Time Series: Forecasting and Long Memory

This lecture by the instructor covers the concepts of forecasting in time series analysis, focusing on ARIMA models and the evaluation of forecasting performance. Additionally, it delves into the notion of long memory in time series processes, discussing the characteristics of long-memory processes and their relation to self-similarity. The lecture explores the fractional differencing process, the spectral behavior of long-memory processes, and the estimation of long-memory parameters. Furthermore, it introduces ARCH models, explaining their application in capturing changes in volatility and modeling outlier behavior in financial time series. The lecture concludes with a detailed explanation of how to estimate ARCH models using conditional likelihood.