Matteo Grigoletto

Bootstrap prediction intervals for autoregressions: some alternatives

Abstract A new method is proposed to obtain interval forecasts for autoregressive models taking into account the variability due to the estimation of the order and the parameters. The procedure improves that introduced by Masarotto (1990) , allows a substantial reduction of the variance of the predictive distribution percentile estimators and should thus be considered as a useful alternative to the classic Box and Jenkins interval forecast. The method uses the bootstrap technique and is distribution-free. An empirical application is considered.

A hierarchical model for the analysis of spatial rainfall extremes

In this article, we propose a spatial model for analyzing extreme rainfall values over the Triveneto region (Italy). We assess the existence of a long-term trend in the extremes. To integrate data coming from the different stations, we propose a hierarchical model. At the first level, for each monitoring station we model data by making use of a generalized extreme value distribution; at the second level, we combine results from the first stage by exploiting recent advances in modeling nonstationary spatial random fields.

Looking for Skewness in Financial Time Series

In this paper, we study marginal and conditional skewness in financial returns for nine time series of major international stock indices. For this purpose, we develop a new variant of the GARCH model with dynamic skewness and kurtosis. Our empirical results indicate that there is no evidence of marginal asymmetry in the nine time series under consideration. We do however find significant time-varying conditional skewness. The economic significance of conditional skewness is analysed in terms of Value-at-Risk measures and Market Risk Capital Requirements set by the Basel Accord. Copyright

Practical implications of higher moments in risk management

In this paper the out-of-sample prediction of Value-at-Risk by means of models accounting for higher moments is studied. We consider models differing in terms of skewness and kurtosis and, in particular, the GARCHDSK model, which allows for constant and dynamic skewness and kurtosis. The issue of VaR prediction performance is approached first from a purely statistical viewpoint, studying the properties concerning correct coverage rates and independence of VaR violations. Then, financial implications of different VaR models, in terms of market risk capital requirements, as defined by the Basel Accord, are considered. Our results, based on the analysis of eight international stock indexes, highlight the presence of conditional skewness and kurtosis, in some case time-varying, and point out that asymmetry plays a significant role in risk management.

Simulation and Estimation of the Meixner Distribution

The Meixner distribution is a special case of the generalized z-distributions. Its properties make it potentially very useful in modeling short-term financial returns. This article proposes an algorithm to simulate the Meixner distribution, and shows how to obtain maximum likelihood estimators of its parameters. A GARCH-type model is then assessed, assuming that the innovation distribution is a standardized Meixner. Goodness-of-fit properties are investigated for some real financial time series, using bootstrap tests based on the empirical process of the residuals.

Bootstrap prediction regions for multivariate autoregressive processes

Abstract.Two new methods for improving prediction regions in the context of vector autoregressive (VAR) models are proposed. These methods, which are based on the bootstrap technique, take into account the uncertainty associated with the estimation of the model order and parameters. In particular, by exploiting an independence property of the prediction error, we will introduce a bootstrap procedure that allows for better estimates of the forecasting distribution, in the sense that the variability of its quantile estimators is substantially reduced, without requiring additional bootstrap replications. The proposed methods have a good performance even if the disturbances distribution is not Gaussian. An application to a real data set is presented.

Prediction intervals for farima processes by bootstrap methods

In this paper we introduce a procedure to compute prediction intervals for FARIMA (p d q) processes, taking into account the variability due to model identification and parameter estimation. To this aim, a particular bootstrap technique is developed. The performance of the prediction intervals is then assessed and compared to that of standard bootstrap percentile intervals. The methods are applied to the time series of Nile River annual minima.

Complex Models and Computational Methods in Statistics

A new unsupervised classification technique through nonlinear non parametric mixed effects models.- Estimation approaches for the apparent diffusion coefficient in Rice-distributed MR signals.- Longitudinal patterns of financial product ownership: a latent growth mixture approach.- Computationally efficient inference procedures for vast dimensional realized covariance models.- A GPU software library for likelihood-based inference of environmental models with large datasets.- Theoretical Regression Trees: a tool for multiple structural-change models analysis.- Some contributions to the theory of conditional Gibbs partitions.- Estimation of traffic matrices for LRD traffic.- A Newtons method for benchmarking time series.- Spatial smoothing for data distributed over non-planar domains.- Volatility swings in the US financial markets.- Semicontinuous regression models with skew distributions.- Classification of multivariate linear-circular data with nonignorable missing values.- Multidimensional connected set detection in clustering based on nonparametric density estimation.- Using integrated nested Laplace approximations for modelling spatial healthcare utilization.- Supply function prediction in electricity auctions.- A hierarchical bayesian model for RNA-Seq data.

Misspecification Testing for the Conditional Distribution Model in GARCH-Type Processes

In this article, we study goodness of fit tests for some distributions of the innovations which are usually adopted to explain the behavior of financial time series. Inference is developed in the context of GARCH-type models. Functional bootstrap tests are employed, assuming that the conditional means and variances of the model are correctly specified. The performances of the functional tests are assessed with a Monte Carlo experiment, based on some of the most common distributions adopted in the financial framework. The results of an application to the series of squared residuals from a PARCH(1,1) model fitted to a series of foreign exchange rates returns are also shown.

Bootstrap prediction intervals for autoregressive models fitted to non-autoregressive processes

The familiar Box and Jenkins method used to build prediction intervals for AR processes neglects the variability due to the estimation of model order and parameters. The purpose of the present paper is to assess the robustness of an approach that takes into account this additional uncertainty when the assumption that the underlying process is AR is not satisfied.