State Space Models (state + space_models)

Distribution by Scientific Domains


Selected Abstracts


Modelling & Controlling Monetary and Economic Identities with Constrained State Space Models

INTERNATIONAL STATISTICAL REVIEW, Issue 2 2007
Gurupdesh S. Pandher
Summary The paper presents a method for modelling and controlling time series with identity structures. The approach is presented in the context of monetary targeting where the monetary identity (e.g. reserve money equals net foreign assets plus domestic credit) is modelled using a constrained state space model and next-period changes in domestic credit (policy variable) are estimated to reach the target level of reserve money. The constrained modelling ensures that aggregation and identity relations among items are dynamically satisfied during estimation, leading to more accurate forecasting and targeting. Applications to Germany, UK and USA show that the constrained state space model provides significant improvements in targeting and forecasting performance over the AR(1) benchmark and the unconstrained model. Reduction in the mean square error of targeting over AR(1) is in the range of 76,95% for the three countries while the gain in targeting efficiency over unconstrained modelling is between 21% and 55%. Beyond monetary targeting, the method has wide application to the dynamic modelling and control of economic and financial time series with identity and aggregation constraints (e.g. balance of payment, national income, purchasing power parity, company balance sheet). Résumé L'article présente une méthode de modélisation et de contrôle des séries temporelles avec des structures d'identité. L'approche est présentée dans le contexte de ciblage monétaire où l'identité monétaire (c. à d. monnaie de réserve égale avoirs étrangers plus crédit intérieur) est modélisée en utilisant un modèle spatial sous contrainte et où les variations du crédit intérieur à la période suivante (variable de politique) sont estimés pour atteindre le niveau visé de monnaie de réserve. La modélisation sous contrainte assure que les relations d'agrégation et d'identité entre items sont satisfaites en dynamique dans l'estimation, ce qui conduit à des prévisions et ciblages plus précis. L'application à l'Allemagne, le Royaume-Uni et les USA montrent que le modèle contraint apporte des améliorations importantes dans la performance de ciblage et de prévision par rapport à l'étalonnage auto-régressif (1) et au modèle sans contrainte. La réduction d'erreur du moindre carré par rapport à l'AR est comprise entre 76 et 95% pour les trois pays tandis que le gain en efficacité de ciblage sur le modèle sans contrainte se situe entre 21 et 55%. Par delà le ciblage monétaire, la méthode a une large application à la modélisation dynamique et au contrôle des séries temporelles économiques et financières avec des contraintes d'identité et d'agrégation (par ex. la balance des paiements, le revenu national, la parité de pouvoir d'achat, le bilan d'une compagnie). [source]


Fast Filtering and Smoothing for Multivariate State Space Models

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2000
S. J. Koopman
This paper investigates a new approach to diffuse filtering and smoothing for multivariate state space models. The standard approach treats the observations as vectors, while our approach treats each element of the observational vector individually. This strategy leads to computationally efficient methods for multivariate filtering and smoothing. Also, the treatment of the diffuse initial state vector in multivariate models is much simpler than in existing methods. The paper presents details of relevant algorithms for filtering, prediction and smoothing. Proofs are provided. Three examples of multivariate models in statistics and economics are presented for which the new approach is particularly relevant. [source]


Best Linear Unbiased Fir Filters For Continuous-Time State Space Models

ASIAN JOURNAL OF CONTROL, Issue 1 2001
Wook Hyun Kwon
ABSTRACT This paper proposes a new linear finite impulse response (FIR) filter called the best linear unbiased FIR (BLUF) filter for the state estimation in continuous-time state space models. The proposed BLUF filter for continuous-time state space models is obtained by a formal limiting procedure of discretized systems. The BLUF filter is represented in an iterative form and then in a standard FIR form. It is shown that the proposed BLUF filter has deadbeat and unbiasedness properties. It is also shown that the BLUF filter is equivalent to the existing receding horizon Kalman FIR (RHKF) filter whose optimality is not clear to understand. The former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state. [source]


Bayesian State Space Models for Inferring and Predicting Temporal Gene Expression Profiles

BIOMETRICAL JOURNAL, Issue 6 2007
Yulan Liang
Abstract Prediction of gene dynamic behavior is a challenging and important problem in genomic research while estimating the temporal correlations and non-stationarity are the keys in this process. Unfortunately, most existing techniques used for the inclusion of the temporal correlations treat the time course as evenly distributed time intervals and use stationary models with time-invariant settings. This is an assumption that is often violated in microarray time course data since the time course expression data are at unequal time points, where the difference in sampling times varies from minutes to days. Furthermore, the unevenly spaced short time courses with sudden changes make the prediction of genetic dynamics difficult. In this paper, we develop two types of Bayesian state space models to tackle this challenge for inferring and predicting the gene expression profiles associated with diseases. In the univariate time-varying Bayesian state space models we treat both the stochastic transition matrix and the observation matrix time-variant with linear setting and point out that this can easily be extended to nonlinear setting. In the multivariate Bayesian state space model we include temporal correlation structures in the covariance matrix estimations. In both models, the unevenly spaced short time courses with unseen time points are treated as hidden state variables. Bayesian approaches with various prior and hyper-prior models with MCMC algorithms are used to estimate the model parameters and hidden variables. We apply our models to multiple tissue polygenetic affymetrix data sets. Results show that the predictions of the genomic dynamic behavior can be well captured by the proposed models. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


A comparison of small gain versus Lyapunov type robust stability bounds

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2001
Jie Chen
Abstract We address stability issues pertaining to perturbed linear time-invariant systems described by state space models. We show that for a class of highly structured uncertainties in the system matrix, a robust stability bound given by the complex structured singular value is less conservative than that obtained via Lyapunov approach. This result thus provides a counterpart to an earlier one pertaining to unstructured uncertainties, and serves to extend and support the statement that frequency domain small gain conditions may often be less conservative than those time domain criteria obtained using Lyapunov approach. Copyright © 2001 John Wiley & Sons, Ltd. [source]


Forecasting volatility by means of threshold models

JOURNAL OF FORECASTING, Issue 5 2007
M. Pilar Muñoz
Abstract The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out-of-sample forecasting ability of the SETAR-Threshold GARCH (SETAR-TGARCH) and the SETAR-Threshold Stochastic Volatility (SETAR-THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ,true' underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR-THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Forecasting multivariate time series with linear restrictions using constrained structural state-space models

JOURNAL OF FORECASTING, Issue 4 2002
Gurupdesh S. Pandher
Abstract This paper presents a methodology for modelling and forecasting multivariate time series with linear restrictions using the constrained structural state-space framework. The model has natural applications to forecasting time series of macroeconomic/financial identities and accounts. The explicit modelling of the constraints ensures that model parameters dynamically satisfy the restrictions among items of the series, leading to more accurate and internally consistent forecasts. It is shown that the constrained model offers superior forecasting efficiency. A testable identification condition for state space models is also obtained and applied to establish the identifiability of the constrained model. The proposed methods are illustrated on Germany's quarterly monetary accounts data. Results show significant improvement in the predictive efficiency of forecast estimators for the monetary account with an overall efficiency gain of 25% over unconstrained modelling. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2009
Håvard Rue
Summary., Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. [source]


Estimability of the linear effects in state space models with an unknown initial condition

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2010
Rajesh Selukar
In the case of state space models with an unknown initial condition, the diffuse Kalman smoother can be used to obtain smoothed state estimates. When the full initial state is not estimable because the available data are insufficient, some linear combinations of the states can still be estimable. This brief note provides a simple method to determine whether a linear combination of a state is estimable. [source]


SMOOTHING WITH AN UNKNOWN INITIAL CONDITION

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2003
Piet De Jong
Abstract. The smoothing filter is appropriately modified for state space models with an unknown initial condition. Modifications are confined to an initial stretch of the data. An application illustrates procedures. [source]


Fast Filtering and Smoothing for Multivariate State Space Models

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2000
S. J. Koopman
This paper investigates a new approach to diffuse filtering and smoothing for multivariate state space models. The standard approach treats the observations as vectors, while our approach treats each element of the observational vector individually. This strategy leads to computationally efficient methods for multivariate filtering and smoothing. Also, the treatment of the diffuse initial state vector in multivariate models is much simpler than in existing methods. The paper presents details of relevant algorithms for filtering, prediction and smoothing. Proofs are provided. Three examples of multivariate models in statistics and economics are presented for which the new approach is particularly relevant. [source]


Semi-strong dynamic style analysis with time-varying selectivity measurement: Applications to Brazilian exchange-rate funds

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2008
Adrian Pizzinga
Abstract This paper deals with restricted linear state space models for dynamic style analysis with time-varying selectivity measurement. Implementation and interpretation of the models are pertinently discussed. Empirical contributions lie on the understanding of how managers of Brazilian US Dollar/Real exchange-rate funds behaved along 2001 and 2002, a period of some political turbulence especially due to the 2002 Brazilian presidential election. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Wavelets in state space models

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2003
Eliana Zandonade
Abstract In this paper, we consider the utilization of wavelets in conjunction with state space models. Specifically, the parameters in the system matrix are expanded in wavelet series and estimated via the Kalman Filter and the EM algorithm. In particular this approach is used for switching models. Two applications are given, one to the problem of detecting the paths of targets using an array of sensors, and the other to a series of daily spreads between two Brazilian bonds. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Best Linear Unbiased Fir Filters For Continuous-Time State Space Models

ASIAN JOURNAL OF CONTROL, Issue 1 2001
Wook Hyun Kwon
ABSTRACT This paper proposes a new linear finite impulse response (FIR) filter called the best linear unbiased FIR (BLUF) filter for the state estimation in continuous-time state space models. The proposed BLUF filter for continuous-time state space models is obtained by a formal limiting procedure of discretized systems. The BLUF filter is represented in an iterative form and then in a standard FIR form. It is shown that the proposed BLUF filter has deadbeat and unbiasedness properties. It is also shown that the BLUF filter is equivalent to the existing receding horizon Kalman FIR (RHKF) filter whose optimality is not clear to understand. The former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state. [source]


Stochastic Model Reduction by Maximizing Independence

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2005
Hui Zhang
By analysing information descriptions in state space models of linear stochastic systems, this paper proposes two model reduction methods via principles of maximizing independence and conditional independence among the reduced state vector, respectively. These methods are based on state aggregation. The independence and conditional independence are measured by the Kullback-Leibler information distance. It is demonstrated that the maximum conditional independence method is not only applicable to stable systems, but also applicable to unstable systems. Simulation results illustrate the efficiency of the present methods. [source]


EXPONENTIAL SMOOTHING AND NON-NEGATIVE DATA

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009
Muhammad Akram
Summary The most common forecasting methods in business are based on exponential smoothing, and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore exponential smoothing state space models for non-negative data under various assumptions about the innovations, or error, process. We first demonstrate that prediction distributions from some commonly used state space models may have an infinite variance beyond a certain forecasting horizon. For multiplicative error models that do not have this flaw, we show that sample paths will converge almost surely to zero even when the error distribution is non-Gaussian. We propose a new model with similar properties to exponential smoothing, but which does not have these problems, and we develop some distributional properties for our new model. We then explore the implications of our results for inference, and compare the short-term forecasting performance of the various models using data on the weekly sales of over 300 items of costume jewelry. The main findings of the research are that the Gaussian approximation is adequate for estimation and one-step-ahead forecasting. However, as the forecasting horizon increases, the approximate prediction intervals become increasingly problematic. When the model is to be used for simulation purposes, a suitably specified scheme must be employed. [source]


Bayesian State Space Models for Inferring and Predicting Temporal Gene Expression Profiles

BIOMETRICAL JOURNAL, Issue 6 2007
Yulan Liang
Abstract Prediction of gene dynamic behavior is a challenging and important problem in genomic research while estimating the temporal correlations and non-stationarity are the keys in this process. Unfortunately, most existing techniques used for the inclusion of the temporal correlations treat the time course as evenly distributed time intervals and use stationary models with time-invariant settings. This is an assumption that is often violated in microarray time course data since the time course expression data are at unequal time points, where the difference in sampling times varies from minutes to days. Furthermore, the unevenly spaced short time courses with sudden changes make the prediction of genetic dynamics difficult. In this paper, we develop two types of Bayesian state space models to tackle this challenge for inferring and predicting the gene expression profiles associated with diseases. In the univariate time-varying Bayesian state space models we treat both the stochastic transition matrix and the observation matrix time-variant with linear setting and point out that this can easily be extended to nonlinear setting. In the multivariate Bayesian state space model we include temporal correlation structures in the covariance matrix estimations. In both models, the unevenly spaced short time courses with unseen time points are treated as hidden state variables. Bayesian approaches with various prior and hyper-prior models with MCMC algorithms are used to estimate the model parameters and hidden variables. We apply our models to multiple tissue polygenetic affymetrix data sets. Results show that the predictions of the genomic dynamic behavior can be well captured by the proposed models. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]