Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.Comment: 30 page

Fundamental frequency estimation in speech signals with variable rate particle filters

Fundamental frequency estimation, known as pitch estimation in speech signals is of interest both to the research community and to industry. Meanwhile, the particle filter is known to be a powerful Bayesian inference method to track dynamic parameters in nonlinear state-space models. In this paper, we propose a speech model under a time-varying source-filter speech model, and use variable rate particle filters (VRPF) to develop methods for estimation of pitch periods in speech signals. A Rao–Blackwellised variable rate particle filter (RBVRPF) is also implemented. The proposed VRPF and RBVRPF are compared with a state-of-the-art pitch estimation algorithm, the YIN algorithm. Simulation results show that more accurate estimation of pitch can be obtained by VRPF and RBVRPF even under strong background noise conditions.The authors would like to thank CSC Cambridge International Scholarship and Natural Science Foundation of China (No.61463035) for providing financial support.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TASLP.2016.253128

A Particle Filter Localisation System for Indoor Track Cycling Using an Intrinsic Coordinate Model

© 2018 ISIF In this paper we address the challenging task of tracking a fast-moving bicycle, in the indoor velodrome environment, using inertial sensors and infrequent position measurements. Since the inertial sensors are physically in the intrinsic frame of the bike, we adopt an intrinsic frame dynamic model for the motion, based on curvilinear dynamical models for manoeuvring objects. We show that the combination of inertial measurements with the intrinsic dynamic model leads to linear equations, which may be incorporated effectively into particle filtering schemes. Position measurements are provided through timing measurements on the track from a camera-based system and these are fused with the inertial measurements using a particle filter weighting scheme. The proposed methods are evaluated on synthesised cycling datasets based on real motion trajectories, showing their potential accuracy, and then real data experiments are reported

Bayesian Fusion of Asynchronous Inertial, Speed and Position Data for Object Tracking

In this paper we present Bayesian methods for tracking scenarios in which an intrinsic coordinate model is considered and inertial mea- surements plus occasional position fixes are available. The methods are first tested using synthetic data, giving a comprehensive evalu- ation as to their performance. Further evaluation on real data also reveals our approaches can be favourable alternatives to existing in- ertial tracking/navigation models

Efficient alternatives to the Ephraim and Malah suppression rule for audio signal enhancement

Audio signal enhancement often involves the application of a time-varying filter, or suppression rule, to the frequency-domain transform of a corrupted signal. Here we address suppression rules derived under a Gaussian model and interpret them as spectral estimators in a Bayesian statistical framework. With regard to the optimal spectral amplitude estimator of Ephraim and Malah, we show that under the same modelling assumptions, alternative methods of Bayesian estimation lead to much simpler suppression rules exhibiting similarly effective behaviour. We derive three of such rules and demonstrate that, in addition to permitting a more straightforward implementation, they yield a more intuitive interpretation of the Ephraim and Malah solution

Sequential inference methods for non-homogeneous poisson processes with state-space prior

© 2018 IEEE. The Non-homogeneous Poisson process is a point process with time-varying intensity across its domain, the use of which arises in numerous areas in signal processing and machine learning. However, applications are largely limited by the intractable likelihood function and the high computational cost of existing inference schemes. We present a sequential inference framework that utilises generative Poisson data and sequential Markov Chain Monte Carlo (SMCMC) algorithm to enable online inference in various applications. The proposed model is compared to competing methods on synthetic datasets and tested with real-world financial data

Sequential Inference Methods for Non-Homogeneous Poisson Processes with State-Space Prior

The non-homogeneous Poisson process provides a generalised framework for the modelling of random point data by allowing the intensity of point generation to vary across its domain of interest (time or space). The use of non-homogeneous Poisson processes have arisen in many areas of signal processing and machine learning, but application is still largely limited by its intractable likelihood function and the lack of computationally efficient inference schemes, although some methods do exist for the batch data case. In this paper, we propose for the first time a sequential framework for intensity inference which combines the non-homogeneous model of Poisson data with continuous-time state-space models for their time-varying intensity. This approach enables us to design efficient online inference schemes, for which we propose a novel sequential Markov chain Monte Carlo (SMCMC) algorithm, as is demanded by many applications where point data arrive sequentially and decisions need to be made with low latency. The proposed approach is compared with competing methods on synthetic datasets and tested with high-frequency financial order book data, showing in general improved performance and better computational efficiency than the main batch-based competitor algorithm, and better performance than a simple baseline kernel estimation scheme