This paper studies the low frequency dynamics in forward looking models where expectations are formed using perpetual learning such as constant gain least squares. We show that if the coefficient on expectations is sufficiently close to unity, perpetual learning induces strong persistence that is empirically indistinguishable from long memory. We apply this result to present value models of stock prices and exchange rates and find that perpetual learning can explain the long memory observed in the data.
Chevillon, G. & Mavroeidis, S. (2018). 'Perpetual learning and apparent long memory'. Journal of Economic Dynamics and Control, 90, pp.343-365.