Introductory Chapter: Time Series Analysis

Abstract

Time series, defined as sequentially observed data points over time [1], find applications across diverse domains such as economics and engineering. The statistical analysis of time series is crucial, and Chatfield's taxonomy identifies six main categories: Economic and Financial Time Series, Physical Time Series, Marketing Time Series, Process Control Data, Binary Processes, and Point Processes.To effectively categorize time series, consideration of features like seasonality, trend, and outliers is essential [1]. Seasonality reflects recurring patterns over time intervals, while trend represents a systematic linear or nonlinear component. Outliers are observations distant from others, often indicating anomalies. The categorization and analysis of time series are pivotal for drawing meaningful inferences from the diverse structures encountered in engineering, science, sociology, and economics [2].The objectives of time series analysis encompass description, explanation, prediction, and control. Description involves plotting observations over time to reveal patterns, while explanation explores relationships between variables. Prediction focuses on forecasting future values, and control utilizes time series to enhance control over physical or economic systems.Possible applications span from land use-cover [3,4] and agriculture changes [5,6], tourism [7,8], socioeconomic vulnerability [9], epidemiology [10], and health [11]. This chapter delves into advanced approaches for time series analysis. Time series analysisTime Series Analysis (TSA) involves constructing predictive models that generate a target variable or label based on sequential observations across a defined period, that is, data that is time-dependent. The analysis of time series involves studying the relationships between variables that change over time [12].There are two types of time series: deterministic and stochastic. Deterministic time series can be predicted with certainty based on previous experience, while stochastic time series have random fluctuations [13]. Time series analysis is widely used in various fields such as economics, finance, and health research [12,14]. It helps in identifying patterns, forecasting future values, and understanding the underlying dynamics of the data [14][15][16]. As such, it has applications in various domains and is important for making inferences about the future based on past observations [12,13,15,17,18].