Discriminant analysis of multivariate time series using wavelets

In analyzing ECG data, the main aim is to differentiate between the signal patterns of those of healthy subjects and those of individuals with specific heart conditions. We propose an approach for classifying multivariate ECG signals based on discriminant and wavelet analyzes. For this purpose we use multiple-scale wavelet variances and wavelet correlations to distinguish between the patterns of multivariate ECG signals based on the variability of the individual components of each ECG signal and the relationships between every pair of these components. Using the results of other ECG classification studies in the literature as references, we demonstrate that our approach applied to 12-lead ECG signals from a particular database, displays quite favourable performance. We also demonstrate with real and synthetic ECG data that our approach to classifying multivariate time series out performs other well-known approaches for classifying multivariate time series. In simulation studies using multivariate time series that have patterns that are different from that of the ECG signals, we also demonstrate very favourably performance of this approach when compared to these other approaches

D-trace estimation of a precision matrix using adaptive Lasso penalties

The accurate estimation of a precision matrix plays a crucial role in the current age of high-dimensional data explosion. To deal with this problem, one of the prominent and commonly used techniques is the ℓ1 norm (Lasso) penalization for a given loss function. This approach guarantees the sparsity of the precision matrix estimate for properly selected penalty parameters. However, the ℓ1 norm penalization often fails to control the bias of obtained estimator because of its overestimation behavior. In this paper, we introduce two adaptive extensions of the recently proposed ℓ1 norm penalized D-trace loss minimization method. They aim at reducing the produced bias in the estimator. Extensive numerical results, using both simulated and real datasets, show the advantage of our proposed estimators.We would like to thank the Associate Editor, Coordinating Editor and two anonymous referees for their helpful comments that led to an improvement of this article. We express our gratitude to Teng Zhang and Hui Zou for sharing their Matlab code that solves the L1 norm penalized D-trace loss minimization problem. Andrés M. Alonso gratefully acknowledges financial support from CICYT (Spain) Grants ECO2012-38442 and ECO2015-66593. Francisco J. Nogales and Vahe Avagyan were supported by the Spanish Government through project MTM2013-44902-P. This paper is based on the first author's dissertation submitted to the Universidad Carlos III de Madrid. At the time of publication, Vahe Avagyan is a Postdoctoral fellow at Ghent University

Improving the Graphical Lasso Estimation for the Precision Matrix Through Roots of the Sample Covariance Matrix

In this article, we focus on the estimation of a high-dimensional inverse covariance (i.e., precision) matrix. We propose a simple improvement of the graphical Lasso (glasso) framework that is able to attain better statistical performance without increasing significantly the computational cost. The proposed improvement is based on computing a root of the sample covariance matrix to reduce the spread of the associated eigenvalues. Through extensive numerical results, using both simulated and real datasets, we show that the proposed modification improves the glasso procedure. Our results reveal that the square-root improvement can be a reasonable choice in practice. Supplementary material for this article is available online.Andrés M. Alonso gratefully acknowledges financial support from CICYT Grants ECO2012-38442 and CO2015-66593. Francisco J. Nogales and Vahe Avagyan were supported by the Spanish Government through project MTM2013-44902-P

A robust procedure to build dynamic factor models with cluster structure

Dynamic factor models provide a useful way to model large sets of time series. These data often have heterogeneity and cluster structure and the formulation and estimation of dynamic factor models should be adapted to these features. This article presents a procedure to fit Dynamic Factor Models with Cluster Structure (DFMCS), where some of the factors are global and others group-specific, to heterogeneous data that may include multivariate additive outliers and level shifts. The procedure starts with an initial cleaning of the times series from outlying effects. Then a first estimation of the possible factors is applied to the cleaned data and these factors are used to build the common component of each series. The groups are found by studying the joint dependency of these common components. Then, additional factors are estimated by using the series in each cluster and, finally, all the factors found are classified as global or group-specific. We show in a Monte Carlo study that the procedure works well and seems to be better than other alternatives in terms of estimation of factors and loadings as well as in terms of misclassification rates for the series. An example of an electricity market is presented to illustrate the advantages of cleaning for outliers and taking into account the cluster structure for understanding and forecasting

A Single Scalable LSTM Model for Short-Term Forecasting of Massive Electricity Time Series

This article belongs to the Special Issue Forecasting in Electricity Markets with Big Data and Artificial Intelligence.Most electricity systems worldwide are deploying advanced metering infrastructures to collect relevant operational data. In particular, smart meters allow tracking electricity load consumption at a very disaggregated level and at high frequency rates. This data opens the possibility of developing new forecasting models with a potential positive impact on electricity systems. We present a general methodology that can process and forecast many smart-meter time series. Instead of using traditional and univariate approaches, we develop a single but complex recurrent neural-network model with long short-term memory that can capture individual consumption patterns and consumptions from different households. The resulting model can accurately predict future loads (short-term) of individual consumers, even if these were not included in the original training set. This entails a great potential for large-scale applications as once the single network is trained, accurate individual forecast for new consumers can be obtained at almost no computational cost. The proposed model is tested under a large set of numerical experiments by using a real-world dataset with thousands of disaggregated electricity consumption time series. Furthermore, we explore how geo-demographic segmentation of consumers may impact the forecasting accuracy of the model.The authors gratefully acknowledge the financial support from the Spanish government through projects MTM2017-88979-P and PID2019-108311GB-I00/AEI/10.13039/501100011033, and from Fundación Iberdrola through “Ayudas a la Investigación en Energía y Medio Ambiente 2018”

Hierarchical clustering for smart meter electricity loads based on quantile autocovariances

In order to improve the efficiency and sustainability of electricity systems, most countries worldwide are deploying advanced metering infrastructures, and in particular household smart meters, in the residential sector. This technology is able to record electricity load time series at a very high frequency rates, information that can be exploited to develop new clustering models to group individual households by similar consumptions patterns. To this end, in this work we propose three hierarchical clustering methodologies that allow capturing different characteristics of the time series. These are based on a set of “dissimilarity” measures computed over different features: quantile auto-covariances, and simple and partial autocorrelations. The main advantage is that they allow summarizing each time series in a few representative features so that they are computationally efficient, robust against outliers, easy to automatize, and scalable to hundreds of thousands of smart meters series. We evaluate the performance of each clustering model in a real-world smart meter dataset with thousands of half-hourly time series. The results show how the obtained clusters identify relevant consumption behaviors of households and capture part of their geo-demographic segmentation. Moreover, we apply a supervised classification procedure to explore which features are more relevant to define each cluster.This work was supported in part by the Spanish Government through Project under Grant MTM2017-88979-P, and in part by the Fundación Iberdrola through “Ayudas a la Investigación en Energía y Medio Ambiente 2018.” The work of Andrés M. Alonso was supported in part by the Spanish Government through Project under Grant ECO2015-66593-P. Paper no. TSG-01702-2019

Robust functional supervised classification for time series

We propose using the integrated periodogram to classify time series. The method assigns a new time series to the group that minimizes the distance between the series integrated periodogram and the group mean of integrated periodograms. Local computation of these periodograms allows the application of this approach to nonstationary time series. Since the integrated periodograms are curves, we apply functional data depth-based techniques to make the classification robust, which is a clear advantage over other competitive procedures. The method provides small error rates for both simulated and real data. It improves existing approaches and presents good computational behavior.All authors supported in part by CICYT (Spain) grants SEJ2007-64500, and MICINN (Spain) grant ECO2008-05080. Research partially supported by grant ECO2011-25706 of the Spanish Ministry of Science and Innovation. A.M. Alonso supported in part by MICINN (Spain) grant ECO2012-38442

Monitoring variance by EWMA charts with time varying smoothing parameter

Memory charts like EWMA-S² or CUSUM-S² can be designed to be optimal to detect a specific shift in the process variance. However, this feature could be a serious inconvenience since, for instance, if the charts are designed to detect small shift, then, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to overcome this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper proposes new adaptive EWMA control charts for the dispersion (AEWMA-S²) based on a timevarying smoothing parameter that takes into account the potential misadjustment in the process variance. The obtained control charts can be interpreted as a combination of EWMA control charts designed to be efficient for different shift values. Markov chain procedures are established to analyse and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals

Electricity prices forecasting by averaging dynamic factor models

In the context of the liberalization of electricity markets, forecasting prices is essential. With this aim, research has evolved to model the particularities of electricity prices. In particular, Dynamic Factor Models have been quite successful in the task, both in the short and long run. However, specifying a single model for the unobserved factors is difficult, and it can not be guaranteed that such a model exists. In this paper, Model Averaging is employed to overcome this difficulty, with the expectation that electricity prices would be better forecast by acombination of models for the factors than by a single model. Although our procedure is applicable in other markets, it is illustrated with applications to forecasting spot prices of the Iberian Market, MIBEL (The Iberian Electricity Market) and the Italian Market. Three combinations of forecasts are successful in providing improved results for alternative forecasting horizons.Acknowledgements: A.M. Alonso acknowledges support of the Spanish Ministry of Economy and Competitiveness, research projects ECO2012-38442, and ECO2015-66593. Carolina García-Martos acknowledges financial support from project DPI2011-23500, Spanish Ministry of Economy and Competitiveness. The authors would like to extend their appreciation to Professor Michael Wiper for his assistance and corrections regarding the proper use of English in this document

BIAS correction for dynamic factor models

In this paper we work with multivariate time series that follow a Dynamic Factor Model. In particular, we consider the setting where factors are dominated by highly persistent AutoRegressive (AR) processes, and samples that are rather small. Therefore, the factors' AR models are estimated using small sample bias correction techniques. A Monte Carlo study reveals that bias-correcting the AR coefficients of the factors allows to obtain better results in terms of prediction interval coverage. As expected, the simulation reveals that bias-correction is more successful for smaller samples. Results are gathered assuming the AR order and number of factors are known as well as unknown. We also study the advantages of this technique for a set of Industrial Production Indexes of several European countries.A.M. Alonso acknowledges support of the Spanish Ministry of Economy and Competitiveness, research projects ECO2012-38442, and ECO2015-66593. Carolina García-Martos acknowledges financial support from project DPI2011-23500, Spanish Ministry of Economy and Competitiveness