Quasi-Maximum Likelihood estimation of Stochastic Volatility models.

Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the volatility as an unobserved vatiable, the logarithm of which is modelled as a linear stochastic process, usually an autoregression. This article analyses the asymptotic and finite sample properties of a Quasi-Maximum Likelihood (QML) estimator based on the Kalman filter. The relative efficiency of the QML estimator when compared with estimators based on the Generalized Method of Moments is shown to be quite high for parameter values often found in empirical applications. The QML estimator can still be employed when the SV model is generalized to allow for distributions with heavier tails than the normal. SV models are finally fitted to daily observations on the yen/dollar exchange rate.Exchange rates; Generalized method of moments; Kalman filter; Quasi- maximum likelihood; Stochastic volatility;

A New Perspective and Extension of the Gaussian Filter

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF from a variational-inference perspective. We analyse how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.Comment: Will appear in Robotics: Science and Systems (R:SS) 201

Generalized Hidden Filter Markov Models Applied to Speaker Recognition

Classification of time series has wide Air Force, DoD and commercial interest, from automatic target recognition systems on munitions to recognition of speakers in diverse environments. The ability to effectively model the temporal information contained in a sequence is of paramount importance. Toward this goal, this research develops theoretical extensions to a class of stochastic models and demonstrates their effectiveness on the problem of text-independent (language constrained) speaker recognition. Specifically within the hidden Markov model architecture, additional constraints are implemented which better incorporate observation correlations and context, where standard approaches fail. Two methods of modeling correlations are developed, and their mathematical properties of convergence and reestimation are analyzed. These differ in modeling correlation present in the time samples and those present in the processed features, such as Mel frequency cepstral coefficients. The system models speaker dependent phonemes, making use of word dictionary grammars, and recognition is based on normalized log-likelihood Viterbi decoding. Both closed set identification and speaker verification using cohorts are performed on the YOHO database. YOHO is the only large scale, multiple-session, high-quality speech database for speaker authentication and contains over one hundred speakers stating combination locks. Equal error rates of 0.21% for males and 0.31% for females are demonstrated. A critical error analysis using a hypothesis test formulation provides the maximum number of errors observable while still meeting the goal error rates of 1% False Reject and 0.1% False Accept. Our system achieves this goal

Application of teh Kalman Filter to Interest Rate Modelling

We give a mild introduction to the Kalman filter and the generalized Vasicek models of the term structure of interest rates with special attention to the application of the Kalman filter equations to one-and two-factor models. After thoroughly reviewing the essential tools that constitute the Kalman filter and the generalized Vasicek models of the term structure of interest rates, we derive the yield on a zero coupon bond with infinite maturity and the Kalman �filter equations of the state space formulation of the generalized Vasicek models. By performing simulations, we illustrate how the Kalman �filter works and the major weakness of the Vasicek model