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The prediction of wind speed is very important when dealing with the production of energy through wind turbines. In this paper, we show a new nonparametric model, based on semi-Markov chains, to predict wind speed. Particularly we use an indexed semi-Markov model that has been shown to be able to reproduce accurately the statistical behavior of wind speed. The model is used to forecast, one step ahead, wind speed. In order to check the validity of the model we show, as indicator of goodness, the root mean square error and mean absolute error between real data and predicted ones. We also compare our forecasting results with those of a persistence model. At last, we show an application of the model to predict financial indicators like the Internal Rate of Return, Duration and Convexity.
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Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the evolution of the sample in a historical record of observations which most closely resembles the current initial data. Here, we introduce a suite of forecasting methods which improve traditional analog forecasting by combining ideas from kernel methods developed in harmonic analysis and machine learning and state-space reconstruction for dynamical systems. A key ingredient of our approach is to replace single-analog forecasting with weighted ensembles of analogs constructed using local similarity kernels. The kernels used here employ a number of dynamics-dependent features designed to improve forecast skill, including Takens delay-coordinate maps (to recover information in the initial data lost through partial observations) and a directional dependence on the dynamical vector field generating the data. Mathematically, our approach is closely related to kernel methods for out-of-sample extension of functions, and we discuss alternative strategies based on the Nystrom method and the multiscale Laplacian pyramids technique. We illustrate these techniques in applications to forecasting in a low-order deterministic model for atmospheric dynamics with chaotic metastability, and interannual-scale forecasting in the North Pacific sector of a comprehensive climate model. We find that forecasts based on kernel-weighted ensembles have significantly higher skill than the conventional approach following a single analog.
Accurate short-term wind speed forecasting is needed for the rapid development and efficient operation of wind energy resources. This is, however, a very challenging problem. Although on the large scale, the wind speed is related to atmospheric pressure, temperature, and other meteorological variables, no improvement in forecasting accuracy was found by incorporating air pressure and temperature directly into an advanced space-time statistical forecasting model, the trigonometric direction diurnal (TDD) model. This paper proposes to incorporate the geostrophic wind as a new predictor in the TDD model. The geostrophic wind captures the physical relationship between wind and pressure through the observed approximate balance between the pressure gradient force and the Coriolis acceleration due to the Earths rotation. Based on our numerical experiments with data from West Texas, our new method produces more accurate forecasts than does the TDD model using air pressure and temperature for 1- to 6-hour-ahead forecasts based on three different evaluation criteria. Furthermore, forecasting errors can be further reduced by using moving average hourly wind speeds to fit the diurnal pattern. For example, our new method obtains between 13.9% and 22.4% overall mean absolute error reduction relative to persistence in 2-hour-ahead forecasts, and between 5.3% and 8.2% reduction relative to the best previous space-time methods in this setting.
Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Levy distributions; we also show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.
We propose a nonparametric approach for probabilistic prediction of the AL index trained with AL and solar wind ($v B_z$) data. Our framework relies on the diffusion forecasting technique, which views AL and $ v B_z $ data as observables of an autonomous, ergodic, stochastic dynamical system operating on a manifold. Diffusion forecasting builds a data-driven representation of the Markov semigroup governing the evolution of probability measures of the dynamical system. In particular, the Markov semigroup operator is represented in an orthonormal basis acquired from data using the diffusion maps algorithm and Takens delay embeddings. This representation of the evolution semigroup is used in conjunction with a Bayesian filtering algorithm for forecast initialization to predict the probability that the AL index is less than a user-selected threshold over arbitrary lead times and without requiring exogenous inputs. We find that the model produces skillful forecasts out to at least two-hour leads despite gaps in the training data.
Recent studies demonstrate that trends in indicators extracted from measured time series can indicate approaching to an impending transition. Kendalls {tau} coefficient is often used to study the trend of statistics related to the critical slowing down phenomenon and other methods to forecast critical transitions. Because statistics are estimated from time series, the values of Kendalls {tau} are affected by parameters such as window size, sample rate and length of the time series, resulting in challenges and uncertainties in interpreting results. In this study, we examine the effects of different parameters on the distribution of the trend obtained from Kendalls {tau}, and provide insights into how to choose these parameters. We also suggest the use of the non-parametric Mann-Kendall test to evaluate the significance of a Kendalls {tau} value. The non-parametric test is computationally much faster compared to the traditional parametric ARMA test.
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