Time Series Analysis

Paper Code: 
24STT422(B)
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This paper is design to help the students in the field of forecasting and monitoring the data points by applying suitable model to time series data

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT422(B)

Time Series Analysis

(Theory)

CO 124: Identify and estimate time series components and outline their applications.

CO 125: Examine appropriate models based on data characteristics and apply them to fit time series data accurately.

CO 126: Demonstrate the ability to apply knowledge related to random component methods and forecasting methods to real world models.

CO 127: Apply various time series tools on multivariate data.

CO 128: Analyze and interpret ARCH, GARCH and nonlinear time series models.

CO 129: Contribute effectively in course-specific interaction.

Approach in teaching: 

Interactive Lectures, 

Group Discussion, 

Classroom Assignment,

Problem Solving Sessions.

 

Learning activities for the students:

Assignments,

Seminar,

Presentation,

Subject based  Activities.

Classroom Quiz,

Assignments,

Class Test,

Individual Presentation.

 

15.00
Unit I: 
Introduction to Time Series Analysis

Definition and its different components, additive and multiplicative models. Different methods of determining trend and seasonal and cyclic fluctuations, their merits and demerits. Time series as discrete parameter stochastic process, auto-covariance and auto-correlation functions and, their properties.

 

15.00
Unit II: 
Stationary Processes and ARIMA Models

Detailed study of the stationary processes: (i) moving average (MA), (ii) auto-regressive (AR),(iii) ARMA, and, (iv) AR integrated MA (ARIMA) models. Box-Jenkins models. Discussion (without proof) of estimation of mean, auto-covariance and auto-correlation functions under large sample theory. Choice of AR and MA orders. Estimation of ARIMA model parameters.

 

15.00
Unit III: 
Spectral Analysis and Forecasting Methods

Spectral analysis of weakly stationary process, peridogram and correlogram analyses, computations based on Fourier transform. Forecasting: Exponential and adaptive Smoothing methods.

 

15.00
Unit IV: 
Multivariate Linear Time Series

Introduction, Cross covariance and correlation matrices, testing of zero cross correlation and model representation. Basic idea of Stationary vector Autoregressive Time Series with orders one: Model Structure, Granger Causality, stationary condition, Estimation, Model checking.

15.00
Unit V: 
Non-Linear Time Series Models and Volatility Modeling

Non-linear time series models, ARCH and GARCH Process, order identification, estimation and diagnostic tests and forecasting. Study of ARCH (1) properties. GARCH (Conception only) process for modelling volatility. 

 

 

Essential Readings: 
  • Box, G.E.P. and Jenkins, G.M. (1976): Time series analysis—Forecasting and Control, Holden-day, San Francisco.
  • Anderson, T.W. (1971): The Statistical Analysis of Time Series, Wiley, N.Y.
  • Montgemory, D.C. and Johnson, L.A. (1977): Forecasting and Time Series Analysis, McGraw Hill.
  • Kendall, Sir Maurice and Ord, J.K. (1990): Time Series (Third Edition), Edward Arnold.

 

SUGGESTED READINGS:

  • Brockwell, P.J. and Davis, R.A.: Time Series: Theory and Methods (Second Edition), Springer- Verlag.
  • Fuller, W.A. (1976): Introduction to Statistical Time Series, John Wiley, N.Y.
  • Granger, C.W.J. and Newbold (1984): Forecasting Econometric Time Series, Third Edition, Academic Press.
  • Priestley, M.B. (1981): Spectral Analysis & Time Series, Griffin, London.
  • Kendall, M.G. and Stuart A. (1966): The Advanced Theory of Statistics, Volume 3, Charles Griffin, London.
  • Bloomfield, P. (1976): Fourier Analysis of Time Series—An Introduction, Wiley.
  • Granger, C.W.J. and Hatanka, M. (1964): Spectral Analysis of Economic Time Series, Princeton Univ. Press, N.J.
  • Koopmans, L.H. (1974). The spectral Analysis of Time Series, Academic Press.
  • Nelson, C.R. (1973): Applied Time Series for Managerial Forecasting, Holden-Day.
  • Findley, D.F. (Ed.) (1981): Applied Time Series Analysis II, Academic Press.

 

e-RESOURCES:

 

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications

 

Academic Year: 
2024-2025
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