1. Time series as a discrete parameter stochastic process, Auto - Covariance, Auto-correlation functions and their properties. Exploratory time series analysis, Test for trend and seasonality, Exponential and moving average smoothing, Holt – Winter smoothing, forecasting based on smoothing. (12 L + 3 T)
2. Wold representation of linear stationary processes, detailed study of the linear time series models: Autoregressive, Moving Average, Autoregressive Moving Average models. Concept of Causality, invertibility, computation of -weights and ψ- weights, computation of ACVF and ACF. Partial auto covariance function. Autoregressive Integrated Moving Average models. (12 L + 3 T)
3. Estimation of ARMA models: Yule-Walker estimation for AR Processes, Maximum likelihood and least squares estimation for ARMA Processes, Discussion (without proof) of estimation of mean, Auto-covariance and auto-correlation function under large samples theory, Residual analysis and diagnostic checking. Forecasting using ARIMA models. (12 L + 3 T)
4. Analysis of seasonal models: parsimonious models for seasonal time series, General multiplicative seasonal models, forecasting, identification, estimation and diagnosis methods for seasonal time series. Spectral analysis of weakly stationary process. Periodogram and correlogram analysis. Introduction to ARCH and GARCH models. (12 L + 3 T)
- Teacher: Hemangi Kulkarni Stats