Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its va...

Recently, we proposed an autoregressive linear mixed effects model for the analysis of longitudinal data in which the current response is regressed on the previous response, fixed effects, and random effects (Funatogawa et al., Statist. Med. 2007; 26:2113-2130). The model represents profiles approaching random equilibriums. Because intermittent missing is an inherent problem of the autoregressi...

In time series problems, noise can be divided into two categories: dynamic noise which drives the process, and observational noise which is added in the measurement process, but does not influence future values of the system. In this framework, we show that empirical volatilities (the squared relative returns of prices) exhibit a significant amount of observational noise. To model and predict t...

Granger causality has long been a prominent method for inferring causal interactions between stochastic variables for a broad range of complex physical systems. However, it has been recognized that a moving average (MA) component in the data presents a serious confound to Granger causal analysis, as routinely performed via autoregressive (AR) modeling. We solve this problem by demonstrating tha...

We describe Bayesian learning in nonlinear state-space models (NSSMs). NSSMs are a general method for the probabilistic modelling of sequences and time-series. They take the form of iterated maps on continuous state-spaces, and can have either discrete or continuous valued output functions. They are generalizations of the more well known state-space models such as Hidden Markov models (HMMs), a...

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccu...

Measurement of stimulus-induced changes in activity in the brain is critical to the advancement of neuroscience. Scientists use a range of methods, including electrode implantation, surface (scalp) electrode placement, and optical imaging of intrinsic signals, to gather data capturing underlying signals of interest in the brain. These data are usually corrupted by artifacts, complicating interp...

We propose a state space model with Markov switching, whose regimes are associated with the model parameters and regime transition probabilities are time-dependent. The estimation is based on maximum likelihood method using the EM algorithm. The distribution of the estimators is assessed using bootstrap. To evaluate the state variables and regime probabilities, the Kalman filter and a probabili...

In this report we consider identiication of linear time-invariant-nite dimensional systems using state-space models. We introduce a new model structure which is fully parametrized, i.e. all matrices are lled with parameters. All multivariable systems of a given order can be described within this model structure and thus relieve us from all the internal structural issues otherwise inherent in th...

Detailed observation of the movement of individual animals offers the potential to understand spatial population processes as the ultimate consequence of individual behaviour, physiological constraints and fine-scale environmental influences. However, movement data from individuals are intrinsically stochastic and often subject to severe observation error. Linking such complex data to dynamical...