Course: (DS4233/DS6233) Time Series Analysis
Instructor’s Office: 406 (available during 4-14 January, 2023) 449 (available during 10-22 April, 2023)
Timings: Saturdays 2:00pm - 4:00pm, with a short break.
TA Sessions: Fridays 5:30pm - 6:30pm; Ajit Mahata (IISER Pune : Discussion room 35) , Shashank Roy (ICTS-TIFR Bengaluru : Google Meet link).
Course meeting venue: LHC 107 Google Meet link
Syllabus: Stationarity, White Noise, Auto-correlations, Seasonality; Tests for stationarity, Auto Regression (AR), Moving Average (MA); ARIMA, ARIMAX, SARIMA models; Exponential Smoothing; G/ARCH models; Anamoly detection, Multivariate Time Series Models, Neural Network Models. Further topics (will be covered depending on the time): Hidden Markov Models, Kalman Filtering, Spectral Analysis, Granger Causality, Functional Time Series.
Prerequisites: Familiarity with the following concepts is expected. Calculus, Statistics (Linear Regression, Estimation, MLE, Hypothesis Testing), Probability (Random Variables, Properties of normal distribution and other named distributions.) Coding (any language or software, preferably R/Python, should be able to implement concepts on the own).
Grading: Continuous assessment (50%, includes assignments, class tests and mid-semester examination), End semester(50%)
References and Resources:
- Introduction to Time Series Analysis by P.J. Brockwell and R.A. Davis
- Time Series Analysis and Its Applications by R.H. Shumway and D.S. Stoffer
- Time Series Analysis: Forecasting and Control by G.E.P. Box, G.M. Jenkins and G.C. Reinsel
- Forecasting: Principles and Practice by R. J. Hyndman and G. Athanasopoulos Available online
Classroom Scribes
| Lecture | Date | Contents | Supplementary material |
|---|---|---|---|
| 1 | 7 January 2023 | Introduction, Examples | Jupyter Notebook for exploratory data analysis. Corresponding data file. |
| 2 | 7 January 2023 | Review: Linear regression | |
| 3 | 14 January 2023 | Multivariate Gaussian distribution | Properties of Gaussian random variables (From a lecture notes by Manjunath Krishnapur ) |
| 4 | 14 January 2023 | White noise, Stationarity | Class Test-I on 20-Jan |
| 5 | 21 January 2023 | Auto-regressive (AR) processes and Moving average (MA) processes | |
| 6 | 21 January 2023 | Auto-correlations, Partial auto-correlations | |
| 7 | 28 January 2023 | Lag operator, Invertibility and Integrated Processes | Class Test-II on 3-Feb |
| 8 | 28 January 2023 | Properties of ARMA processes | |
| 9 | 4 February 2023 | Makeup lecture | Class Test-III on 10-Feb |
| 10 | 4 February 2023 | Makeup lecture | |
| 11 | 11 February 2023 | Computing ACF and PACF | |
| 12 | 11 February 2023 | Computing ACF and PACF | |
| 24 February 2023 | Mid Semester | ||
| 13 | 25 February 2023 | Tests for White noise | |
| 14 | 25 February 2023 | Tests for White noise | |
| 15 | 4 March 2023 | Makeup lecture | |
| 16 | 4 March 2023 | Makeup lecture | |
| 17 | 11 March 2023 | Smoothing | |
| 18 | 11 March 2023 | Forecasting | |
| 19 | 18 March 2023 | (G)ARCH models | |
| 20 | 18 March 2023 | (G)ARCH models | Refer Section 4.3 in Quantitative Risk Management: Concepts, Techniques and Tools by Alexander J. McNeil, Rüdiger Frey, and Paul Embrechts |
| 21 | 1 April 2023 | Makeup Lecture | |
| 22 | 1 April 2023 | Functional forms | |
| 23 | 8 April 2023 | Multivariate time series | |
| 24 | 8 April 2023 | Vector Autoregression (VAR) models | Refer Section 2.1 in New introduction to multiple time series analysis by Helmut Lütkepohl |
| 25 | 15 April 2023 | Project Presentations | |
| 26 | 15 April 2023 | Project Presentations | |
| 21 April 2023 | End Semester |
| Problem Sets: | Set-1 | Set-2 | Set-3 | Set-4 | Set-5 |