This course provides an introduction to time series analysis with an emphasis on mathematical understanding and its software implementation. Programming uses Python, R, or Julia. Covered topics include the following. Modeling time series, trend, seasonality and residual process. Autocovariance function, multivariate time series, moving average and autoregression. Stationary processes, linear processes, linear filtering. Confidence intervals for the mean and the autocorrelation, hypothesis tests for a time series model. ARMA models, partial autocorrelation function, parameter estimation methods, forecasting, model selection. Stationary processes in the frequency domain, spectral density, periodogram, smoothing, spectral window. Nonstationary time series, ARIMA models. State-space representation, Kalman recursions. Recurrent neural networks as time allows. Prerequisite: MATH 290 or MATH 291, and MATH 526 or MATH 628.