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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 leave-one-out cross-validation 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 type-I and type-II 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; cross-validation; 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:35fba511-2931-47d5-a9ba-30b1229e9093&r=all |
| By: | Marc Hallin; Gilles Nisol; Shahin Tavakoli |
| Abstract: | In this paper, we set up the theoretical foundations for a high-dimensional 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 cross-section 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 cross-correlated 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 high-dimensional (scalar) time series. Our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well-established 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, High-dimensional 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 Berenguer-Rico (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 1-step Huber-skip 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 cut-off in the rule for selecting outliers. |
| Keywords: | 1-step Huber skip, Asymptotic theory, Empirical processes, Gauge, Marked and Weighted Empirical processes, Non-stationarity, Robust Statistics, Stationarity. |
| JEL: | C01 C22 |
| Date: | 2019–05–24 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2019-12&r=all |