Advanced Time Series

Paper Code: 
25STT143(C)
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This paper is designed to introduce a variety of statistical models for time series and monitoring the data points by applying suitable linear and non-linear models to time series data.

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Unit I                                                                                                                          

Review of Linear Models: Model building in time series analysis. AR, MA, ARMA and ARIMA model and model building by Box-Jenkins approach. Stationarity and invertibility conditions, ARIMA(p,d,q) model, estimation of parameters for AR, MA, ARMA and ARIMA processes, identification of processes with ACF PACF, Model order estimation techniques-AIC, AICC, BIC, EDC, FPE and forecasting.

 

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Unit II                                                                                                                        

Forms of non-stationarity in time series, Unit root: Dickey-Fuller, augmented Dickey-Fuller and Phillips-Perron tests. Panel data models: Balance and unbalance panel data, estimation in random effect and fixed effect models. ARCH and GARCH processes and models with ARCH, GARCH errors.

 

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Unit III                                                                                                                      

Multivariate time series processes and their properties:  Vector autoregressive (VAR), vector moving average (VMA) and vector autoregressive moving average (VARMA) processes.

 

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Unit IV                                                                                                                       

Non Linear Time Series Models: Non-linear auto regression, Threshold principle and threshold models. Amplitude-dependent exponential autoregressive (EXPAR), fractional autoregressive (FAR), Product Autoregressive Model (PAR), random coefficient autoregressive (RCAR), discrete state space auto regressive bilinear (BL), non-linear moving average, autoregressive models with conditional heteroskedasticity (ARCH).

 

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Unit V                                                                                                                        

Non-linear Least Square Prediction: Non-linear least square prediction in non-linear autoregressive, nonlinear moving average, Bilinear and random coefficient autoregressive models.

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.
  • 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.

 

Academic Year: 
2025-2026
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