arXiv subjects

Pedro Galeano

Publications and source records attributed to Pedro Galeano.

8 recordsLinked to original sources

arXiv2024

Testing for linearity in scalar-on-function regression with responses missing at random

A goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The test statistic relies on a marked empirical process indexed by the projected functional covariate and its distribution under the null hypothesis is calibrated using a wild bootstrap procedure. The computation and performance of the test rely on having an accurate estimator of the functional slope of the FLMSR when the sample has MAR responses. Three estimation methods based on the Functional Principal Components (FPCs) of the covariate are considered. First, the simplified method estimates the functional slope by simply discarding observations with missing responses. Second, the imputed method estimates the functional slope by imputing the missing responses using the simplified estimator. Third, the inverse probability weighted method incorporates the missing response generation mechanism when imputing. Furthermore, both cross-validation and LASSO regression are used to select the FPCs used by each estimator. Several Monte Carlo experiments are conducted to analyze the behavior of the testing procedure in combination with the functional slope estimators. Results indicate that estimators performing missing-response imputation achieve the highest power. The testing procedure is applied to check for linear dependence between the average number of sunny days per year and the mean curve of daily temperatures at weather stations in Spain.

stat.ME↗

arXiv2024

Structured factor copulas for modeling the systemic risk of European and United States banks

In this paper, we employ Credit Default Swaps (CDS) to model the joint and conditional distress probabilities of banks in Europe and the U.S. using factor copulas. We propose multi-factor, structured factor, and factor-vine models where the banks in the sample are clustered according to their geographic location. We find that within each region, the co-dependence between banks is best described using both, systematic and idiosyncratic, financial contagion channels. However, if we consider the banking system as a whole, then the systematic contagion channel prevails, meaning that the distress probabilities are driven by a latent global factor and region-specific factors. In all cases, the co-dependence structure of bank CDS spreads is highly correlated in the tail. The out-of-sample forecasts of several measures of systematic risk allow us to identify the periods of distress in the banking sector over the recent years including the COVID-19 pandemic, the interest rate hikes in 2022, and the banking crisis in 2023.

q-fin.ST↗

arXiv2015

Functional outlier detection by a local depth with application to NOx levels

This paper proposes methods to detect outliers in functional data sets and the task of identifying atypical curves is carried out using the recently proposed kernelized functional spatial depth (KFSD). KFSD is a local depth that can be used to order the curves of a sample from the most to the least central, and since outliers are usually among the least central curves, we present a probabilistic result which allows to select a threshold value for KFSD such that curves with depth values lower than the threshold are detected as outliers. Based on this result, we propose three new outlier detection procedures. The results of a simulation study show that our proposals generally outperform a battery of competitors. We apply our procedures to a real data set consisting in daily curves of emission levels of nitrogen oxides (NOx) since it is of interest to identify abnormal NOx levels to take necessary environmental political actions.

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arXiv2014

Spatial Depth-Based Classification for Functional Data

We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful for studying functional samples that require an analysis at a local level. In addition, we consider supervised functional classification problems, focusing on cases in which the differences between groups are not extremely clear-cut or the data may contain outlying curves. We perform classification by means of some available robust methods that involve the use of a given functional depth, including FSD and KFSD, among others. We use the functional \textit{k}-nearest neighbor classifier as a benchmark procedure. The results of a simulation study indicate that the KFSD-based classification approach leads to good results. Finally, we consider two real classification problems, obtaining results that are consistent with the findings observed with simulated curves.

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arXiv2014

Bayesian Inference Methods for Univariate and Multivariate GARCH Models: a Survey

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non-parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non-parametric approach.

math.ST↗

arXiv2014

A Bayesian Non-Parametric Approach to Asymmetric Dynamic Conditional Correlation Model With Application to Portfolio Selection

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 GJR-GARCH models. The ADCC-GJR-GARCH model takes into consideration the asymmetries in individual assets' volatilities, as well as in the correlations. The errors are modeled using a Dirichlet location-scale mixture of multivariate Gaussian distributions allowing for a great flexibility in the return distribution in terms of skewness and kurtosis. Model estimation and prediction are developed using MCMC methods based on slice sampling techniques. We carry out a simulation study to illustrate the flexibility of the proposed approach. We find that the proposed DPM model is able to adapt to several frequently used distribution models and also accurately estimates the posterior distribution of the volatilities of the returns, without assuming any underlying distribution. Finally, we present a financial application using Apple and NASDAQ Industrial index data to solve a portfolio allocation problem. We find that imposing a restrictive parametric distribution can result into underestimation of the portfolio variance, whereas DPM model is able to overcome this problem.

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arXiv2014

Multiple break detection in the correlation structure of random variables

Correlations between random variables play an important role in applications, e.g.\ in financial analysis. More precisely, accurate estimates of the correlation between financial returns are crucial in portfolio management. In particular, in periods of financial crisis, extreme movements in asset prices are found to be more highly correlated than small movements. It is precisely under these conditions that investors are extremely concerned about changes on correlations. A binary segmentation procedure to detect the number and position of multiple change points in the correlation structure of random variables is proposed. The procedure assumes that expectations and variances are constant and that there are sudden shifts in the correlations. It is shown analytically that the proposed algorithm asymptotically gives the correct number of change points and the change points are consistently estimated. It is also shown by simulation studies and by an empirical application that the algorithm yields reasonable results.

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arXiv2013

The Mahalanobis distance for functional data with applications to classification

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 that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regularized square root inverse operator in Hilbert spaces. Some of the main characteristics of the functional Mahalanobis semi-distance are shown. Afterwards, new versions of several well known functional classification procedures are developed using the Mahalanobis distance for functional data as a measure of proximity between functional observations. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples.

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