Machine Learning Approach and Extreme Value Theory to Correlated Stochastic Time Series with Application to Tree Ring Data

The main goal of machine learning (ML) is to study and improve mathematical models which can be trained with data provided by the environment to infer the future and to make decisions without necessarily having complete knowledge of all influencing elements. In this work, we describe how ML can be a powerful tool in studying climate modeling. Tree ring growth was used as an implementation in different aspects, for example, studying the history of buildings and environment. By growing and via the time, a new layer of wood to beneath its bark by the tree. After years of growing, time series can be applied via a sequence of tree ring widths. The purpose of this paper is to use ML algorithms and Extreme Value Theory in order to analyse a set of tree ring widths data from nine trees growing in Nottinghamshire. Initially, we start by exploring the data through a variety of descriptive statistical approaches. Transforming data is important at this stage to find out any problem in modelling algorithm. We then use algorithm tuning and ensemble methods to improve the k-nearest neighbors (KNN) algorithm. A comparison between the developed method in this study ad other methods are applied. Also, extreme value of the dataset will be more investigated. The results of the analysis study show that the ML algorithms in the Random Forest method would give accurate results in the analysis of tree ring widths data from nine trees growing in Nottinghamshire with the lowest Root Mean Square Error value. Also, we notice that as the assumed ARMA model parameters increased, the probability of selecting the true model also increased. In terms of the Extreme Value Theory, the Weibull distribution would be a good choice to model tree ring data.