Combining domain knowledge and statistical models in time series analysis

This paper describes a new approach to time series modeling that combines subject-matter knowledge of the system dynamics with statistical techniques in time series analysis and regression. Applications to American option pricing and the Canadian lynx data are given to illustrate this approach.Comment: Published at http://dx.doi.org/10.1214/074921706000001049 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Forecasting high waters at Venice Lagoon using chaotic time series analisys and nonlinear neural netwoks

Time series analysis using nonlinear dynamics systems theory and multilayer neural networks models have been applied to the time sequence of water level data recorded every hour at 'Punta della Salute' from Venice Lagoon during the years 1980-1994. The first method is based on the reconstruction of the state space attractor using time delay embedding vectors and on the characterisation of invariant properties which define its dynamics. The results suggest the existence of a low dimensional chaotic attractor with a Lyapunov dimension, DL, of around 6.6 and a predictability between 8 and 13 hours ahead. Furthermore, once the attractor has been reconstructed it is possible to make predictions by mapping local-neighbourhood to local-neighbourhood in the reconstructed phase space. To compare the prediction results with another nonlinear method, two nonlinear autoregressive models (NAR) based on multilayer feedforward neural networks have been developed. From the study, it can be observed that nonlinear forecasting produces adequate results for the 'normal' dynamic behaviour of the water level of Venice Lagoon, outperforming linear algorithms, however, both methods fail to forecast the 'high water' phenomenon more than 2-3 hours ahead.Publicad

Nonlinear autoregressive moving average-L2 model based adaptive control of nonlinear arm nerve simulator system

This paper considers the trouble of the usage of approximate strategies for realizing the neural controllers for nonlinear SISO systems. In this paper, we introduce the nonlinear autoregressive moving average (NARMA-L2) model which might be approximations to the NARMA model. The nonlinear autoregressive moving average (NARMA-L2) model is an precise illustration of the input–output behavior of finite-dimensional nonlinear discrete time dynamical systems in a neighborhood of the equilibrium state. However, it isn't always handy for purposes of neural networks due to its nonlinear dependence on the manipulate input. In this paper, nerves system based arm position sensor device is used to degree the precise arm function for nerve patients the use of the proposed systems. In this paper, neural network controller is designed with NARMA-L2 model, neural network controller is designed with NARMA-L2 model system identification based predictive controller and neural network controller is designed with NARMA-L2 model based model reference adaptive control system. Hence, quite regularly, approximate techniques are used for figuring out the neural controllers to conquer computational complexity. Comparison were made among the neural network controller with NARMA-L2 model, neural network controller with NARMA-L2 model system identification based predictive controller and neural network controller with NARMA-L2 model reference based adaptive control for the preferred input arm function (step, sine wave and random signals). The comparative simulation result shows the effectiveness of the system with a neural network controller with NARMA-L2 model based model reference adaptive control system. Index Terms--- Nonlinear autoregressive moving average, neural network, Model reference adaptive control, Predictive controller DOI: 10.7176/JIEA/10-3-03 Publication date: April 30th 202

A Learning-Based Framework for Two-Dimensional Vehicle Maneuver Prediction over V2V Networks

Situational awareness in vehicular networks could be substantially improved utilizing reliable trajectory prediction methods. More precise situational awareness, in turn, results in notably better performance of critical safety applications, such as Forward Collision Warning (FCW), as well as comfort applications like Cooperative Adaptive Cruise Control (CACC). Therefore, vehicle trajectory prediction problem needs to be deeply investigated in order to come up with an end to end framework with enough precision required by the safety applications' controllers. This problem has been tackled in the literature using different methods. However, machine learning, which is a promising and emerging field with remarkable potential for time series prediction, has not been explored enough for this purpose. In this paper, a two-layer neural network-based system is developed which predicts the future values of vehicle parameters, such as velocity, acceleration, and yaw rate, in the first layer and then predicts the two-dimensional, i.e. longitudinal and lateral, trajectory points based on the first layer's outputs. The performance of the proposed framework has been evaluated in realistic cut-in scenarios from Safety Pilot Model Deployment (SPMD) dataset and the results show a noticeable improvement in the prediction accuracy in comparison with the kinematics model which is the dominant employed model by the automotive industry. Both ideal and nonideal communication circumstances have been investigated for our system evaluation. For non-ideal case, an estimation step is included in the framework before the parameter prediction block to handle the drawbacks of packet drops or sensor failures and reconstruct the time series of vehicle parameters at a desirable frequency

A Comparative Study of Reservoir Computing for Temporal Signal Processing

Reservoir computing (RC) is a novel approach to time series prediction using recurrent neural networks. In RC, an input signal perturbs the intrinsic dynamics of a medium called a reservoir. A readout layer is then trained to reconstruct a target output from the reservoir's state. The multitude of RC architectures and evaluation metrics poses a challenge to both practitioners and theorists who study the task-solving performance and computational power of RC. In addition, in contrast to traditional computation models, the reservoir is a dynamical system in which computation and memory are inseparable, and therefore hard to analyze. Here, we compare echo state networks (ESN), a popular RC architecture, with tapped-delay lines (DL) and nonlinear autoregressive exogenous (NARX) networks, which we use to model systems with limited computation and limited memory respectively. We compare the performance of the three systems while computing three common benchmark time series: H{\'e}non Map, NARMA10, and NARMA20. We find that the role of the reservoir in the reservoir computing paradigm goes beyond providing a memory of the past inputs. The DL and the NARX network have higher memorization capability, but fall short of the generalization power of the ESN

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets

A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method