Multivariate Time Series with Application On Recurrent Neural Networks
Safa Nader Mustafa Shanaa
صفاء نادر مصطفى شناعة
Multivariate time series data in practical applications, such as health care, geosciences, engineering, and biology. This thesis introduces a survey study of time series analysis to recurrent neural networks research, an analytic domain that has been essential for understanding and predicting the behavior of variables across many diverse fields, in this research the following were investigated. First, the characteristics and preliminaries of time series data are investigated and discussed, including various time series models, specially, Autoregressive Models such as, AR, MA, ARMA, and ARIMA. Frequently one wishes to fit a parametric model to time-series data and determine accurate values of the parameters and reliable estimates for the uncertainties in those parameters. It is important to gain a thorough understanding of the noise and develop appropriate methods for parameter estimation, so that various approaches of parameter estimates will be considered in this thesis, such as, yules walker method, least square method, method of moments and maximum likelihood approach. Second, different time series modeling techniques are surveyed that can address various topics of interest to artificial neural networks researchers, including describing the pattern of change in a variable, modeling seasonal effects, assessing the immediate and long-term impact of a salient event, and forecasting future values. The structure of the artificial neural networks especially the recurrent neural networks were discussed in details in this research, concerning on GRUs and LSTMs, and their properties, also some difficulties that arises in recurrent neural networks such as vanished gradient and the overfitting were discussed. To illustrate these approaches, an illustrative application based on Monte Carlo and bootstrapping methods is used throughout the research, constructing a one layer hidden recurrent neural networks and applied back-propagation, for the purpose of comparison, the variance of error in each method was estimated.