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Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model

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The expectati on of the excess holding yield on a long bond is postulated to depend upon its conditional variance. Engle's ARCH model is extended to allow the conditional variance to be a determinant of the mean and is called ARCH-M. Estimation and infer ence procedures are proposed, and the model is applied to three interest rate data sets. In most cases the ARCH process and the time varying risk premium are highly significant. A collection of LM diagnostic tests reveals the robustness of the model to various specification changes such as alternative volatility or ARCH measures, regime changes, and interest rate formulations. The model explains and interprets the recent econometric failures of the expectations hypothesis of the term structure. Copyright 1987 by The Econometric Society.
... The ARCH model has become a popular one because its variance specification can capture commonly observed features of the time series of financial variables; in particular, it is useful for modeling volatility and especially changes in volatility over time (Hill, et al 2008) The basic idea of ARCH models is that (a) the mean at is serially uncorrelated, but dependent and (b) the dependence of at can be described by a simple quadratic function of its lagged values Ruey (2002). Specifically, an ARCH (m) model assumes that (Engle, Robert F. (1987). ...
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