Stefano Federico Tonellato

A multivariate time series model for the analysis and prediction of carbon monoxide atmospheric concentrations

We use a Bayesian multivariate time series model for the analysis of the dynamics of carbon monoxide atmospheric concentrations. The data are observed at four sites. It is assumed that the logarithm of the observed process can be represented as the sum of unobservable components: a trend, a daily periodicity, a stationary autoregressive signal and an erratic term. Bayesian analysis is performed via Gibbs sampling. In particular, we consider the problem of joint temporal prediction when data are observed at a few sites and it is not possible to fit a complex space–time model. A retrospective analysis of the trend component is also given, which is important in that it explains the evolution of the variability in the observed process.

Spatial Prediction With Space-Time Models

In this paper we deal with the problem of spatial prediction for a spatiotemporal process. Our method is based on the state-space representation of the observed spatial time series and requires the implementation of MCMC techniques. We can use the mean of the predictive distribution as a point predictor and we can quantify the uncertainty of our predictions, since we can sample from the predictive distribution. We will show through an application to Ireland wind speed data ((1989)) that although point predictions can be quite precise, the predictive distribution might show a counterintuitive behaviour when the space-time process is not temporally stationary.

A comparison between parallel algorithms for system parameter estimation in dynamic linear models

When dealing with high-frequency time series, statistical procedures giving reliable estimates of unknown parameters and forecasts in real time are required. This is why recursive estimation methods are usually preferred to maximum-likelihood estimators. In the paper, a recursive estimation algorithm for the system parameter of dynamic linear models is proposed. A comparison with some other algorithms is given via Monte Carlo simulations. Consistency properties of the algorithms are also empirically verified. Copyright

Recursive Estimation of System Parameter in Environmental Time Series Models

Dealing with high-frequency time series, such as environmental ones, raises important inferential and computational problems. Environmental monitoring and forecasting, for instance, require statistical procedures giving reliable estimates of unknown parameters and forecasts in real time. In this paper we consider dynamic linear models as a basic tool for the analysis of such kind of data and propose a recursive estimator for system parameter. A comparison of this estimator with some other estimation methods is provided via Monte Carlo simulations. The estimator we propose is computationally efficient and very easy to implement. Moreover, in our simulation study, it exhibits good asymptotic properties.

A merging algorithm for Gaussian mixture components

In finite mixture model clustering, each component of the fitted mixture is usually associated with a cluster. In other words, each component of the mixture is interpreted as the probability distribution of the variables of interest conditionally on the membership to a given cluster. The Gaussian mixture model (GMM) is very popular in this context for its simplicity and flexibility. It may happen, however, that the components of the fitted model are not well separated. In such a circumstance, the number of clusters is often overestimated and a better clustering could be obtained by joining some subsets of the partition based on the fitted GMM. Some methods for the aggregation of mixture components have been recently proposed in the literature. In this work, we propose a hierarchical aggregation algorithm based on a generalisation of the definition of silhouette-width taking into account the Mahalanobis distances induced by the precison matrices of the components of the fitted GMM. The algorithm chooses the number of groups corresponding to the hierarchy level giving rise to the highest average-silhouette-width. Some simulation experiments and real data applications indicate that its performance is at least as good as the one of other existing methods.

On the Comparison of Model-Based Clustering Solutions

In this paper we propose a new similarity index, which can be used to compare model-based clustering solutions. We define also an adjusted-for-chance version, although we advise that, whenever feasible, bootstrap replications should be preferred to chance-corrected similarity indices. We describe the properties of the proposed index and of its chance-corrected version. Finally, we present some applications on simulated and real data.

A Bayesian Approach to the Analysis of Spatial Time Series

In this paper a class of models for conditionally Gaussian space-time processes is proposed in a state-space setup. These models have two main purposes: describing and forecasting the temporal evolution of the observed phenomena. Observed processes are assumed to be the sum of unobservable components, such as a time varying level, a periodic component, a stationary autoregressive component and a measurement error. We give sufficient conditions for model identifiability and show how Bayesian analysis can be performed via Gibbs sampling. We present the results of an application to some simulated spatial time series.