
on Econometric Time Series 
By:  Kleijnen, Jack (Tilburg University, Center For Economic Research); van Beers, W.C.M. (Tilburg University, Center For Economic Research) 
Abstract:  We derive new statistical tests for leaveoneout crossvalidation of Kriging models. Graphically, we present these tests as scatterplots augmented with confi…dence intervals. We may wish to avoid extrapolation, which we de…fine as prediction of the output for a point that is a vertex of the convex hull of the given input combinations. Moreover, we may use bootstrapping to estimate the true variance of the Kriging predictor. The resulting tests (with or without extrapolation or bootstrapping) have typeI and typeII error probabilities, which we estimate through Monte Carlo experiments. To illustrate the application of our tests, we use an example with two inputs and the popular borehole example with eight inputs. 
Keywords:  validation; crossvalidation; Kriging; Gaussian process; extrapolation; convex hull; Monte Carlo Technique 
JEL:  C0 C1 C9 C15 C44 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:35fba511293147d5a9ba30b1229e9093&r=all 
By:  Marc Hallin; Gilles Nisol; Shahin Tavakoli 
Abstract:  In this paper, we set up the theoretical foundations for a highdimensional functional factor model approach in the analysis of large panels of functional time series (FTS). We first establish a representation result stating that if the first r eigenvalues of the covariance operator of a crosssection of N FTS are unbounded as N diverges and if the (r + 1) th one is bounded, then we can represent each FTS as a sum of a common component driven by r factors, common to (almost) all the series, and a weakly crosscorrelated idiosyncratic component (all the eigenvalues of the idiosyncratic covariance operator are bounded as N !1). Our model and theory are developed in a general Hilbert space setting that allows for panels mixing functional and scalar time series. We then turn to the estimation of the factors, their loadings, and the common components. We derive consistency results in the asymptotic regime where the number N of series and the number T of time observations diverge, thus exemplifying the “blessing of dimensionality” that explains the success of factor models in the context of highdimensional (scalar) time series. Our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, wellestablished results (Bai & Ng 2002).We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide finer understanding of the interplay between N and T for estimation purposes. We conclude with an empirical illustration on a dataset of intraday S&P100 and Eurostoxx 50 stock returns, along with their scalar overnight returns. 
Keywords:  Functional time series, Highdimensional time series, Factor model, Panel data, Functional data analysis.. 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/288340&r=all 
By:  Vanessa BerenguerRico (University of Oxford); Søren Johansen (University of Copenhagen and CREATES); Bent Nielsen (University of Oxford) 
Abstract:  A uniform weak consistency theory is presented for the marked and weighted empirical distribution function of residuals. New and weaker sufficient conditions for uniform consistency are derived. The theory allows for a wide variety of regressors and error distributions. We apply the theory to 1step Huberskip estimators. These estimators describe the widespread practice of removing outlying observations from an intial estimation of the model of interest and updating the estimation in a second step by applying least squares to the selected observations. Two results are presented. First, we give new and weaker conditions for consistency of the estimators. Second, we analyze the gauge, which is the rate of false detection of outliers, and which can be used to decide the cutoff in the rule for selecting outliers. 
Keywords:  1step Huber skip, Asymptotic theory, Empirical processes, Gauge, Marked and Weighted Empirical processes, Nonstationarity, Robust Statistics, Stationarity. 
JEL:  C01 C22 
Date:  2019–05–24 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201912&r=all 