STAT 510 | Applied Time Series Analysis

About this course

Welcome to the course notes for STAT 501: Regression Methods. These notes are designed and developed by Penn State’s Department of Statistics and offered as open educational resources. These notes are free to use under Creative Commons license CC BY-NC 4.0.

This course is part of the Online Master of Applied Statistics program offered by Penn State’s World Campus.

Ready to enroll?

Currently enrolled?

If you are a current student in this course, please see Canvas for your syllabus, assignments, lesson videos, and communication from your instructor.

Course Overview

The objective of this course is to learn and apply statistical methods for the analysis of data that have been observed over time. Our challenge in this course is to account for the correlation between measurements that are close in time. Topics covered in this course include methods for:

Modeling univariate time series data with Autoregressive and Moving Average Models (denoted as ARIMA models, sometimes called Box Jenkins models).
Tools for model identification, model estimation, and assessment of the suitability of the model.
Using a model for forecasting and determining prediction intervals for forecasts.
Smoothing methods and trend/seasonal decomposition methods. Smoothing methods include moving averages, exponential smoothing, and Lowess smoothers.
Relationships between time series variables, cross correlation, lagged regression models
Intervention Analysis (basically before/after analysis of a time series to assess effect of a new policy, treatment, etc.)
Longitudinal Analysis and Repeated Measures Models for comparing treatments when the response is a time series.
Vector Autoregressive Models for Multivariate Time Series
ARCH Models for changing variation and periods of volatility in a series
Analyzing the frequency domain - Periodograms, Spectral Density, Identifying the important periodic components of a series.

We will need to use a statistical software program to analyze time series data. The course assignments and notes include R code to analyze our data. If you are unfamiliar with R (or need to brush up), please take some time to follow through the following introduction: STAT Online: Introduction to R

Contributors

This is the STAT 510 online course materials website. There are lots of examples, notes, and lecture materials on this website. You may want to make a bookmark for this site in your browser.

Featured on this site are the online notes created and maintained by Dr. Megan Romer.

Resources

Lessons

Time Series Basics

5/15/25

MA Models, Partial Autocorrelation, Notational Conventions

5/15/25

Identifying and Estimating ARIMA models; Using ARIMA models to forecast future values

R Code

ARIMA

Statistical significance

p-value

Forecasting

5/15/25

Seasonal Models

Seasonal ARIMA

Differencing

Seasonal models

5/15/25

Smoothing and Decomposition Methods and More Practice with ARIMA Models

Smoothing

Decomposition

R code

5/15/25

The Periodogram

Periodogram

Period

Frequency

5/15/25

Exam Week

5/15/25

Regression with ARIMA errors, Cross correlation functions, and Relationships between 2 Time Series

Regression

Linear Regression

R code

5/15/25

Prewhitening; Intervention Analysis

Prewhitening

R code

Intervention analysis

5/15/25

Longitudinal Analysis/ Repeated Measures

Longitudinal analysis

Repeated measures

Generalized Least Squares

R Code

5/15/25

Vector Autoregressive Models/ ARCH Models

Vector Autoregressive Models

ARCH/GARCH Models

Trend-stationary

Stationary

5/15/25

Spectral Analysis

Spectral analysis

Spectral density

R Code

5/15/25

Fractional Differencing and Threshold Models

5/15/25

--- title-block-banner: fiveten_banner.png title-block-banner-color: light titlegraphic: fiveten_banner.png listing: id: lessons categories: cloud contents: - Lesson01.qmd - Lesson02.qmd - Lesson03.qmd - Lesson04.qmd - Lesson05.qmd - Lesson06.qmd - Lesson07.qmd - Lesson08.qmd - Lesson09.qmd - Lesson10.qmd - Lesson11.qmd - Lesson12.qmd - Lesson13.qmd type: grid grid-columns: 4 grid-item-align: center fields: [image,title, categories, file-modified] field-display-names: title: "Lessons" file-modified: "Updated:" date-format: short sort: "filename" --- ## About this course {.unnumbered} Welcome to the course notes for STAT 501: Regression Methods. These notes are designed and developed by [Penn State's Department of Statistics](https://science.psu.edu/stat) and offered as open educational resources. These notes are free to use under Creative Commons license [CC BY-NC 4.0](https://creativecommons.org/licenses/by-nc/4.0/). This course is part of the Online Master of Applied Statistics program offered by Penn State's World Campus. <center><a href="https://www.worldcampus.psu.edu/register-or-schedule-courses" class="btn btn-primary btn-lg active" role="button" aria-pressed="true">Ready to enroll?</a></center> ::: {.border-start .border-success .ms-3 .ps-2 } ### Currently enrolled? If you are a current student in this course, please see [Canvas](https://psu.instructure.com/) for your syllabus, assignments, lesson videos, and communication from your instructor. ::: ## Course Overview ![](assets/graph_56.gif){ fig-alt="Time series waves" .float-sm-end .w-50 .ps-3 } The objective of this course is to learn and apply statistical methods for the analysis of data that have been observed over time. Our challenge in this course is to account for the correlation between measurements that are close in time. Topics covered in this course include methods for: * Modeling univariate time series data with Autoregressive and Moving Average Models (denoted as ARIMA models, sometimes called Box Jenkins models). * Tools for model identification, model estimation, and assessment of the suitability of the model. * Using a model for forecasting and determining prediction intervals for forecasts. * Smoothing methods and trend/seasonal decomposition methods. Smoothing methods include moving averages, exponential smoothing, and Lowess smoothers. * Relationships between time series variables, cross correlation, lagged regression models * Intervention Analysis (basically before/after analysis of a time series to assess effect of a new policy, treatment, etc.) * Longitudinal Analysis and Repeated Measures Models for comparing treatments when the response is a time series. * Vector Autoregressive Models for Multivariate Time Series * ARCH Models for changing variation and periods of volatility in a series * Analyzing the frequency domain - Periodograms, Spectral Density, Identifying the important periodic components of a series. We will need to use a statistical software program to analyze time series data. The course assignments and notes include R code to analyze our data. If you are unfamiliar with R (or need to brush up), please take some time to follow through the following introduction: [STAT Online: Introduction to R](https://online.stat.psu.edu/statprogram/tutorials/statistical-software/r) ### Contributors This is the STAT 510 online course materials website. There are lots of examples, notes, and lecture materials on this website. You may want to make a bookmark for this site in your browser. Featured on this site are the online notes created and maintained by Dr. Megan Romer. ### Resources * [Introduction to R](https://online.stat.psu.edu/statprogram/tutorials/statistical-software/r) * [Learning Online Orientation](https://online.stat.psu.edu/statprogram/orientation) ## Lessons

Categories

About this course

Currently enrolled?

Course Overview

Contributors

Resources

Lessons

Time Series Basics

MA Models, Partial Autocorrelation, Notational Conventions

Identifying and Estimating ARIMA models; Using ARIMA models to forecast future values

Seasonal Models

Smoothing and Decomposition Methods and More Practice with ARIMA Models

The Periodogram

Exam Week

Regression with ARIMA errors, Cross correlation functions, and Relationships between 2 Time Series

Prewhitening; Intervention Analysis

Longitudinal Analysis/ Repeated Measures

Vector Autoregressive Models/ ARCH Models

Spectral Analysis

Fractional Differencing and Threshold Models