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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.
 

Week

Topics

1.

Introduction & Overview; Review of Probability & Statistics – Parts 1 & 2

2.

 Introduction to Random Processes; Stationarity & Ergodicity

3.

Auto- and cross-correlation functions; Partial correlation functions

4.

Linear random processes; Auto-regressive, Moving average and ARMA models

5.

Models for non-stationary processes; Trends, heteroskedasticity and ARIMA models

6.

Fourier analysis of deterministic signals; DFT and periodogram

7.

Spectral densities and representations; Wiener-Khinchin theorem; Harmonic processes; SARIMA models

8.

Introduction to estimation theory; Goodness of estimators; Fisher’s information

9.

Properties of estimators; bias, variance, efficiency; C-R bound; consistency

10.

Least squares, WLS and non-linear LS estimators

11.

Maximum likelihood and Bayesian estimators.

12.

 Estimation of signal properties, time-series models; Case studies

Basics of probability and statistics; View MOOC videos on "Intro to Statistical Hypothesis Testing"


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