State-Space vs. VAR models for Stock Returns
Manuscript July 24 2008. In a “state-space” model, you write a process for expected returns and another one for expected dividend growth, and then you find prices (dividend yields) and returns by present value relations. I connect state-space models with VAR models for expected returns. What are the VAR or return-forecast-regression implications of a state-space model? What state-space model does a VAR imply? I start optimistic. An AR(1) state-space model gives a nice return-forecasting formula, in which you use both the dividend yield and a moving average of past returns to forecast future returns. The general formulas leave me pessimistic however. One can write any VAR in state-space form, and we don’t really have solid economic reasons to restrict either VAR or state-space representations. Still, the connections between the two representations are worth exploring, and if you’re doing that this paper might save you weeks of algebra.