Time Series: Stochastic Properties and Modelling

This lecture covers the stochastic properties of time series, defining them as sets of observations recorded at different times. It delves into autocovariance functions, stationarity concepts, and special classes of stochastic processes like moving average and autoregressive processes. The lecture also explores harmonic processes, trends in observed signals, spectral density, and digital filters. Estimation methods for mean, spectral density, and autoregressive processes are discussed, along with forecasting techniques for ARMA models. The lecture concludes with long-memory covariance models, ARCH models, parameter estimation, state space models, Kalman filter, and multivariate time series modelling.