Intraday forecasts of a volatility index: Functional time series methods with dynamic updating

As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick values as realisations of a collection of curves observed sequentially on equally spaced and dense grids over time and utilise functional data analysis techniques to produce one-day-ahead forecasts of these curves. The proposed method facilitates the investigation of dynamic changes in the index over very short time intervals as showcased using the 15-second high-frequency VIX index values. With the help of dynamic updating techniques, our point and interval forecasts are shown to enjoy improved accuracy over conventional time series models.Comment: 29 pages, 5 figures, To appear at the Annals of Operations Researc

Modeling and forecasting electricity spot prices: A functional data perspective

Classical time series models have serious difficulties in modeling and forecasting the enormous fluctuations of electricity spot prices. Markov regime switch models belong to the most often used models in the electricity literature. These models try to capture the fluctuations of electricity spot prices by using different regimes, each with its own mean and covariance structure. Usually one regime is dedicated to moderate prices and another is dedicated to high prices. However, these models show poor performance and there is no theoretical justification for this kind of classification. The merit order model, the most important micro-economic pricing model for electricity spot prices, however, suggests a continuum of mean levels with a functional dependence on electricity demand. We propose a new statistical perspective on modeling and forecasting electricity spot prices that accounts for the merit order model. In a first step, the functional relation between electricity spot prices and electricity demand is modeled by daily price-demand functions. In a second step, we parameterize the series of daily price-demand functions using a functional factor model. The power of this new perspective is demonstrated by a forecast study that compares our functional factor model with two established classical time series models as well as two alternative functional data models.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS652 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uncovering predictability in the evolution of the WTI oil futures curve

Accurately forecasting the price of oil, the world's most actively traded commodity, is of great importance to both academics and practitioners. We contribute by proposing a functional time series based method to model and forecast oil futures. Our approach boasts a number of theoretical and practical advantages including effectively exploiting underlying process dynamics missed by classical discrete approaches. We evaluate the finite-sample performance against established benchmarks using a model confidence set test. A realistic out-of-sample exercise provides strong support for the adoption of our approach with it residing in the superior set of models in all considered instances.Comment: 28 pages, 4 figures, to appear in European Financial Managemen

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

The Mathematical description of lactation curves in dairy cattle

This review gives an overview of the mathematical modelling of lactation curves in dairy cattle. Over the last ninety years, the development of this field of study has followed the main requirements of the dairy cattle industry. Non-linear parametric functions have represented the preferred tools for modelling average curves of homogeneous groups of animals, with the main aim of predicting yields for management purposes. The increased availability of records per individual lactations and the genetic evaluation based on test day records has shifted the interest of modellers towards more flexible and general linear functions, as polynomials or splines. Thus the main interest of modelling is no longer the reconstruction of the general pattern of the phenomenon but the fitting of individual deviations from an average curve. Other specific approaches based on the modelling of the correlation structure of test day records within lactation, such as mixed linear models or principal component analysis, have been used to test the statistical significance of fixed effects in dairy experiments or to create new variables expressing main lactation curve traits. The adequacy of a model is not an absolute requisite, because it has to be assessed according to the specific purpose it is used for. Occurrence of extended lactations and of new productive and functional traits to be described and the increase of records coming from automatic milking systems likely will represent some of the future challenges for the mathematical modelling of the lactation curve in dairy cattle

Pathway-Based Genomics Prediction using Generalized Elastic Net.

We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach

An intertemporally-consistent and arbitrage-free version of the Nelson and Siegel class of yield curve models

This article derives a generic, intertemporally-consistent, and arbitrage-free version of the popular class of yield curve models originally introduced by Nelson and Siegel (1987). The derived model has a theoretical foundation (conferred via the Heath, Jarrow and Morton (1992) framework) that allows it to be used in applications that involve an implicit or explicit time-series context. As an example of the potentialapplication of the model, the intertemporal consistency is exploited to derive a theoretical time-series process that may be used to forecast the yield curve. The empirical application of the forecasting framework to United States data results in out-of-sample forecasts that outperform the random walk over a sample period of almost 50 years, for forecast horizons ranging from six months to three years