Introduction: Review of various components of time series, plots and descriptive statistics, discrete-parameter stochastic processes-- strong and weak stationarity, autocovariance and autocorrelation.
Spectral Analysis and Different Processes: Spectral analysis of weakly stationary processes-- periodogram, fast Fourier transform; Moving average, autoregressive, autoregressive moving average (ARMA) and autoregressive integrated moving average processes (ARIMA); Box-Jenkins model, state-space model.
Forecasting and Model Selection: Linear filters, signal processing through filters, inference in ARMA and ARIMA models; Forecasting-- ARIMA and state-space models, Kalman filter; Model building-- residuals and diagnostic checking; Model selection-- strategies for missing data.
Time-frequency Analysis: Short-term Fourier transform, wavelets, data analysis with computer packages.
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