We study the adaptive filtering for risk premium and system parameters in electricity futures modes. Introducing the jump augmented Vasicek model as the spot price mode, the factor model of the electricity futures is constructed as the stochastic hyperbolic systems with jumps. Representing the main spike phenomena of the electricity spot price from one observed futures data by proxy, the filtering of the stochastic risk premium and its system parameters are developed in a Gaussian framework. By using the parallel filtering algorithm, the online system parameter estimation procedure is proposed.

We study the sequential identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility is constructed. The systems parameters are sequentially estimated with the aid of parallel filtering algorithm. To improve the estimation performance for unknown parameters, the new resampling procedure is proposed. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

We study the identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility and its systems parameters is constructed. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

We study the problem of optimal reduced-dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal. In the mean square estimation context this involves finding the optimal signal representation based on multiple incomplete or only partial observations that are correlated. In particular, this leads to the study of finding the optimal Karhunen-Loeve basis based on the censored observations. The problem has been considered previously by Gastpar, Dragotti, and Vetterli in the context of jointly Gaussian random variables based on using conditional covariances. In this paper, we derive the estimation results in the more general setting of second-order random variables with arbitrary distributions, using entirely different techniques based on the idea of innovations. We explicitly solve the single transform coder case, give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problem.

The robust form of the likelihood ratio for a signal in the presence of white noise has an additional term in the exponent called the correction factor which corresponds to the trace of the conditional covariance of the signal given the observations. The authors show that this correction term is nothing but the trace of the symmetrized Frechet derivative of the nonlinear filter map and hence the likelihood ratio can be completely represented in terms of the observations and the filter map.>

A factorization of the covariance operator (I+R) is derived for the observation process of a 2-parameter random field. This result can be applied to express the determinant term appearing in L.A. Shepp's (1966) expression for the likelihood ratio in terms of the system parameters. This means that, in practice, one of the problems in computing the likelihood ratio for random fields is solved. Extensions to the multiparameter case are straightforward. The expression of the determinant of (I+R) in terms of the system parameters may also be used to reexpress the Wong-Zakai correction term (1977).>