1. Semester: III/IV
2. Number of credits: 4

Preamble
This is a four credit course. The objective of this course is to impart the necessary econometric understanding required to model and forecast time series data. It emphasises empirical implementation strategies as well as theoretical understanding.  It is assumed that the student is familiar with basic concepts of statistical inference that are taught in the Statistical Foundations of Econometrics course. Empirical applications will emphasise the ability to write the relevant algorithms in R programming language.

Evaluation
The examination pattern will consist of four ten mark examinations (one for each module to be held after the completion of teaching of the respective module) and an end semester examination for sixty marks.

Module 1: Theoretical Foundations (12 Lectures)
Definition and special features of time series data-Introduction to complex numbers-AR(P) process- Random walks-Ergodicity, stationarity and covariance stationarity-Lag operators, eigenvalues and stationarity-Law of large numbers for serially dependent processes- martingale difference sequence- central limit theorem for martingale difference sequence (without proof)- distribution of OLS estimators for random walk processes- tests for Unit roots: ADF, KPSS, HEGY and Canova-Hansen.

Module 2: ARIMA models (12 lectures)
AR and  Invertible MA processes –autocorrelation and partial autocorrelation functions – Yule-Walker equation- Identification of ARMA models- Estimation of ARMA models – Diagnostic testing- Forecasting.

Module 3: Vector Auto Regression and Volatility (12 lectures)
Identification and Estimation  in  VAR models - Causality– Impulse Response Function- Variance Decomposition-Cointegration  in VAR models- ARCH and GARCH models – testing for ARCH effects- FGLS estimation of ARCH(1) – ARCH in mean, EGARCH models.

Module 4: Spectral Analysis (12 lectures)
Cyclical behaviour and periodicity- The spectral representation theorem- The spectral density- Periodogram and the discrete Fourier transform- parametric and non-parametric estimation of the spectrum – Cross spectrum - Bivariate Granger causality in the frequency domain.