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Time Series Analysis
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
Students will able to
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Course |
Learning outcomes (at course level |
Learning and teaching strategies |
Assessment Strategies
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Paper Code |
Paper Title |
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STT-422(C) |
Time Series Analysis |
CO 109: Define time series components and their uses
CO 110: Predict the time series data using different stationary time series data.
CO 111: Construct stationary time series models, nonlinear stochastic models and their applications
CO 112: Demonstrate their ability to apply statistics in other fields at an appropriate level
CO 113: Demonstrate their ability to apply knowledge acquired from their major to real world models.
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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 |
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.
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 (withoutproof) 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
Spectral analysis of weakly stationary process, peridogram and correlogram analyses, computations based on Fourier transform. Forecasting: Exponential and adaptive Smoothing methods
Multivariate Liner 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.
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.
● 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:
· https://epgp.inflibnet.ac.in/
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
· Stochastic Modeling and Applications, MUK Publications and Distributions
