Expected Value Models: A New Approach

Two approaches dominate the time series literature for modeling expected value models. The first one is based on observable variables and includes ARMA and GARCH models, while the second one is based on latent variables and includes state space and stochastic volatility (or SV) models. The first approach is appealing because it allows to compute conditional expectations (e.g., for forecasting purpose) and to use the Quasi Maximum Likelihood (QML) type of estimation. However, its main limitation is that it imposes some indirect restrictions that are not desirable. For instance a GARCH model, which captures volatility dynamics, imposes that some marginal moments are not bounded, which is a clear limitation of the model. In contrast, state-space models do not impose such restrictions and are more flexible. However, the state space models do not allow to compute conditional expectation given observable variables (rather than latent variables) and do not allow the use of QML techniques for inference purposes. The main contribution of this paper is to introduce a new approach that has the advantages of ARMA and state space models. The model we propose is a latent variable model where one can compute explicitly the conditional expectations of the variable of interest and, consequently, to use QML estimation. In other words, we bridge the gap between ARMA (or GARCH) and state space (SV) models. We apply our approach in two examples. In the first one, we deal with modeling volatility, i.e., we introduce a SV model and derive the first four conditional moments. This allows us to give a structural interpretation for the time varying effects of skewness and kurtosis recently highlighted by the literature. The second example deals with asset pricing models. More precisely, we start by assuming some Euler equations fulfilled by utility function of a representative agent, where the relevant consumption is not observable. We then derive the Euler equations based on the observable consumption. This allows us to reconsider the equity premium puzzle from a different perspective than the traditional approaches.