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Abstract: Several methods have recently been proposed in the ultra-high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility error”. As such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step-ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; (iii) even the partially corrected recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of . An empirical example for S&P 500 data is used to demonstrate the techniques developed in this paper. [Copyright &y& Elsevier]

Abstract: In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these “hierarchical time series”. They are commonly forecast using either a “bottom-up” or a “top-down” method. In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-down or a bottom-up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions. We show in a simulation study that our method performs well compared to the top-down approach and the bottom-up method. We demonstrate our proposed method by forecasting Australian tourism demand where the data are disaggregated by purpose of travel and geographical region. [Copyright &y& Elsevier]

Multi-task learning is increasingly used to investigate the association structure between multiple responses and a single set of predictor variables in many applications. In the era of big data, the coexistence of incomplete outcomes, large number of responses, and high dimensionality in predictors poses unprecedented challenges in estimation, prediction and computation. In this paper, we propose a scalable and computationally efficient procedure, called PEER, for large-scale multi-response regression with incomplete outcomes, where both the numbers of responses and predictors can be high-dimensional. Motivated by sparse factor regression, we convert the multi-response regression into a set of univariate-response regressions, which can be efficiently implemented in parallel. Under some mild regularity conditions, we show that PEER enjoys nice sampling properties including consistency in estimation, prediction, and variable selection. Extensive simulation studies show that our proposal compares favorably with several existing methods in estimation accuracy, variable selection, and computation efficiency. [ABSTRACT FROM AUTHOR]

Abstract: The question of variable selection in a regression model is a major open research topic in econometrics. Traditionally two broad classes of methods have been used. One is sequential testing and the other is information criteria. The advent of large datasets used by institutions such as central banks has exacerbated this model selection problem. A solution in the context of information criteria is provided in this paper. The solution rests on the judicious selection of a subset of models for consideration using nonstandard optimisation algorithms for information criterion minimisation. In particular, simulated annealing and genetic algorithms are considered. Both a Monte Carlo study and an empirical forecasting application to UK CPI inflation suggest that the proposed methods are worthy of further consideration. [Copyright &y& Elsevier]

Partially varying coefficient model (PVCM) provides a useful class of tools for modeling complex data by incorporating a combination of constant and time-varying covariate effects. One natural question is that how to decide which covariates correspond to constant coefficients and which correspond to time-dependent coefficient functions. To handle this two-type structure selection problem on PVCM, those existing methods are either based on a finite truncation way of coefficient functions, or based on a two-phase procedure to estimate the constant and function parts separately. This paper attempts to provide a complete theoretical characterization for estimation and structure selection issues of PVCM, via proposing two new penalized methods for PVCM within a reproducing kernel Hilbert space (RKHS). The proposed strategy is partially motivated by the so-called "Non-Constant Theorem" of radial kernels, which ensures a unique and unified representation of each candidate component in the hypothesis space. Within a high-dimensional framework, minimax convergence rates for the prediction risk of the first method is established when each unknown time-dependent coefficient can be well approximated within a specified RKHS. On the other hand, under certain regularity conditions, it is shown that the second proposed estimator is able to identify the underlying structure correctly with high probability. Several simulated experiments are implemented to examine the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the partially functional linear regression model in which there are both functional predictors and traditional multivariate predictors. The existing approach is based on approximation using functional principal component analysis which has some limitations. We propose an alternative framework based on reproducing kernel Hilbert spaces (RKHS) which has not been investigated in the literature for the partially functional case. Asymptotic normality of the non-functional part is also shown. Even when reduced to the purely functional linear regression, our results extend the existing results in two aspects: rates are established using both prediction risk and RKHS norm, and faster rates are possible if greater smoothness is assumed. Some simulations are used to demonstrate the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]