Maria Lucia Parrella

Neural networks for bandwidth selection in local linear regression of time series

The problem of automatic bandwidth selection in nonparametric regression is considered when a local linear estimator is used to derive nonparametrically the unknown regression function. A plug-in method for choosing the smoothing parameter based on the use of the neural networks is presented. The method applies to dependent data generating processes with nonlinear autoregressive time series representation. The consistency of the method is shown in the paper, and a simulation study is carried out to assess the empirical performance of the procedure.

Clustering Complex Time Series Databases

Time series data account for a large fraction of the data stored in financial, medical and scientific database. As a consequence, in the last decade there has been an explosion of interest in mining time series data and several new algorithms to index, classify, cluster and segment time series have been introduced. In this paper we focus on clustering of time series from a large database provided by a large Italian electric company, and the power consumption of a specific class of power users, that is the business and industrial customers, is measured. The aim of this paper is to propose an effective clustering technique in the frequency domain where the need of computational and memory resources is much reduced in order to make the algorithm efficient for large and complex temporal data bases.

Multiple Testing for Different Structures of Spatial Dynamic Panel Data Models

In the econometric field, spatio-temporal data is often modeled by spatial dynamic panel data models (SDPD). In the last decade, several versions of the SDPD model have been proposed, based on different assumptions on the spatial parameters and different properties of the estimators. In particular, the classic version of the model assumes that the spatial parameters are homogeneous over location. Another version, proposed recently and called generalized SDPD, assumes that the spatial parameters are adaptive over location. In this work we propose a strategy for testing the particular structure of the spatial dynamic panel data model, by means of a multiple testing procedure that allows to choose between the generalized version of the model and some specific versions derived from the general one by imposing particular constraints on the parameters. The multiple test is made using the Bonferroni technique and the distribution of the multiple test statistic is derived by a residual bootstrap resampling procedure.

Bias-corrected inference for multivariate nonparametric regression

The local polynomial estimator is particularly affected by the curse of dimensionality, which reduces the potential of this tool for large-dimensional applications. We propose an estimation procedure based on the local linear estimator and a sparseness condition that focuses on nonlinearities in the model. Our procedure, called BID (bias inflation-deflation), is automatic and easily applicable to models with many covariates without requiring any additivity assumption. It is an extension of the RODEO method, and introduces important new contributions: consistent estimation of the multivariate optimal bandwidth (the tuning parameter of the estimator); consistent estimation of the multivariate bias-corrected regression function and confidence bands; and automatic identification and separation of nonlinear and linear effects. Some theoretical properties of the method are discussed. In particular, we show the nonparametric oracle property. For linear models, BID automatically reaches the optimal rate O p ( n - 1 / 2 ) , equivalent to the parametric case. A simulation study shows the performance of the procedure for finite samples.

Local Polynomials for Variable Selection

Nonparametric estimators are particularly affected by the curse of dimensionality. An interesting method has been proposed recently, the RODEO, which uses the nonparametric local linear estimator for high dimensional regression, avoiding the curse of dimensionality when the model is sparse. This method can be used for variable selection as well, but it is blind to linear dependencies. For this reason, it is suggested to use the RODEO on the residuals of a LASSO. In this paper we propose an alternative solution, based on the adaptation of the well-known asymptotic results for the local linear estimator. The proposal can be used to complete the RODEO, avoiding the necessity of filtering the data through the LASSO. Some theoretical properties and the results of a simulation study are shown.

On the RODEO Method for Variable Selection

In this work, we work around an iterative estimation procedure which has been proposed recently by Lafferty and Wasserman. The procedure is called RODEO and can be used to select the relevant covariates of a sparse regression model. A drawback of the RODEO is that it fails to isolate some relevant covariates, in particular those which have linear effects on the model, and for such reason it is suggested to use the RODEO on the residuals of a LASSO. Here we propose a test which can be integrated to the RODEO procedure in order to fill this gap and complete the final step of the variable selection procedure. A two-stage procedure is therefore proposed. The results of a simulation study show a good performance of the new procedure.

Detecting Short-Term Cycles in Complex Time Series Databases

Time series characterize a large part of the data stored in financial, medical and scientific databases. The automatic statistical modelling of such data may be a very hard problem when the time series show “complex” features, such as nonlinearity, local nonstationarity, high frequency, long memory and periodic components. In such a context, the aim of this paper is to analyze the problem of detecting automatically the different periodic components in the data, with particular attention to the short term components (weakly, daily and intra-daily cycles). We focus on the analysis of real time series from a large database provided by an Italian electric company. This database shows complex features, either for the high dimension or the structure of the underlying process. A new classification procedure we proposed recently, based on a spectral analysis of the time series, was applied on the data. Here we perform a sensitivity analysis for the main tuning parameters of the procedure. A method for the selection of the optimal partition is then proposed.

Evaluating the behavior of a function in kernel based regression

Given a specific model and a regression function, this work analyses the sensitivity of the kernel estimator on the bandwidth, considered as a function parameter. The problem is well known and has been investigated quite thoroughly. The novelty of our study is that we invert the perspective: instead of examining the estimated regression function and the influence of the bandwidth function, we analyse the complexity of the bandwidth function that is determined by the structure of the process. We show that preliminary evaluation of the structure of the unknown function can improve the results of the kernel regression and, contextually, may significantly simplify the estimation procedure.

Empirical likelihood based nonparametric testing for CAPM

The Capital Asset Pricing Model (CAPM) predicts a linear relation between assets’ return and their betas. However, there is empirical evidence that such a relationship does not necessarily occur, and in some cases it might even be nonlinear. In this paper we explore a nonparametric approach where the linear specification is tested against a nonparametric alternative. This methodology is implemented on S&P500 data.

Neural Networks for Bandwidth Selection in Non-Parametric Derivative Estimation

In this paper we consider the problem of bandwidth selection in local polynomial estimation of derivative functions. We use a dependent data context, and analyze time series which are realizations of strictly stationary processes. We consider the estimation of the first derivative of the conditional mean function for a non-linear autoregressive model. First of all, we emphasize the role assumed by the smoothing parameter, by showing how the choice of the bandwidth is crucial for the consistency of the non-parametric estimation procedure, through an example on simulated data. We then use a new approach for the selection of such a parameter, based on the neural network technique. Such alternative method presents several advantages with respect to the traditional approach used so far.