Linear Stochastic Difference Equations

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published by Princeton University Press

Published in print December 2013 | ISBN: 9780691042770
Published online October 2017 | e-ISBN: 9781400848188
Linear Stochastic Difference Equations

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This chapter describes the vector first-order linear stochastic difference equation. It is first used to represent information flowing to economic agents, then again to represent competitive equilibria. The vector first-order linear stochastic difference equation is associated with a tidy theory of prediction and a host of procedures for econometric application. Ease of analysis has prompted the adoption of economic specifications that cause competitive equilibria to have representations as vector first-order linear stochastic difference equations. Because it expresses next period's vector of state variables as a linear function of this period's state vector and a vector of random disturbances, a vector first-order vector stochastic difference equation is recursive. Disturbances that form a “martingale difference sequence” are basic building blocks used to construct time series. Martingale difference sequences are easy to forecast, a fact that delivers convenient recursive formulas for optimal predictions of time series.

Keywords: vector first-order; linear stochastic difference equation; competitive equilibria; state variables; random disturbance; martingale difference sequence; time series

Chapter.  6227 words. 

Subjects: History of Economic Thought

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