Linear State-Space Model with Time-Varying Dynamics

This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model allowing the model to learn how the dynamics of the process changes. Previous approaches have used switching models which have a small set of possible state dynamics matrices and the model selects one of those matrices at each time, thus jumping between them. Our model forms the dynamics as a linear combination and the changes can be smooth and more continuous. The model is motivated by physical processes which are described by linear partial differential equations whose parameters vary in time. An example of such a process could be a temperature field whose evolution is driven by a varying wind direction. The posterior inference is performed using variational Bayesian approximation. The experiments on stochastic advection-diffusion processes and real-world weather processes show that the model with time-varying dynamics can outperform previously introduced approaches.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44851-9_2

Graphical State Space Model

In this paper, a new framework, named as graphical state space model, is proposed for the real time optimal estimation of a class of nonlinear state space model. By discretizing this kind of system model as an equation which can not be solved by Extended Kalman filter, factor graph optimization can outperform Extended Kalman filter in some cases. A simple nonlinear example is given to demonstrate the efficiency of this framework

Network estimation in State Space Model with L1-regularization constraint

Biological networks have arisen as an attractive paradigm of genomic science ever since the introduction of large scale genomic technologies which carried the promise of elucidating the relationship in functional genomics. Microarray technologies coupled with appropriate mathematical or statistical models have made it possible to identify dynamic regulatory networks or to measure time course of the expression level of many genes simultaneously. However one of the few limitations fall on the high-dimensional nature of such data coupled with the fact that these gene expression data are known to include some hidden process. In that regards, we are concerned with deriving a method for inferring a sparse dynamic network in a high dimensional data setting. We assume that the observations are noisy measurements of gene expression in the form of mRNAs, whose dynamics can be described by some unknown or hidden process. We build an input-dependent linear state space model from these hidden states and demonstrate how an incorporated $L_{1}$ regularization constraint in an Expectation-Maximization (EM) algorithm can be used to reverse engineer transcriptional networks from gene expression profiling data. This corresponds to estimating the model interaction parameters. The proposed method is illustrated on time-course microarray data obtained from a well established T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4, CASP4, CD69, and C3X1 to have higher number of inwards directed connections and FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed connections. We recommend these genes to be object for further investigation. Caspase 4 is also found to activate the expression of JunD which in turn represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359

A Tractable State-Space Model for Symmetric Positive-Definite Matrices

Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$ there are several well-known modeling components and computational tools that may be profitably combined to achieve these tasks. However, there are scenarios, like tracking an object in a video or tracking a covariance matrix of financial assets returns, when the latent states are restricted to a curve within $\mathbb{R}^n$ and these models and tools do not immediately apply. Within this constrained setting, most work has focused on filtering and less attention has been paid to the other aspects of Bayesian state-space inference, which tend to be more challenging. To that end, we present a state-space model whose latent states take values on the manifold of symmetric positive-definite matrices and for which one may easily compute the posterior distribution of the latent states and the system's parameters, in addition to filtered distributions and one-step ahead predictions. Deploying the model within the context of finance, we show how one can use realized covariance matrices as data to predict latent time-varying covariance matrices. This approach out-performs factor stochastic volatility.Comment: 22 pages: 16 pages main manuscript, 4 pages appendix, 2 pages reference

A non-Gaussian continuous state space model for asset degradation

The degradation model plays an essential role in asset life prediction and condition based maintenance. Various degradation models have been proposed. Within these models, the state space model has the ability to combine degradation data and failure event data. The state space model is also an effective approach to deal with the multiple observations and missing data issues. Using the state space degradation model, the deterioration process of assets is presented by a system state process which can be revealed by a sequence of observations. Current research largely assumes that the underlying system development process is discrete in time or states. Although some models have been developed to consider continuous time and space, these state space models are based on the Wiener process with the Gaussian assumption. This paper proposes a Gamma-based state space degradation model in order to remove the Gaussian assumption. Both condition monitoring observations and failure events are considered in the model so as to improve the accuracy of asset life prediction. A simulation study is carried out to illustrate the application procedure of the proposed model

Forecasting macroeconomic variables using a structural state space model

This paper has a twofold purpose; the first is to present a small macroeconomic model in state space form, the second is to demonstrate that it produces accurate forecasts. The first of these objectives is achieved by fitting two forms of a structural state space macroeconomic model to Australian data. Both forms model short and long run relationships. Forecasts from these models are subsequently compared to a structural vector autoregressive specification. This comparison fulfills the second objective demonstrating that the state space formulation produces more accurate forecasts for a selection of macroeconomic variables.State space, multivariate time series, macroeconomic model, forecast, SVAR

Interactive and common knowledge in the state-space model

This paper deals with the prevailing formal model for knowledge in contemporary economics, namely the state-space model introduced by Robert Aumann in 1976. In particular, the paper addresses the following question arising in this formalism: in order to state that an event is interactively or commonly known among a group of agents, do we need to assume that each of them knows how the information is imparted to the others? Aumann answered in the negative, but his arguments apply only to canonical, i.e., completely specified state spaces, while in most applications the state space is not canonical. This paper addresses the same question along original lines, demonstrating that the answer is negative for both canonical and not-canonical state spaces. Further, it shows that this result ensues from two counterintuitive properties held by knowledge in the state-space model, namely Substitutivity and Monotonicity.

A semiparametric state space model

This paper considers the problem of estimating a linear univariate Time Series State Space model for which the shape of the distribution of the observation noise is not specified a priori. Although somewhat challenging computationally, the simultaneous estimation of the parameters of the model and the unknown observation noise density is made feasible through a combination of Gaussian-sum Filtering and Smoothing algorithms and Kernel Density Estimation methods. The bottleneck in these calculations consists in avoiding the geometric increase, with time, of the number of simultaneous Kalman filter components. It is the aim of this paper to show that this can be achieved by the use of standard techniques from Cluster Analysis and unsupervised Classification. An empirical illustration of this new methodology is included; this consists in the application of a semiparametric version of the Local Level model to the analysis of the wellknown river Nile data series