ESMA 710 Times Series Analysis Modeling and Prediction
This course will cover modeling and prediction of time series. The emphasis will be on the time domain, although the frequency domain will also be explored. The structure of the model will depend on the physical knowledge of the process, as well as the form of the observed data. Models that relate the present value of a series to past values and past prediction errors are called ARIMA models (Autoregressive Integrated Moving Average). Central problems are the properties of different models and their prediction ability, estimation of the model parameters, and the model's ability to accurately describe the data. Particular attention will be given to linear modeling of time series: meaning of linearity, autoregressive and moving average models and their statistical properties, likelihood estimation and residual analysis, forecasting and simulation. An integral part of the course is the use of a statistical or numerical software such as MATLAB or R for simulation, calculation, and implementation of time series analysis techniques.