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Forecasting nonlinear time series with neural network sieve bootstrap

A new method to construct nonparametric prediction intervals for nonlinear time series data is proposed. Within the framework of the recently developed sieve bootstrap, the new approach employs neural network models to approximate the original nonlinear process. The method is flexible and easy to implement as a standard residual bootstrap scheme while retaining the advantage of being a nonparametric technique. It is model-free within a general class of nonlinear processes and avoids the specification of a finite dimensional model for the data generating process. The results of a Monte Carlo study are reported in order to investigate the finite sample performances of the proposed procedure.

Variable selection in neural network regression models with dependent data: a subsampling approach

The problem of variable selection in neural network regression models with dependent data is considered. In this framework, a test procedure based on the introduction of a measure for the variable relevance to the model is discussed. The main difficulty in using this procedure is related to the asymptotic distribution of the test statistic which is not one of the familiar tabulated distributions. Moreover, it depends on matrices which are very difficult to estimate because of their complex structure. To overcome these analytical issues and to get a consistent approximation for the sampling distribution of the statistic involved, a subsampling scheme is proposed. The procedure, which takes explicitly into account the dependence structure of the data, will be justified from an asymptotic point of view and evaluated in finite samples by a small Monte Carlo study.

Mathematical and statistical methods in insurance and finance

Least Squares Predictors for Threshold Models: Properties and Forecast Evaluation.- Estimating Portfolio Conditional Returns Distribution Through Style Analysis Models.- A Full Monte Carlo Approach to the Valuation of the Surrender Option Embedded in Life Insurance Contracts.- Spatial Aggregation in Scenario Tree Reduction.- Scaling Laws in Stock Markets. An Analysis of Prices and Volumes.- Bounds for Concave Distortion Risk Measures for Sums of Risks.- Characterization of Convex Premium Principles.- FFT, Extreme Value Theory and Simulation to Model Non-Life Insurance Claims Dependences.- Dynamics of Financial Time Series in an Inhomogeneous Aggregation Framework.- A Liability Adequacy Test for Mathematical Provision.- Iterated Function Systems, Iterated Multifunction Systems, and Applications.- Remarks on Insured Loan Valuations.- Exploring the Copula Approach for the Analysis of Financial Durations.- Analysis of Economic Fluctuations: A Contribution from Chaos Theory.- Generalized Influence Functions and Robustness Analysis.- Neural Networks for Bandwidth Selection in Non-Parametric Derivative Estimation.- Comparing Mortality Trends via Lee-Carter Method in the Framework of Multidimensional Data Analysis.- Decision Making in Financial Markets Through Multivariate Ordering Procedure.- A Biometric Risks Analysis in Long Term Care Insurance.- Clustering Financial Data for Mutual Fund Management.- Modeling Ultra-High-Frequency Data: The S&P 500 Index Future.- Simulating a Generalized Gaussian Noise with Shape Parameter 1/2.- Further Remarks on Risk Profiles for Life Insurance Participating Policies.- Classifying Italian Pension Funds via GARCH Distance.- The Analysis of Extreme Events - Some Forecasting Approaches.

Input Variable Selection in Neural Network Models

One of the most important issues in using neural networks for the analysis of real-world problems is the input variable selection problem. This article connects input variable selection with multiple testing in the neural network regression models. In the proposed procedure, the number and the type of input neurons are selected by means of a testing scheme, based on appropriate measures of relevance of a given input variable to the model. In order to avoid the data snooping problem, family-wise error rate is controlled by using the StepM method proposed by Romano and Wolf (2005). The testing procedure is calibrated by using the subsampling, which is shown to deliver consistent results under weak assumptions on the data generating process and on the structure of the neural network model.

Neural network modeling by subsampling

The aim of the paper is to develop hypothesis testing procedures both for variable selection and model adequacy to facilitate a model selection strategy for neural networks. The approach, based on statical inference tools, uses the subsampling to overcome the analytical and probabilistic difficulties related to the estimation of the sampling distribution of the test statistics involved. Some illustrative examples are also discussed.

Neural Network Modelling with Applications to Euro Exchange Rates

Neural networks have shown considerable success when used to model financial data series. However, a major weakness of this class of models is the lack of established procedures for misspecification testing and tests of statistical significance for the various estimated parameters. These issues are particularly important in the case of financial engineering where data generating processes are very complex and dominantly stochastic. After a brief review of neural network models, an input selection algorithm is proposed and discussed. It is based on a multistep multiple testing procedure calibrated by using subsampling. The simulation results show that the proposed testing procedure is an effective criterion for selecting a proper set of relevant inputs for the network. When applied to Euro exchange rates, the selected network models show that information contained in past percentage changes can be relevant to the prediction of future percentage changes of certain time series. The apparent predictability for some countries which we analysed does not seem to be an artifact of data snooping. Rather, it is the result of a testing procedure constructed to keep the family wise error rate under control. The results also remain stable while changing the subseries length.

Bootstrap Variables Selection in Neural Network Regression Models

In this paper we consider the problem of variables selection in a non linear regression model with dependent errors. In this framework, we discuss the use of some measures for the variables relevance to the neural network model and we propose the use of the moving block bootstrap technique to estimate the variability of these measures. The performance of the procedure is evaluated by a small Monte Carlo experiment which shows how the proposed approach determines a correct ranking among relevant and irrelevant variables.

A Sequential Test for Evaluating Air Quality

The present paper provides a simple sequential test for evaluating air quality, to verify a relative higher health risk of some area. The proposed procedure is based on the identification of a Poisson process representing the number of a particular pollutant at day t in a given year. A maximized sequential probability ratio test based on a composite alternative hypothesis has been implemented. The test is performed on emissions of air pollutants in the area of Salerno in which only partial data are available.

Non Linear Time Series Analysis of Air Pollutants with Missing Data

This paper investigates the jointly use of local polynomials and feedforward neural networks for estimating the probability of exceedance of the daily average for \(PM_{10}\) in the presence of missing data. In contrast to other approaches focusing on some assumption on the distribution of \(PM_{10}\), the reconstruction of the unobserved time series is obtained by using a procedure involving two nonparametric steps based on the estimation of the trend-cycle and of the superimposed nonlinear stochastic component of the series. By using Neural Network Sieve Bootstrap, the probability to overcross the limit established by the European Union for \(PM_{10}\) is evaluated at the dates where time series shows missing values. An application to real data is also presented and discussed.

Testing the Weak Form Market Efficiency: Empirical Evidence from the Italian Stock Exchange

This paper investigates the use of feed forward neural networks for testing the weak form market efficiency. In contrast to approaches that compare out-of-sample predictions of non-linear models to those generated by the random walk model, we directly focus on testing for unpredictability by considering the null hypothesis that a given set of past lags has no effect on current returns. To avoid the data-snooping problem the testing procedure is based on the StepM approach in order to control the familiwise error rate. The procedure is used to test for predictive power in FTSE-MIB index of the italian stock market.