382 research outputs found
Exact goodness-of-fit tests for censored dats
The statistic introduced in Fortiana and GranĂŠ (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
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 GranĂŠ (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 CramĂŠr-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
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 Studentâs t-distributed GARCH(1,1) model directly to the data. The former group includes the proposal of GranĂŠ 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 GranĂŠ (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 GranĂŠ (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
Karhunen-loève basis in goodness-of-fit tests decomposition: an evaluation
In a previous paper (GranÊ 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 CramÊr-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
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
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