Course

Unit I

Time series, components of time series, additive and multiplicative models, determination of trend, analysis of seasonal fluctuations

Unit II

Test for trend and seasonality, exponential and moving average smoothing, holt-winter smoothing, forecasting based on smoothing.

Unit III

Time series as a discrete parameter stochastic process, auto covariance and auto correlation functions and their properties, stationary processes, test for stationarity, unit root test, stationary processes in the frequency domain, spectral analysis of time series.

Unit IV

Detailed study of the stationary processes: moving average (MA), autoregressive (AR), autoregressive moving average (ARMA) and autoregressive integrated moving average(ARIMA) models.

Unit V

Estimation of ARMA models, maximum likelihood method (the likelihood function for a Gaussian AR(1) and a Gaussian MA(1)) and Least squares, Yule-Walker estimation for AR Processes, choice of AR and MA periods, forecasting, residual analysis and diagnostic checking.

Course Outcomes
CO1: To gain knowledge about pattern classification and dimensionality reduction method
CO2: To understand the use of Maximum-likelihood and Bayesian Parameter Estimation
CO3: To understand and apply Nonparametric Techniques and Linear Discriminant Functions
CO4: To apply Nonmetric methods and Algorithm-independent Machine Learning
CO5: To implement clustering methods under unsupervised learning

1. Peter J Brockwell and Richard A Davis, Introduction to Time Series and Forecasting, Springer 2002
2. Anderson, T.W. The Statistical Analysis of Time Series, John Wiley, New York, 1971
3. Box, G.E.P. and Jenkins, G.M. Time Series Analysis– Forecasting and Control, Holden-day, San Francisco,1976.
4. Kendall, Sir Maurice and Ord, J.K., Time Series, Edward Arnold, London, 1990.