Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userProbabilistic prediction of the AL index with the diffusion forecasting model
88
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
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.
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively small time intervals. This paper proposes an interpolation expression for the identification of anomalous diffusion in complex signals for the cases when the dynamics of the system under study reaches a steady state (large time intervals). This interpolation expression uses the chaotic difference moment (transient structural function) of the second order as an average characteristic of displacements. A general procedure for identifying anomalous diffusion and calculating its parameters in real stochastic signals, which includes the removal of the regular (low-frequency) components from the source signal and the fitting of the chaotic part of the experimental difference moment of the second order to the interpolation expression, is presented. The procedure was applied to the analysis of the dynamics of magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray emission from accreting objects. For all three applications, the interpolation was able to adequately describe the chaotic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these natural signals. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified. The relation between the interpolation expression and a diffusion model, which is derived in the paper, allows one to simulate the chaotic processes in the open complex systems with anomalous diffusion.
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.
We investigate the time evolution of the scores of the second most popular sport in world: the game of cricket. By analyzing the scores event-by-event of more than two thousand matches, we point out that the score dynamics is an anomalous diffusive process. Our analysis reveals that the variance of the process is described by a power-law dependence with a super-diffusive exponent, that the scores are statistically self-similar following a universal Gaussian distribution, and that there are long-range correlations in the score evolution. We employ a generalized Langevin equation with a power-law correlated noise that describe all the empirical findings very well. These observations suggest that competition among agents may be a mechanism leading to anomalous diffusion and long-range correlation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
