Stat 556: Advanced Time Series Analysis

This is the note I am taking in class for Stat 556, the advanced time series analysis.

Lecture 02 (Jan 24, 2022)

Calculate the variance and convergence rates for autocorrelation sample estimator by central limit theorem. Introduce statistical tests for ACF.

Lecture 07 (Feb 07, 2022)

Introduction to MA model and conditional loglikelihood maximization method. Introdcution to ARMA model

Lecture 10 (Feb 14, 2022)

Spectral density as the Fourier transform of autocovariance, the sample version spectral representation theory and sample periodogram

Lecture 11 (Feb 16, 2022)

Spectral representation sample version proof. Variance decomposition into Fourier components. Estimate spectral density