Miguel Jerez

An Exact Multivariate Model-based Structural Decomposition

We propose a simple and structured procedure for decomposing a vector of time series into trend, cycle, seasonal, and irregular components. Contrary to common practice, we do not assume these components to be orthogonal conditional on their past. However, the state–space representation employed ensures that their estimates converge to values with null variances and covariances. Null variances are very important, as they ensure that the components do not change when the sample increases. This lack of “revisions” is the most important feature of our method, in comparison with most alternative procedures. On the other hand, null covariances provide a solid statistical foundation for the decomposition, as it ensures that a given component can be analyzed and interpreted independently of any other component(s). Other convenient properties of our method derive from the use of a state–space approach. First, defining the problem in state–space avoids dependence on particular model specifications, so the same procedure can be applied to a wide class of data representations, including ARIMA, VARMAX, univariate transfer functions, and structural time series models. Also, state–space methods deal easily with nonstandard situations, such as samples with missing values or constraints upon the structural components. Practical application of the procedure is illustrated with both simulated and real data. A MATLAB toolbox for time series modeling and decomposition is available via the Internet.

A fast and stable method to compute the likelihood of time invariant state-space models

Abstract We propose two fast and stable methods to compute the likelihood of time invariant state-space models. The first one exploits the properties of the Kalman filter when applied to steady-state innovations models. The second procedure allows for more general structures.

Exact smoothing for stationary and non-stationary time series

Abstract In this work we derive an analytical relationship between exact fixed-interval smoothed moments and those obtained from an arbitrarily initialized smoother. Combining this result with a conventional smoother we obtain an exact algorithm that can be applied to stationary, non-stationary or partially non-stationary systems. Other advantages of our method are its computational efficiency and numerical stability. Its extension to forecasting, filtering, fixed-point and fixed-lag smoothing is immediate, as it only requires modification of a conditioning information set. Three examples illustrate the adverse effect of an inadequate initialization on smoothed estimates.

Fast estimation methods for time series models in state-space form

We propose two new, fast and stable methods to estimate time-series models written in their equivalent state–space form. They are useful both to obtain adequate initial conditions for a maximum likelihood iteration and to provide final estimates when maximum likelihood is considered inadequate or computationally expensive. The state–space foundation of these procedures provides flexibility, as they can be applied to any linear fixed-coefficients model, such as ARIMA, VARMAX or structural time-series models. A simulation exercise shows that their computational costs and finite-sample performance are very good.

Original article: From general state-space to VARMAX models

Fixed coecients State-Space and VARMAX models are equivalent, meaning that they are able to represent the same linear dynamics, being indistinguishable in terms of overall fit. However, each representation can be specically adequate for certain uses, so it is relevant to be able to choose between them. To this end, we propose two algorithms to go from general State-Space models to VARMAX forms. The rst one computes the coecients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coecients of a VARMAX echelon. These procedures supplement the results already available in the literature allowing one to obtain the State-Space model matrices corresponding to any VARMAX. The paper also discusses some applications of these procedures by solving several theoretical and practical problems.

Unit roots and cointegration modelling through a family of flexible information criteria

We propose a fast and consistent procedure to detect unit roots based on subspace methods. It has three distinctive features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, whose loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a model for the analysed series. In addition, we provide a subspace-based consistent estimator for the cointegrating rank and the cointegrating matrix. Simulation exercises show that these procedures have good finite sample properties.

Decomposition of a state-space model with inputs

This article shows how to compute the in-sample effect of exogenous inputs on the endogenous variables in any linear model written in a state–space form. Estimating this component may be either interesting by itself, or a previous step before decomposing a time series into trend, cycle, seasonal and error components. The practical application and usefulness of this method is illustrated by estimating the effect of advertising on the monthly sales of Lydia Pinkhams vegetable compound.

Combined use of pharmacophoric models together with drug metabolism and genotoxicity "in silico" studies in the hit finding process.

In this study we propose a virtual screening strategy based on the generation of a pharmacophore hypothesis, followed by an in silico evaluation of some ADME-TOX properties with the aim to apply it to the hit finding process and, specifically, to characterize new chemical entities with potential to control inflammatory processes mediated by T lymphocytes such as multiple sclerosis, systemic lupus erithematosus or rheumatoid arthritis. As a result, three compounds with completely novel scaffolds were selected as final hits for future hit-to-lead optimization due to their anti-inflammatory profile. The biological results showed that the selected compounds increased the intracellular cAMP levels and inhibited cell proliferation in T lymphocytes. Moreover, two of these compounds were able to increase the production of IL-4, an immunoregulatory cytokine involved in the selective deviation of T helper (Th) immune response Th type 2 (Th2), which has been proved to have anti-inflammatory properties in several animal models for autoimmune pathologies as multiple sclerosis or rheumatoid arthritis. Thus our pharmacological strategy has shown to be useful to find molecules with biological activity to control immune responses involved in many inflammatory disorders. Such promising data suggested that this in silico strategy might be useful as hit finding process for future drug development.

Identification of Canonical Models for Vectors of Time Series: A Subspace Approach

In this paper we propose a new method to specify linear models for vectors of time series with some convenient properties: First, it provides a unique modeling approach for single and multiple time series, as the same decisions are required in both cases. Second, it is scalable, meaning that it provides quickly a possibly crude but statistically adequate model, which can be refined in further modeling phases if required. Third, it is optionally automatic, meaning that the specification depends on a few key parameters that can be determined either automatically or by human decision. And last it is parsimonious, as it allows one to impose a canonical structure, which can be further simplified through exclusion constraints. Several examples with simulated and real data illustrate the practical application of this procedure and a MATLAB implementation is freely distributed through the Internet.

Single and multiple error state-space models for signal extraction

We compare the results obtained by applying the same signal-extraction procedures to two observationally equivalent state-space forms. The first model has different errors affecting the states and the observations, while the second has a single perturbation term which coincides with the one-step-ahead forecast error. The signals extracted from both forms are very similar but their variances are drastically different, because the states for the single-source error representation collapse to exact values while those coming from the multiple-error model remain uncertain. The implications of this result are discussed both with theoretical arguments and practical examples. We find that single error representations have advantages to compute the likelihood or to adjust for seasonality, while multiple error models are better suited to extract a trend indicator. Building on this analysis, it is natural to adopt a ‘best of both worlds’ approach, which applies each representation to the task in which it has comparative advantage.