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Time/Room: WF 10am at APM 2402
Instructor: Dimitris Politis
Office hours: W 11:30-12:30pm and F 11:30-12 at APM 5701 or by appointment (email: dpolitis@ucsd.edu)
TA: Kejin Wu (email: kwu@ucsd.edu); office hours: M 2-3 PM at HSS 5053 and Tu 2-3 PM through Zoom ID 341 099 7409
Weak and strict stationarity of time series, i.e. stochastic processes in discrete time. Breakdowns of stationarity and remedies (differencing, trend estimation, etc.). Optimal (from the point of view of Mean Squared Error) one-step-ahead prediction and interpolation; connection with Hilbert space methods, e.g. orthogonal projection. Autoregressive (AR), Moving Average (MA), and Autoregressive-Moving Average (ARMA) models for stationary time series; causality, invertibility, and spectral density. Maximum Entropy models for time series, and Kolmogorov's formula for prediction error. Estimation of the ARMA parameters given data; determination of the ARMA model order using criteria such as the AIC and BIC. Nonparametric estimation of the mean, the autocovariance function, and the spectral density in the absence of model assumptions. Confidence intervals for the estimated quantities via asymptotic normality and/or bootstrap methods. Prerequisite: a basic statistics and probability course or instructor consent.
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