Statistical Methods for Discrete Response, Time Series, and Panel Data

3 units

Visualization techniques for cross-section and time series data / Key concepts in probability and mathematical statistics / Classical linear regression models / Variable transformation / Model specification / Causal inference / Instrumental variable estimation / Autoregressive (AR) models / Moving Average (MA) models / Autoregressive Moving Average (ARMA) models / Autoregressive Integrated Moving Average (ARIMA) models / Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models / Vector Autoregressive (VAR) models / Statistical forecasting / Regression with time series data

R / R libraries

Paul Laskowski and Jeffrey Yau

Classical linear regression and time series models are workhorses of modern statistics, with applications in nearly all areas of data science. This course takes a more advanced look at both classical linear and linear regression models, including techniques for studying causality, and introduces the fundamental techniques of time series modeling. Mathematical formulation of statistical models, assumptions underlying these models, the consequence when one or more of these assumptions are violated, and the potential remedies when assumptions are violated are emphasized throughout. Major topics include classical linear regression modeling, casual inference, identification strategies, and a class of time series models that are popular among industry professionals. The course emphasizes formulating, choosing, applying, and implementing statistical techniques to capture key patterns exhibited in data. All of the techniques introduced in this course come with real-world examples and R code that is explained in weekly sessions. Students who successfully complete this course will be able to decide what techniques are appropriate for a given question, and to make trade-offs between model complexity, ease of interpreting results, and timing implementation in real-world applications. As concepts in probability theory and mathematical statistics are used extensively; students should feel comfortable with the definition, manipulation, and application of these concepts in mathematical notations.

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