Estimating the system order by subspace methods

This paper discusses how to determine the order of a state-space model. To do so, we start by revising existing approaches and find in them three basic shortcomings: i) some of them have a poor performance in short samples, ii) most of them are not robust and iii) none of them can accommodate seasonality. We tackle the first two issues by proposing new and refined criteria. The third issue is dealt with by decomposing the system into regular and seasonal sub-systems. The performance of all the procedures considered is analyzed through Monte Carlo simulations

Unit Roots and Cointegrating Matrix Estimation using Subspace Methods

We propose a new procedure to detect unit roots based on subspace methods. It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series.State-space models, subspace methods, unit roots, cointegration.

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

We propose two fast, stable and consistent methods to estimate time series models expressed in their equivalent state-space form. They are useful both, to obtain adequate initial conditions for a maximum-likelihood iteration, or to provide final estimates when maximum-likelihood is considered inadequate or costly. The state-space foundation of these procedures implies that they can estimate any linear fixed-coefficients model, such as ARIMA, VARMAX or structural time series models. The computational and finitesample performance of both methods is very good, as a simulation exercise shows.State-space models, subspace methods, Kalman Filter, system identification.

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 specifically 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 first one computes the coeficients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coeficients 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.State-Space, VARMAX models, Canonical forms, Echelon.

Decomposition of state-space Model with inputs: The theory and an application to estimate the ROI of advertising

This paper shows how to compute the in-sample effect of exogenous inputs on the endogenous variables in any linear model written in 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 monthly sales of the Lydia Pinkham vegetable compound.State-space, Signal extraction, Time series decomposition, Seasonal adjustment, Advertising, Lydia Pinkham

Estimating position & velocity in 3D space from monocular video sequences using a deep neural network

This work describes a regression model based on Convolutional Neural Networks (CNN) and Long-Short Term Memory (LSTM) networks for tracking objects from monocular video sequences. The target application being pursued is Vision-Based Sensor Substitution (VBSS). In particular, the tool-tip position and velocity in 3D space of a pair of surgical robotic instruments (SRI) are estimated for three surgical tasks, namely suturing, needle-passing and knot-tying. The CNN extracts features from individual video frames and the LSTM network processes these features over time and continuously outputs a 12-dimensional vector with the estimated position and velocity values. A series of analyses and experiments are carried out in the regression model to reveal the benefits and drawbacks of different design choices. First, the impact of the loss function is investigated by adequately weighing the Root Mean Squared Error (RMSE) and Gradient Difference Loss (GDL), using the VGG16 neural network for feature extraction. Second, this analysis is extended to a Residual Neural Network designed for feature extraction, which has fewer parameters than the VGG16 model, resulting in a reduction of ~96.44 % in the neural network size. Third, the impact of the number of time steps used to model the temporal information processed by the LSTM network is investigated. Finally, the capability of the regression model to generalize to the data related to "unseen" surgical tasks (unavailable in the training set) is evaluated. The aforesaid analyses are experimentally validated on the public dataset JIGSAWS. These analyses provide some guidelines for the design of a regression model in the context of VBSS, specifically when the objective is to estimate a set of 1D time series signals from video sequences.Peer ReviewedPostprint (author's final draft

Un método de inicialización del filtrado para modelos en espacio de los estados con inputs estocásticos

En este trabajo se derivan las expresiones exactas de la media y varianza condicional del estado inicial de un modelo en espacio de los estados con inputs estocásticos, generalizando los resultados teóricos obtenidos por De Jong y Chu-Chun-Lin (1994). Se muestra que las condiciones iniciales exactas dependen del carácter estacionario o no estacionario del modelo y que las estimaciones finales de los parámetros son sensibles a la presencia de inputs estocásticos, siendo ésta una situación frecuente en Econometría

Determination of chemical properties in ‘calçot’ (Allium cepa L.) by near infrared spectroscopy and multivariate calibration

‘Calçots’, the immature floral stems of second-year onion resprouts, are an economically important traditional crop in Catalonia (Spain). Classical approaches to evaluating the chemical properties of ‘calçots’ are time consuming and expensive; near-infrared spectroscopy (NIRS) may be faster and cheaper. We used NIRS to develop partial least square (PLS) models to predict dry matter, soluble solid content, titratable acidity, and ash content in cooked ‘calçots’. To guarantee the robustness of the models, calibration samples were grown and analyzed in a first season (2014–15) and validation samples in a second season (2015–16). NIRS on puree spectra estimated dry matter and soluble solid content with excellent accuracy (R2pred¿=¿0.953, 0.985 and RPD¿=¿4.571, 8.068, respectively). However, good estimation of titratable acidity and ash content required using ground dried puree spectra (R2pred¿=¿0.852, 0.820 and RPD¿=¿2.590, 1.987, respectively). NIRS can be a helpful tool for ‘calçots’ breeding and quality control.Peer ReviewedPostprint (author's final draft