Syllabus  |   Lectures  |   Downloads  |   FAQ  |   Ask a question  |  
Course Co-ordinated by IIT Madras
Coordinators
 

 

Download Syllabus in PDF format



Untitled Document

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 of the methods in R are illustrated throughout.nsport rates in chemical processes, and gives rise to many of the empirical correlations used in chemical engineering design.

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 representations of random processes; Wiener-Khinchin theorem; Harmonic processes and SARIMA models

8

Introduction to estimation theory; Goodness of estimators; Fisher 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
Time-Series Analysis with Applications in R by Shumway and Stoffer;
Introduction to Time-Series and Forecasting by Brockwell and Davis;
Principles of System Identification, Theory and Practice by Arun K. Tangirala


Important: Please enable javascript in your browser and download Adobe Flash player to view this site
Site Maintained by Web Studio, IIT Madras. Contact Webmaster: nptel@iitm.ac.in