Optimal model-free prediction from multivariate time series

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal pre-selection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used sub-optimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure

Optimal model-free prediction from multivariate time series

© 2015 American Physical Society.Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal preselection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used suboptimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Niño Southern Oscillation

Wavelet Neural Networks: A Practical Guide

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications

Forecasting Models for Integration of Large-Scale Renewable Energy Generation to Electric Power Systems

Amid growing concerns about climate change and non-renewable energy sources deple¬tion, vari¬able renewable energy sources (VRESs) are considered as a feasible substitute for conventional environment-polluting fossil fuel-based power plants. Furthermore, the transition towards clean power systems requires additional transmission capacity. Dynamic thermal line rating (DTLR) is being considered as a potential solution to enhance the current transmission line capacity and omit/postpone transmission system expansion planning, while DTLR is highly dependent on weather variations. With increasing the accommodation of VRESs and application of DTLR, fluctuations and variations thereof impose severe and unprecedented challenges on power systems operation. Therefore, short-term forecasting of large-scale VERSs and DTLR play a crucial role in the electric power system op¬eration problems. To this end, this thesis devotes on developing forecasting models for two large-scale VRESs types (i.e., wind and tidal) and DTLR. Deterministic prediction can be employed for a variety of power system operation problems solved by deterministic optimization. Also, the outcomes of deterministic prediction can be employed for conditional probabilistic prediction, which can be used for modeling uncertainty, used in power system operation problems with robust optimization, chance-constrained optimization, etc. By virtue of the importance of deterministic prediction, deterministic prediction models are developed. Prevalently, time-frequency decomposition approaches are adapted to decompose the wind power time series (TS) into several less non-stationary and non-linear components, which can be predicted more precisely. However, in addition to non-stationarity and nonlinearity, wind power TS demonstrates chaotic characteristics, which reduces the predictability of the wind power TS. In this regard, a wind power generation prediction model based on considering the chaosity of the wind power generation TS is addressed. The model consists of a novel TS decomposition approach, named multi-scale singular spectrum analysis (MSSSA), and least squares support vector machines (LSSVMs). Furthermore, deterministic tidal TS prediction model is developed. In the proposed prediction model, a variant of empirical mode decomposition (EMD), which alleviates the issues associated with EMD. To further improve the prediction accuracy, the impact of different components of wind power TS with different frequencies (scales) in the spatiotemporal modeling of the wind farm is assessed. Consequently, a multiscale spatiotemporal wind power prediction is developed, using information theory-based feature selection, wavelet decomposition, and LSSVM. Power system operation problems with robust optimization and interval optimization require prediction intervals (PIs) to model the uncertainty of renewables. The advanced PI models are mainly based on non-differentiable and non-convex cost functions, which make the use of heuristic optimization for tuning a large number of unknown parameters of the prediction models inevitable. However, heuristic optimization suffers from several issues (e.g., being trapped in local optima, irreproducibility, etc.). To this end, a new wind power PI (WPPI) model, based on a bi-level optimization structure, is put forward. In the proposed WPPI, the main unknown parameters of the prediction model are globally tuned based on optimizing a convex and differentiable cost function. In line with solving the non-differentiability and non-convexity of PI formulation, an asymmetrically adaptive quantile regression (AAQR) which benefits from a linear formulation is proposed for tidal uncertainty modeling. In the prevalent QR-based PI models, for a specified reliability level, the probabilities of the quantiles are selected symmetrically with respect the median probability. However, it is found that asymmetrical and adaptive selection of quantiles with respect to median can provide more efficient PIs. To make the formulation of AAQR linear, extreme learning machine (ELM) is adapted as the prediction engine. Prevalently, the parameters of activation functions in ELM are selected randomly; while different sets of random values might result in dissimilar prediction accuracy. To this end, a heuristic optimization is devised to tune the parameters of the activation functions. Also, to enhance the accuracy of probabilistic DTLR, consideration of latent variables in DTLR prediction is assessed. It is observed that convective cooling rate can provide informative features for DTLR prediction. Also, to address the high dimensional feature space in DTLR, a DTR prediction based on deep learning and consideration of latent variables is put forward. Numerical results of this thesis are provided based on realistic data. The simulations confirm the superiority of the proposed models in comparison to traditional benchmark models, as well as the state-of-the-art models

Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread

Forecasting Exchange-Rates via Local Approximation Methods and Neural Networks

There has been an increased number of papers in the literature in recent years, applying several methods and techniques for exchange - rate prediction. This paper focuses on the Greek drachma using daily observations of the drachma rates against four major currencies, namely the U.S. Dollar (USD), the Deutsche Mark (DM), the French Franc (FF) and the British Pound (GBP) for a period of 11 years, aiming at forecasting their short-term course by applying local approximation methods based on both chaotic analysis and neural networks.Key Words: Exchange Rates, Forecasting, Neural Networks

Hybrid Advanced Optimization Methods with Evolutionary Computation Techniques in Energy Forecasting

More accurate and precise energy demand forecasts are required when energy decisions are made in a competitive environment. Particularly in the Big Data era, forecasting models are always based on a complex function combination, and energy data are always complicated. Examples include seasonality, cyclicity, fluctuation, dynamic nonlinearity, and so on. These forecasting models have resulted in an over-reliance on the use of informal judgment and higher expenses when lacking the ability to determine data characteristics and patterns. The hybridization of optimization methods and superior evolutionary algorithms can provide important improvements via good parameter determinations in the optimization process, which is of great assistance to actions taken by energy decision-makers. This book aimed to attract researchers with an interest in the research areas described above. Specifically, it sought contributions to the development of any hybrid optimization methods (e.g., quadratic programming techniques, chaotic mapping, fuzzy inference theory, quantum computing, etc.) with advanced algorithms (e.g., genetic algorithms, ant colony optimization, particle swarm optimization algorithm, etc.) that have superior capabilities over the traditional optimization approaches to overcome some embedded drawbacks, and the application of these advanced hybrid approaches to significantly improve forecasting accuracy