FORECAST OF THE EXPECTED NON-EPIDEMIC MORBIDITY OF ACUTE DISEASES USING RESAMPLING METHODS

In epidemiological surveillance it is important that any unusual increase of reported cases be detected as rapidly as possible. Reliable forecasting based on a suitable time series model for an epidemiological indicator is necessary for estimating the expected non-epidemic indicator and to elaborate an alert threshold. Time series analysis of acute diseases often use Gaussian autoregressive integrated moving average models. However, these approaches could be adversely affected by departures from the true underlying distribution. The objective of this paper is to introduce a bootstrap procedure for obtaining prediction intervals in linear models in order to avoid the normality assumption. We present a Monte Carlo study comparing the finite sample properties of the bootstrap prediction intervals with those of alternative methods. Finally, we illustrate the performance of the proposed method with a meningococcal disease incidence series.

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.Time series, Wavelet Variances, Wavelet Correlations, Discriminant Analysis

JMASM23: Cluster Analysis In Epidemiological Data (Matlab)

Matlab functions for testing the existence of time, space and time-space clusters of disease occurrences are presented. The classical scan test, the Ederer, Myers and Mantel’s test, the Ohno, Aoki and Aoki’s test, and the Knox’s test are considered

A methodology for population projections: an application to Spain

This paper looks at projections for the Spanish population by sex and age for the period of 2005 to 2050. These were carried out using forecasts for birth and mortality rates, and migration. These rates are calculated using two main sources of information. First, a multivariate time series model was applied for the series of variables from the 1970 to 2001 period. Second a model was estimated for life expectancy and for a synthetic fertility index. Both sources of information were combined to obtain the forecasts for the rates. Immigration rates are predicted by assuming three possible scenarios based on the maximum proportion that immigrants will represent in the Spanish population. With these variables a structure of ages and sex for the Spanish population is estimated using a cohort component model.Population projections, Time series, Factorial model, Bootstrap

Seasonal dynamic factor analysis and bootstrap inference : application to electricity market forecasting

Year-ahead forecasting of electricity prices is an important issue in the current context of electricity markets. Nevertheless, only one-day-ahead forecasting is commonly tackled up in previous published works. Moreover, methodology developed for the short-term does not work properly for long-term forecasting. In this paper we provide a seasonal extension of the Non-Stationary Dynamic Factor Analysis, to deal with the interesting problem (both from the economic and engineering point of view) of long term forecasting of electricity prices. Seasonal Dynamic Factor Analysis (SeaDFA) allows to deal with dimensionality reduction in vectors of time series, in such a way that extracts common and specific components. Furthermore, common factors are able to capture not only regular dynamics (stationary or not) but also seasonal one, by means of common factors following a multiplicative seasonal VARIMA(p,d,q)×(P,D,Q)s model. Besides, a bootstrap procedure is proposed to be able to make inference on all the parameters involved in the model. A bootstrap scheme developed for forecasting includes uncertainty due to parameter estimation, allowing to enhance the coverage of forecast confidence intervals. Concerning the innovative and challenging application provided, bootstrap procedure developed allows to calculate not only point forecasts but also forecasting intervals for electricity prices

Seasonal dynamic factor analysis and bootstrap inference : application to electricity market forecasting

Year-ahead forecasting of electricity prices is an important issue in the current context of electricity markets. Nevertheless, only one-day-ahead forecasting is commonly tackled up in previous published works. Moreover, methodology developed for the short-term does not work properly for long-term forecasting. In this paper we provide a seasonal extension of the Non-Stationary Dynamic Factor Analysis, to deal with the interesting problem (both from the economic and engineering point of view) of long term forecasting of electricity prices. Seasonal Dynamic Factor Analysis (SeaDFA) allows to deal with dimensionality reduction in vectors of time series, in such a way that extracts common and specific components. Furthermore, common factors are able to capture not only regular dynamics (stationary or not) but also seasonal one, by means of common factors following a multiplicative seasonal VARIMA(p,d,q)×(P,D,Q)s model. Besides, a bootstrap procedure is proposed to be able to make inference on all the parameters involved in the model. A bootstrap scheme developed for forecasting includes uncertainty due to parameter estimation, allowing to enhance the coverage of forecast confidence intervals. Concerning the innovative and challenging application provided, bootstrap procedure developed allows to calculate not only point forecasts but also forecasting intervals for electricity prices.Dynamic factor analysis, Bootstrap, Forecasting, Confidence intervals

Classification of functional data: a weighted distance approach

A popular approach for classifying functional data is based on the distances from the function or its derivatives to group representative (usually the mean) functions or their derivatives. In this paper, we propose using a combination of those distances. Simulation studies show that our procedure performs very well, resulting in smaller testing classication errors. Applications to real data show that our procedure performs as well as –and in some cases better than– other classication methods

Forecasting time series with sieve bootstrap

In this paper we consider bootstrap methods for constructing nonparametric prediction intervals for a general class of linear processes. Our approach uses the sieve bootstrap procedure of Biihlmann (1997) based on residual resampling from an autoregressive approximation to the given process. We show that the sieve bootstrap provides consistent estimators of the conditional distribution of future values given the observed data, assuming that the order of the autoregressive approximation increases with the sample size at a suitable rate and some restrictions about polynomial decay of the coefficients ~ j t:o of the process MA(oo) representation. We present a Monte Carlo study comparing the finite sample properties of the sieve bootstrap with those of alternative methods. Finally, we illustrate the performance of the proposed method with real data examples

Resampling time series by missing values techniques

For strongly dependent data, deleting blocks of observations is expected to produce bias as in the moving block jackknife of KOnsch (1989) and Liu and Singh (1992). We propose an alternative technique which considers the blocks of deleted observations in the blockwise jackknife as missing data which are replaced by missing values estimates incorporating the observations dependence structure. Thus, the variance estimator is a weighted sample variance of the statistic evaluated in a "complete" series. We establish consistency for the variance and distribution of the sample mean. Also we extent this missing values approach to the blockwise bootstrap by assuming some missing observations among two consecutive blocks. We present the results of an extensive Monte Carlo study to evaluate the performance of the proposed methods in finite sample sizes in which it is shown that our proposal produces estimates of the variance of several time series statistics with smaller mean squared error than previous procedures

Improving the graphical lasso estimation for the precision matrix through roots ot the sample convariance matrix

In this paper, we focus on the estimation of a high-dimensional precision matrix. We propose a simple improvement of the graphical lasso framework (glasso) that is able to attain better statistical performance without sacrificing too much the computational cost. The proposed improvement is based on computing a root of the covariance matrix to reduce the spread of the associated eigenvalues, and maintains the original convergence rate. Through extensive numerical results, using both simulated and real datasets, we show the proposed modification outperforms the glasso procedure. Finally, our results show that the square-root improvement may be a reasonable choice in practiceAlonso gratefully acknowledge financial support from the Spanish Ministry of Science and Innovation grants ECO2011-25706 and ECO2012-3844