General State-space Model Research Articles

A Statistical Model for Predicting the Liquid Steel Temperature in Ladle and Tundish by Bootstrap Filter

A statistical model for predicting the liquid steel temperature in the ladle and in the tundish is developed. Given a large data set in a steelmaking process, the proposed model predicts the temperature in a seconds with a good accuracy. The data are divided into four phases at the mediation of five temperature measurements: before tapping from the converter (CV), after throwing ferroalloys into the ladle, before and after the Ruhrstahl-Heraeus (RH) processing, and after casting into the tundish in the continuous casting (CC) machine. Based on the general state space modeling, the bootstrap filter predicts the temperature phase by phase. The particle approximation technique enables to compute general-shaped probability distributions. The proposed model gives a prediction not as a point but as a probability distribution, or a predictive distribution. It evaluates both uncertainty of the prediction and ununiformity of the temperature. It is applicable to sensitivity analysis, process scheduling and temperature control.

Quasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes

We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing condition on the output process of the state space model. In the second part of the paper, we investigate probabilistic and analytical properties of equidistantly sampled continuous-time state space models and apply our results from the discrete-time setting to derive the asymptotic properties of the QML estimator of discretely recorded MCARMA processes. Under natural identifiability conditions, the estimators are again consistent and asymptotically normally distributed for any sampling frequency. We also demonstrate the practical applicability of our method through a simulation study and a data example from econometrics.

Nonparametric particle filtering and smoothing with quasi-Monte Carlo sampling

Sequential Monte Carlo methods (also known as particle filters and smoothers) are used for filtering and smoothing in general state-space models. These methods are based on importance sampling. In practice, it is often difficult to find a suitable proposal which allows effective importance sampling. This article develops an original particle filter and an original particle smoother which employ nonparametric importance sampling. The basic idea is to use a nonparametric estimate of the marginally optimal proposal. The proposed algorithms provide a better approximation of the filtering and smoothing distributions than standard methods. The methods’ advantage is most distinct in severely nonlinear situations. In contrast to most existing methods, they allow the use of quasi-Monte Carlo (QMC) sampling. In addition, they do not suffer from weight degeneration rendering a resampling step unnecessary. For the estimation of model parameters, an efficient on-line maximum-likelihood (ML) estimation technique is proposed which is also based on nonparametric approximations. All suggested algorithms have almost linear complexity for low-dimensional state-spaces. This is an advantage over standard smoothing and ML procedures. Particularly, all existing sequential Monte Carlo methods that incorporate QMC sampling have quadratic complexity. As an application, stochastic volatility estimation for high-frequency financial data is considered, which is of great importance in practice. The computer code is partly available as supplemental material.

On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization

This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is "matched" to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.

Extended Kalman Filter frequency tracker for nonstationary harmonic signals

In this paper, we propose a frequency tracking algorithm based on an Extended Kalman Filter (EKF). We introduce a generalized state space model to estimate and track frequency of a harmonic signal embedded in broad-band noise. Such nonstationary noisy harmonic signals are characterized by time-varying frequencies and amplitudes. Developing a modified state-space model, we improve performance of EKF frequency tracker for these signals. The proposed method is also used in an adaptive algorithm to estimate noise variance which is assumed to be unknown. Simulation results reveal superiority of the proposed method compared with typical EKF, short time Fourier transform, and interpolated discrete Fourier transform.

A study of outliers in the exponential smoothing approach to forecasting

Outliers in time series have the potential to affect parameter estimates and forecasts when using exponential smoothing. The aim of this study is to show the way in which important types of outliers can be incorporated into linear innovations state space models for exponential smoothing methods. The types of outliers include an additive outlier, a level shift, and a transitory change. The general innovations state space model and a special case which encompasses the common linear exponential smoothing methods are examined. A method for identifying outliers using innovations state space models is proposed. This method is investigated using both simulations and applications to real time series. The impact of an outlier’s location on the forecasts and the estimation of parameters is examined. The forecasts from outlier and basic non-outlier models are compared. An automatic method is found to result in improved forecasts for both the simulated and real data.

Density-Tempered Marginalized Sequential Monte Carlo Samplers

We propose a density-tempered marginalized sequential Monte Carlo (SMC) sampler, a new class of samplers for full Bayesian inference of general state-space models. The dynamic states are approximately marginalized out using a particle filter, and the parameters are sampled via a sequential Monte Carlo sampler over a density-tempered bridge between the prior and the posterior.Our approach delivers exact draws from the joint posterior of the parameters and the latent states for any given number of state particles, and thus easily parallelizable in implementation. We also build into the proposed method a device that can automatically select a suitable number of state particles. Since the method incorporates sample information in a smooth fashion, it delivers good performance in the presence of outliers. We check the performance of the density-tempered SMC algorithm using simulated data based on a linear Gaussian state space model with and without mis-specification. We also apply it on real stock prices using a GARCH-type model with microstructure noise.

Rate estimation in partially observed Markov jump processes with measurement errors

We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data, we embed the Markov jump process into the framework of a general state space model. We do not use diffusion approximations. Markov chain Monte Carlo and particle filter type algorithms are introduced which allow sampling from the posterior distribution of the rate parameters and the Markov jump process also in data-poor scenarios. The algorithms are illustrated by applying them to rate estimation in a model for prokaryotic auto-regulation and the stochastic Oregonator, respectively.

State-Observation Sampling and the Econometrics of Learning Models

In nonlinear state-space models, sequential learning about the hidden state can proceed by particle filtering when the density of the observation conditional on the state is available analytically (e.g. Gordon et al. 1993). This condition need not hold in complex environments, such as the incomplete-information equilibrium models considered in financial economics. In this paper, we make two contributions to the learning literature. First, we introduce a new filtering method, the state-observation sampling (SOS) filter, for general state-space models with intractable observation densities. Second, we develop an indirect inference-based estimator for a large class of incomplete-information economies. We demonstrate the good performance of these techniques on an asset pricing model with investor learning applied to over 80 years of daily equity returns.

Nonlinear Predictor-Based Dynamic Resource Allocation Over Point-to-Multipoint (P2MP) Networks: A Control Theoretical Approach

Most broadband access networks such as passive optical networks (PONs) adopt the point-to-multipoint (P2MP) topology. One critical issue in such networks is the upstream resource management and allocation mechanism. Nonlinear predictor-based dynamic resource allocation (NLPDRA) schemes for improving the P2MP network upstream transmission efficiency have been investigated in an ad hoc manner. In this paper, we establish a general state space model to analyze the controllability and stability of the NLPDRA schemes from the P2MP network system’s point of view and propose controller design guidelines to maintain the system stability under different scenarios. Analytical results show that NLPDRA maintains the P2MP network system controllability even when the loaded network traffic changes drastically. We further prove that a P2MP network system with NLPDRA is stable by proper pole placements as the traffic changes. Finally, we provide guidelines to design a optimal compensator to achieve system accuracy.

W201 データ同化によるヘテロ情報の統融合(WS2-1 CFDとEFDの融合研究,ワークショップ2)

Data Assimilation (DA) is a technique for a synthesis of information from a dynamic numerical model and observation data. In statistical methodology, DA can be formulated in the generalized state space model. We briefly explain a recent advancement in the ensemble-based sequential DA (EnSDA), and discuss on how EnSDA is employed in combining CFD and EFD.

Estimation of trend in state-space models: Asymptotic mean square error and rate of convergence

The focus of this paper is on trend estimation for a general state-space model Y t = μ t + e t , where the dth difference of the trend {μ t } is assumed to be i.i.d., and the error sequence {e t is assumed to be a mean zero stationary process. A fairly precise asymptotic expression of the mean square error is derived for the estimator obtained by penalizing the dth order differences. Optimal rate of convergence is obtained, and it is shown to be asymptotically equivalent to a nonparametric estimator of a fixed trend model of smoothness of order d — 0.5. The results of this paper show that the optimal rate of convergence for the stochastic and nonstochastic cases are different. A criterion for selecting the penalty parameter and degree of difference d is given, along with an application to the global temperature data, which shows that a longer term history has nonlinearities that are important to take into consideration.

Observation-driven generalized state space models for categorical time series

Observation-driven state space models are presented for categorical time series as an alternative to the regression type models which are commonly used in the literature. As an application to multi-categorical time series, we present a DNA data analysis and demonstrate the advantages of using state space models.

An Overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, provide very good numerical approximations to the associated optimal state estimation problems. However, in many scenarios, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard SMC methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models. We discuss the advantages and limitations of these methods.

Extracting a common stochastic trend: Theory with some applications

Abstract This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models—those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models we explicitly consider comprise a special–yet useful–class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices.

Pairwise Likelihood Inference for General State Space Models

This article concerns parameter estimation for general state space models, following a frequentist likelihood-based approach. Since exact methods for computing and maximizing the likelihood function are usually not feasible, approximate solutions, based on Monte Carlo or numerical methods, have to be considered. Here, we concentrate on a different approach based on a simple pseudolikelihood, called “pairwise likelihood.” Its merit is to reduce the computational burden so that it is possible to fit highly structured statistical models, even when the use of standard likelihood methods is not possible. We discuss pairwise likelihood inference for state space models, and we present some touchstone examples concerning autoregressive models with additive observation noise and switching regimes, the local level model and a non-Makovian generalization of the dynamic Tobit model.

Practical Filtering with Sequential Parameter Learning

SummaryThe paper develops a simulation-based approach to sequential parameter learning and filtering in general state space models. Our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions. Parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms. We avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling. The method is illustrated by using two examples: a benchmark auto-regressive model with observation error and a high dimensional dynamic spatiotemporal model. We show that the method provides accurate inference in the presence of outliers, model misspecification and high dimensionality.

Bayesian Inference on Dynamic Models with Latent Factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.

ディジタルコンテンツ制作―ＤＣＳ’０７関連―個人撮影映像を対象とした映像速覧のための“笑い”シーン検出法

A method is described for detecting a “laughter” scene in a Consumer Generated Video (CGV). The growing number of CGVs is growing, so a video skimming method that allows viewers to quickly find “enjoyable” scenes would be useful. An experiment showed that viewers tend to find CGVs that include a “laughter” scene “enjoyable”. On that basis, we developed a method for detecting “laughter” scenes using prosodic information such as pitch, energy, power spectrum densities and their differential components to estimate the probability of laughter in the soundtrack. In this method, a generalized state space model, which consists of acoustic models and a state-transition model, calculates the probability of laughter to detect a “laughter” scene. An experiment showed that the precision rate of the method was about 83%, which suggests that the method enables effective video skimming.

A note on arbitrage-free asset prices with and without personal income taxes

We study the implications of the absence of arbitrage possibilities on asset pricing with and without personal income taxes. While no-arbitrage conditions in frictionless markets have sufficiently been investigated, personal income taxation is still beyond of being fully integrated into arbitrage theory. In extending the primary analysis of Ross (J Polit Econ 95:371–393, 1987) to a multiperiod framework allowing for dynamic trading strategies, we take a major step in this direction. The existence of a positive linear pricing functional is proven in a general discrete time and discrete state space model. In order to obtain the linearity of the pricing functional, one has to allow for short sales or, at most, to restrict sales to positions initially given. Hints at far-reaching economic applications are available.