Forecasting of Climate With The Help of Time Series Analysis

Abstract - The aim of analysis of time series plot and calculation of range of attractor is to gain a future insight of climate which is depend on the atmospheric temperature. We are interested in attractors of the solution to predict the future behavior of the system. We analyzed both stochastic and chaotic behavior of the time series data. For stochastic behavior we applied, ARIMA and for chaotic behavior we evaluated Lyapunov exponent. Lyapunov exponent decides rate of divergence of nearby trajectories in state space. A positive value of Lyapunov exponent calculated from time series data of a single variable is an evidence of presence of chaos. One of the simplest routs to chaos is the logistic map equation, x_(n+1)=μx_n (1−x_n). In this equation a single past value of the variable decides its next future value and every future value is decided by iteration. μ is called control parameter, which encompasses other conditions influencing the variable. Keywords - Logistic Map, Attractors, Lyapunov Exponent, Time Series Plot