Structural Multi-Equation Macroeconomic Models: Identification-Robust Estimation and Fit

Weak identification is likely to be prevalent in multi-equation macroeconomic models such as in dynamic stochastic general equilibrium setups. Identification difficulties cause the breakdown of standard asymptotic procedures, making inference unreliable. While the extensive econometric literature now includes a number of identification-robust methods that are valid regardless of the identification status of models, these are mostly limited-information-based approaches, and applications have accordingly been made on single-equation models such as the New Keynesian Phillips Curve. In this paper, we develop a set of identification-robust econometric tools that, regardless of the model's identification status, are useful for estimating and assessing the fit of a system of structural equations. In particular, we propose a vector auto-regression (VAR) based estimation and testing procedure that relies on inverting identification-robust multivariate statistics. The procedure is valid in the presence of endogeneity, structural constraints, identification difficulties, or any combination of these, and also provides summary measures of fit. Furthermore, it has the additional desirable features that it is robust to missing instruments, errors-in-variables, the specification of the data generating process, and the presence of contemporaneous correlation in the disturbances. We apply our methodology, using U.S. data, to the standard New Keynesian model such as the one studied in Clarida, Gali, and Gertler (1999). We find that, despite the presence of identification difficulties, our proposed method is able to shed some light on the fit of the considered model and, particularly, on the nature of the NKPC. Notably our results show that (i) confidence intervals obtained using our system-based approach are generally tighter than their single-equation counterparts, and thus are more informative, (ii) most model coefficients are significant at conventional levels, and (iii) the NKPC is preponderantly forward-looking, though not purely so.Inflation and prices; Econometric and statistical methods

Overview of total least squares methods

We review the development and extensions of the classical total least squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data matrix. The weighted and structured total least squares problems have no such analytic solution and are currently solved numerically by local optimization methods. We explain how special structure of the weight matrix and the data matrix can be exploited for efficient cost function and first derivative computation. This allows to obtain computationally efficient solution methods. The total least squares family of methods has a wide range of applications in system theory, signal processing, and computer algebra. We describe the applications for deconvolution, linear prediction, and errors-in-variables system identification

Contribuições para o uso de regularização em técnicas de identificação de sistemas

A partir de trabalhos recentes e inovadores da área de aprendizado de máquina, uma ferramenta matemática conhecida como regularização ganhou notoriedade para o contexto de identificação de sistemas, principalmente devido a novas metodologias para a estimação da matriz de regularização, relacionadas a informações a priori sobre o sistema, e a resultados promissores exibidos em trabalhos que empregam tal ferramenta, os quais atingem modelos mais precisos comparados às técnicas clássicas de identificação. Neste sentido, este trabalho apresenta contribuições que exploram o uso dessa ferramenta de regularização para estender técnicas de identificação de sistemas com ruído colorido na saída, identificação de sistemas com erros nas variáveis e controle baseado em dados. No âmbito de identificação de sistemas com ruído colorido na saída, este trabalho apresenta o método dos mínimos quadrados ponderados regularizados, assim como a dedução de matrizes ótimas de regularização e ponderação para este cenário. No contexto de identificação com erros nas variáveis, o trabalho apresenta uma análise de propriedades estatísticas da técnica de estimação por variáveis instrumentais e usa a ferramenta de regularização para minimizar um critério relacionado ao erro médio quadrático das estimativas. No contexto de controle baseado em dados, o desenvolvimento para sistemas com erros nas variáveis é estendido para o método da referência virtual, com as particularidades e interpretações voltadas para controle.Due to recent and innovative papers from the machine learning area, a mathematical tool known as regularization earned notoriety also for the system identification context, especially due to new methodologies to estimate the regularization matrix, which are related to a priori information, and promising results demonstrated on works that use this tool. In this scenario, this work presents contributions that explore the use of the regularization tool to extend methods for identification of systems with colored output noise, for errors-in-varibles system identification and for one data-driven control method. Regarding the identification of systems with colored output noise, this work introduces the regularized weighted least-squares method, as well as the computation of the optimal weighting and regularization matrices. In the errors-in-variables system identification scenario, this work presents the statistical properties analysis of the regularized version of the instrumental variable method and it also presents the optimization of the mean square error by using regularization. Finally, regarding the data-driven control contribution, this work extends the errors-in-variables results to the Virtual Reference Feedback Tuning method, according to its characteristics and interpretations that are considered for control

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

We propose an automatic methodology framework for short- and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Nonparametric residual variance estimation plays a key role in driving the identification and learning procedures. Concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems. The learn from examples method introduced by Wang and Mendel (W&M) is used for identification. The Levenberg–Marquardt (L–M) optimization method is then applied for tuning. The W&M method produces compact and potentially accurate inference systems when applied after a proper variable selection stage. The L–M method yields the best compromise between accuracy and interpretability of results, among a set of alternatives. Delta test based residual variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs. Experiments on a diverse set of time series prediction benchmarks are compared against least-squares support vector machines (LS-SVM), optimally pruned extreme learning machine (OP-ELM), and k-NN based autoregressors. The advantages of the proposed methodology are shown in terms of linguistic interpretability, generalization capability and computational cost. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications.Ministerio de Ciencia e Innovación TEC2008-04920Junta de Andalucía P08-TIC-03674, IAC07-I-0205:33080, IAC08-II-3347:5626

Analysis of measurement and simulation errors in structural system identification by observability techniques

This is the peer reviewed version of the following article: [Lei, J., Lozano-Galant, J. A., Nogal, M., Xu, D., and Turmo, J. (2017) Analysis of measurement and simulation errors in structural system identification by observability techniques. Struct. Control Health Monit., 24: . doi: 10.1002/stc.1923.], which has been published in final form at http://onlinelibrary.wiley.com/wol1/doi/10.1002/stc.1923/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.During the process of structural system identification, errors are unavoidable. This paper analyzes the effects of measurement and simulation errors in structural system identification based on observability techniques. To illustrate the symbolic approach of this method a simply supported beam is analyzed step-by-step. This analysis provides, for the very first time in the literature, the parametric equations of the estimated parameters. The effects of several factors, such as errors in a particular measurement or in the whole measurement set, load location, measurement location or sign of the errors, on the accuracy of the identification results are also investigated. It is found that error in a particular measurement increases the errors of individual estimations, and this effect can be significantly mitigated by introducing random errors in the whole measurement set. The propagation of simulation errors when using observability techniques is illustrated by two structures with different measurement sets and loading cases. A fluctuation of the observed parameters around the real values is proved to be a characteristic of this method. Also, it is suggested that a sufficient combination of different load cases should be utilized to avoid the inaccurate estimation at the location of low curvature zones.Peer ReviewedPostprint (author's final draft

Kernel-based system identification from noisy and incomplete input-output data

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.Comment: 16 pages, submitted to IEEE Conference on Decision and Control 201

Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV

Benchmark of structured machine learning methods for microbial identification from mass-spectrometry data

Microbial identification is a central issue in microbiology, in particular in the fields of infectious diseases diagnosis and industrial quality control. The concept of species is tightly linked to the concept of biological and clinical classification where the proximity between species is generally measured in terms of evolutionary distances and/or clinical phenotypes. Surprisingly, the information provided by this well-known hierarchical structure is rarely used by machine learning-based automatic microbial identification systems. Structured machine learning methods were recently proposed for taking into account the structure embedded in a hierarchy and using it as additional a priori information, and could therefore allow to improve microbial identification systems. We test and compare several state-of-the-art machine learning methods for microbial identification on a new Matrix-Assisted Laser Desorption/Ionization Time-of-Flight mass spectrometry (MALDI-TOF MS) dataset. We include in the benchmark standard and structured methods, that leverage the knowledge of the underlying hierarchical structure in the learning process. Our results show that although some methods perform better than others, structured methods do not consistently perform better than their "flat" counterparts. We postulate that this is partly due to the fact that standard methods already reach a high level of accuracy in this context, and that they mainly confuse species close to each other in the tree, a case where using the known hierarchy is not helpful