement this delay as well (they feed two arrays inputData & targetData, into the network where one is delayed by one element relative to the other). I am noticing that the larger the delay, the worse the fit.

Why is this done? My interest is eventually to forecast past sample data.