Overview

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This course introduces basic time series analysis and forecasting methods. Topics include stationary processes, ARMA models, modeling and forecasting using ARMA models, nonstationary and seasonal time series models, state-space models, and forecasting techniques. By the end of this course, students will be able to: - Describe important time series models and their applications in various fields. - Formulate real life problems using time series models. - Use statistical software to estimate models from real data and draw conclusions and develop solutions from the estimated models. - Use visual and numerical diagnostics to assess the soundness of their models. - Communicate the statistical analyses of substantial data sets through explanatory text, tables, and graphs. - Combine and adapt different statistical models to analyze larger and more complex data.

Syllabus

Module 1: Course Introduction and Intuition for Stationarity

Welcome to Introduction to Time Series! In this module we'll define time series and time series models, and we'll develop some intuition for the fundamental concept of stationarity, and why it's useful.

Module 2: Basic Analysis of Stationary Processes

In this module, we'll discuss stationarity in more detail. We'll learn the technical definitions of weak and strong stationarity, and explain why the weaker version is more practical to use. We'll discuss the autocovariance and autocorrelation functions for stationary processes---concepts that will be with us for the rest of the course. And finally, we'll see some examples of ARMA processes, which we'll treat more deeply in the coming modules.

Module 3: ARMA processes and their Autocorrelation Functions

In this module, we'll focus on ARMA processes, and what is arguably their most important feature, namely their autocorrelation structure. We'll see how to compute these "from scratch" (with a little help from R for the computations), and look at plots of the autocorrelation function (ACF) to get some intuition for how the ACF of an ARMA process behaves and what it can tell us.

Module 4: More About the ACF; Best Linear Predictors, Autocorrelation, and Partial Autocorrelation

In this module, we begin by discussing the ACF's of more complicated ARMA processes. Our main focus, though, is on one-step-ahead forecasts. We learn about the best linear predictor: both how it is defined and how to use it. Finally, we use what we have learned in order to define the Partial Autocorrelation Function (PACF), which is another fundamental tool in the study of stationary processes.

Module 5: Fitting Data to ARMA models

In this module, we learn about fitting a stationary time series model to data. The fitting process involves determining what values of the parameters to use. We discuss preliminary estimation and maximum likelihood estimation of these parameters.

Module 6: Diagnostics and Order Selection

In this module, we discuss model diagnostics and order selection. Given an ARMA order, we've already seen how to best fit the parameters of the associated model. Given several different fitted models, the tools we develop in this module will allow us to make an intelligent choice about which one to use.

Module 7: Nonstationary processes: ARIMA and SARIMA Models

This module introduces students to ARIMA and SARIMA modeling techniques, essential for analyzing non-stationary and seasonal time series data. In the first lesson, students will learn to define ARIMA processes, use the Dickey-Fuller test to determine the need for differencing, and fit ARIMA models using R. The second lesson extends these skills to SARIMA models, focusing on identifying seasonality and fitting these models to capture seasonal patterns in data.

Module 8: More on Forecasting

This module equips students with more sophisticated forecasting techniques beyond one-step-ahead predictions. We treat both (S)ARIMA models and exponential smoothing models and show how to handle forecasts in R. For the simplest of these models, we look inside the "black box" a little bit and demonstrate how these forecasts are generated.

Summative Course Assessment

This module contains the summative course assessment that has been designed to evaluate your understanding of the course material and assess your ability to apply the knowledge you have acquired throughout the course.