This article uses Projection Pursuit methods to develop a procedure for detecting outliers in a multivariate time series. We show that testing for outliers in some projection directions could be more powerful than testing the multivariate series directly. The optimal directions for detecting...

We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach...

In this note we analyze the relationship between one-step ahead prediction errors and interpolation errors in time series. We obtain an expression of the prediction errors in terms of the interpolation errors and then we show that minimizing the sum of squares of the one step-ahead standardized...

This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures are considered. The first is based on the likelihood ratio test and the second on cusum statistics. These two procedures are compared in...

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are...

The comparison of the means of two independent samples is one of the most popular problems in real-world data analysis. In the multivariate context, two-sample Hotelling's T² frequently used to test the equality of means of two independent Gaussian random samples assuming either the same or a...

We propose a Bayesian non-parametric approach for modeling the distribution of multiple returns. In particular, we use an asymmetric dynamic conditional correlation (ADCC) model to estimate the time-varying correlations of financial returns where the individual volatilities are driven by...

This paper proposes methods to detect outliers in functional datasets. We are interested in challenging scenarios where functional samples are contaminated by outliers that may be difficult to recognize. The task of identifying a typical curves is carried out using the recently proposed...

This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations...

Financial returns often present a complex relation with previous observations, along with a slight skewness and high kurtosis. As a consequence, we must pursue the use of flexible models that are able to seize these special features: a financial process that can expose the intertemporal relation...