Applied Time-Series Analysis

Overview

The course introduces the concepts and methods of time-series analysis. Specifically, the topics include (i) stationarity and ergodicity (ii) auto-, cross- and partial-correlation functions (iii) linear random processes - definitions (iv) auto-regressive, moving average, ARIMA and seasonal ARIMA models (v) spectral (Fourier) analysis and periodicity detection and (vi) parameter estimation concepts and methods. Practical implementations in R are illustrated at each stage of the course.The subject of time-series analysis is of fundamental interest to data analysts in all fields of engineering, econometrics, climatology, humanities and medicine. Only few universities across the globe include this course on this topic despite its importance. This subject is foundational to all researchers interested in modelling uncertainties, developing models from data and multivariate data analysis.INTENDED AUDIENCE : Students, researchers and practitioners of data analysis from all disciplines of engineering, economics, humanities and medicinePREREQUISITES : Basics of probability and statistics; View MOOC videos on "Intro to Statistical Hypothesis Testing"INDUSTRIES SUPPORT: Gramener, Honeywell, ABB, GyanData, GE, Ford, Siemens, and all companies that work on Data Analytics

Syllabus

Week 1: Introduction & Overview; Review of Probability & Statistics – Parts 1 & 2Week 2: Introduction to Random Processes; Stationarity & ErgodicityWeek 3: Auto- and cross-correlation functions; Partial correlation functionsWeek 4: Linear random processes; Auto-regressive, Moving average and ARMA modelsWeek 5: Models for non-stationary processes; Trends, heteroskedasticity and ARIMA modelsWeek 6: Fourier analysis of deterministic signals; DFT and periodogramWeek 7: Spectral densities and representations; Wiener-Khinchin theorem; Harmonic processes; SARIMA modelsWeek 8: Introduction to estimation theory; Goodness of estimators; Fisher’s informationWeek 9: Properties of estimators; bias, variance, efficiency; C-R bound; consistencyWeek 10: Least squares, WLS and non-linear LS estimatorsWeek 11: Maximum likelihood and Bayesian estimators.Week 12: Estimation of signal properties, time-series models; Case studies