Exact goodness-of-fit tests for censored dats

The statistic introduced in Fortiana and Grané (2003) is modified so that it can be used to test the goodness-of-fit of a censored sample, when the distribution function is fully specified. Exact and asymptotic distributions of three modified versions of this statistic are obtained and exact critical values are given for different sample sizes. Empirical power studies show the good performance of these statistics in detecting symmetrical alternatives

Volatility modelling and accurate minimun capital risk requirements : a comparison among several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest that an accurate modeling of extreme returns obtained for long and short trading investment positions is possible with a simple autoregressive stochastic volatility model. Moreover, modeling volatility as a fractional integrated process produces, in general, excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates. The performance of models is assessed with the help of out-of-sample tests and p-values of them are reported

Sensitivity and robustness in MDS configurations for mixed-type data: a study of the economic crisis impact on socially vulnerable Spanish people

Multidimensional scaling (MDS) techniques are initially proposed to produce pictorial representations of distance, dissimilarity or proximity data. Sensitivity and robustness assessment of multivariate methods is essential if inferences are to be drawn from the analysis. To our knowledge, the literature related to MDS for mixed-type data, including variables measured at continuous level besides categorical ones, is quite scarce. The main motivation of this work was to analyze the stability and robustness of MDS configurations as an extension of a previous study on a real data set, coming from a panel-type analysis designed to assess the economic crisis impact on Spanish people who were in situations of high risk of being socially excluded. The main contributions of the paper on the treatment of MDS configurations for mixed-type data are: (i) to propose a joint metric based on distance matrices computed for continuous, multi-scale categorical and/or binary variables, (ii) to introduce a systematic analysis on the sensitivity of MDS configurations and (iii) to present a systematic search for robustness and identification of outliers through a new procedure based on geometric variability notions.Gower distance, MDS configurations, Mixed-type data, Outliers identification, Related metric scaling, Survey data

Local linear regression for functional predictor and scalar response

The aim of this work is to introduce a new nonparametric regression technique in the context of functional covariate and scalar response. We propose a local linear regression estimator and study its asymptotic behaviour. Its finite-sample performance is compared with a Nadayara-Watson type kernel regression estimator via a Monte Carlo study and the analysis of two real data sets. In all the scenarios considered, the local linear regression estimator performs better than the kernel one, in the sense that the mean squared prediction error and its standard deviation are lower

Outliers in Garch models and the estimation of risk measures

In this paper we focus on the impact of additive level outliers on the calculation of risk measures, such as minimum capital risk requirements, and compare four alternatives of reducing these measures' estimation biases. The first three proposals proceed by detecting and correcting outliers before estimating these risk measures with the GARCH(1,1) model, while the fourth procedure fits a Student’s t-distributed GARCH(1,1) model directly to the data. The former group includes the proposal of Grané and Veiga (2010), a detection procedure based on wavelets with hard- or soft-thresholding filtering, and the well known method of Franses and Ghijsels (1999). The first results, based on Monte Carlo experiments, reveal that the presence of outliers can bias severely the minimum capital risk requirement estimates calculated using the GARCH(1,1) model. The message driven from the second results, both empirical and simulations, is that outlier detection and filtering generate more accurate minimum capital risk requirements than the fourth alternative. Moreover, the detection procedure based on wavelets with hard-thresholding filtering gathers a very good performance in attenuating the effects of outliers and generating accurate minimum capital risk requirements out-of-sample, even in pretty volatile periodsMinimum capital risk requirements, Outliers, Wavelets

A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions

In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffding's maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper we propose a scalefree adaptive statistic for testing exponentiality with optimal power against a specific alternative. We obtain its exact distribution and compare it with other scale-free statistics for testing exponentiality, such as the Stephens' modification of the Shapiro-Wilk statistic, the Gini statistic and the Qn statistic defined in Fortiana and Grané (2002)

Wavelet-based detection of outliers in volatility models

Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. This paper focuses on these issues and proposes a general detection and correction method based on wavelets that can be applied to a large class of volatility models. The effectiveness of our proposal is tested by an intensive Monte Carlo study for six well known volatility models and compared to alternative proposals in the literature, before applying it to three daily stock market indexes. The Monte Carlo experiments show that our method is both very effective in detecting isolated outliers and outlier patches and much more reliable than other wavelet-based procedures since it detects a significant smaller number of false outliers

The effect of realised volatility on stock returns risk estimates

In this paper, we estimate minimum capital risk requirements for short, long positions and three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes; and, most importantly, we analyse the models performance when realised volatility is included as an explanatory variable into the models' variance equations. The results suggest that the inclusion of realised volatility improves the models forecastability and their capacity to calculate accurate measures of minimum capital risk requirements

Asymptotic properties of a goodness-of-fit test based on maximum correlations

We study the efficiency properties of the goodness-of-fit test based on the Qn statistic introduced in Fortiana and Grané (2003) using the concepts of Bahadur asymptotic relative efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with those based on the Kolmogorov-Smirnov, the Cramér-von Mises and the Anderson-Darling statistics. We also describe the distribution families for which the test based on Qn is asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the presence of hidden periodicities in a stationary time series

Karhunen-loève basis in goodness-of-fit tests decomposition: an evaluation

In a previous paper (Grané and Fortiana 2006) we studied a flexible class of goodness-of-fit tests associated with an orthogonal sequence, the Karhunen-Loève decomposition of a stochastic process derived from the null hypothesis. Generally speaking, these tests outperform Kolmogorov-Smirnov and Cramér-von Mises, but we registered several exceptions. In this work we investigate the cause of these anomalies and, more precisely, whether and when such poor behaviour may be attributed to the orthogonal sequence itself, by replacing it with the Legendre polynomials, a commonly used basis for smooth tests. We find an easily computable formula for the Bahadur asymptotic relative efficiency, a helpful quantity in choosing an adequate basis