A paradigm of statistical mechanics of financial markets (SMFM) using nonlinear nonequilibrium algorithms, first published in L. Ingber, Mathematical Modelling, 5, 343-361 (1984), is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta are thereby derived and used as technical indicators in a recursive ASA optimization process to tune trading rules. These trading rules are then used on out-ofsample data, to demonstrate that they can profit from the SMFM model, to illustrate that these markets are likely not efficient.

Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or non-Gaussian state estimation problems have been developed. Numerical integration becomes extremely computer-intensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integration with importance sampling, resampling, rejection sampling, Markov chain Monte Carlo and so on are utilized, which can be easily applied to multi-dimensional cases. Thus, in the last decade, several kinds of nonlinear and non-Gaussian filters and smoothers have been proposed using various computational techniques. The objective of this paper is to introduce the nonlinear and non-Gaussian filters and smoothers which can be applied to any nonlinear and/or non-Gaussian cases. Moreover, by Monte Carlo studies, each procedure is compared by the root mean square error criterion.

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This paper suggests a new state space approach to analysis of stock return predictability. Acknowledging that expected returns and expected dividends are unobservable, the Kalman filter technique is used to extract them from the observed history of realized dividends and returns. This approach explicitly accounts for the variation in expected dividend growth and allows to make estimates more robust to structural breaks in the means of dividend growth and returns. The constructed predictor outperforms the dividend-price ratio both in and out of sam-ple, providing statistically and economically significant forecasts. The finite sample likelihood ratio test reliably rejects the hypothesis of constant expected returns.

to both institutions for their hospitality. Financial support was provided by

Abstract. If theory-consistent models can ever hope to forecast well and to be useful for policy, they have to relate to data which though rich in information is uncertain, unbalanced and sometimes forecasts from external sources about the future path of other variables. One example from many is financial market data, which can help but only after smoothing out irrelevant short-term volatility. In this paper we propose combining different types of useful but awkward data set with a linearised forward-looking DSGE model through a Kalman Filter fixed-interval smoother to improve the utility of these models as policy tools. We apply this scheme to a model for Colombia.