About this course: Welcome to Practical Time Series Analysis! Many of us are "accidental" data analysts. We trained in the sciences, business, or engineering and then found ourselves confronted with data for which we have no formal analytic training. This course is designed for people with some technical competencies who would like more than a "cookbook" approach, but who still need to concentrate on the routine sorts of presentation and analysis that deepen the understanding of our professional topics. In practical Time Series Analysis we look at data sets that represent sequential information, such as stock prices, annual rainfall, sunspot activity, the price of agricultural products, and more. We look at several mathematical models that might be used to describe the processes which generate these types of data. We also look at graphical representations that provide insights into our data. Finally, we also learn how to make forecasts that say intelligent things about what we might expect in the future. Please take a few minutes to explore the course site. You will find video lectures with supporting written materials as well as quizzes to help emphasize important points. The language for the course is R, a free implementation of the S language. It is a professional environment and fairly easy to learn. You can discuss material from the course with your fellow learners. Please take a moment to introduce yourself! Time Series Analysis can take effort to learn- we have tried to present those ideas that are "mission critical" in a way where you understand enough of the math to fell satisfied while also being immediately productive. We hope you enjoy the class!
Created by: The State University of New York
Taught by: Tural Sadigov, Lecturer
Applied Mathematics
Taught by: William Thistleton, Associate Professor
Applied Mathematics
| Level | Intermediate |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
WEEK 1: Basic Statistics
During this first week, we show how to download and install R on Windows and the Mac. We review those basics of inferential and descriptive statistics that you'll need during the course.
12 videos, 4 readings
- Video: Course Introduction
- Video: Week 1 Welcome Video
- Reading: Welcome to Week 1
- Reading: Getting Started with R
- Video: Getting Started in R: Download and Install R on Windows
- Video: Getting Started in R: Download and Install R on Mac
- Video: Getting Started in R: Using Packages
- Notebook: Codes for Concatenation, Five-number summary, Standard Deviation
- Video: Concatenation, Five-number summary, Standard Deviation
- Notebook: Codes for Histogram
- Video: Histogram in R
- Notebook: Codes for Scatterplot
- Video: Scatterplot in R
- Reading: Basic Statistics Review (with linear regression and hypothesis testing)
- Video: Review of Basic Statistics I - Simple Linear Regression
- Video: Reviewing Basic Statistics II More Linear Regression
- Video: Reviewing Basic Statistics III - Inference
- Reading: Measuring Linear Association with the Correlation Function
- Video: Reviewing Basic Statistics IV
Graded: Visualization
Graded: Basic Statistics Review
WEEK 2
Week 2: Visualizing Time Series, and Beginning to Model Time Series
In this week, we begin to explore and visualize time series available as acquired data sets. We also take our first steps on developing the mathematical models needed to analyze time series data.
10 videos, 1 reading
- Video: Week 2 Welcome Video
- Reading: All slides together for the next two lessons
- Video: Introduction
- Video: Time plots
- Video: First Intuitions on (Weak) Stationarity
- Video: Autocovariance function
- Video: Autocovariance coefficients
- Video: Autocorrelation Function (ACF)
- Video: Random Walk
- Video: Introduction to Moving Average Processes
- Notebook: Simulating MA(2) process - codes for the next video lecture
- Video: Simulating MA(2) process
Graded: Noise Versus Signal
Graded: Random Walk vs Purely Random Process
Graded: Time plots, Stationarity, ACV, ACF, Random Walk and MA processes
WEEK 3
Week 3: Stationarity, MA(q) and AR(p) processes
In Week 3, we introduce few important notions in time series analysis: Stationarity, Backward shift operator, Invertibility, and Duality. We begin to explore Autoregressive processes and Yule-Walker equations.
13 videos, 7 readings
- Video: Week 3 Welcome Video
- Reading: Stationarity - Examples -White Noise, Random Walks, and Moving Averages
- Reading: Stationarity - Intuition and Definition
- Reading: Stationarity - ACF of a Moving Average
- Video: Stationarity - Intuition and Definition
- Video: Stationarity - First Examples...White Noise and Random Walks
- Video: Stationarity - First Examples...ACF of Moving Average
- Reading: All slides together for lesson 2 and 4
- Video: Series and Series Representation
- Video: Backward shift operator
- Video: Introduction to Invertibility
- Video: Duality
- Video: Mean Square Convergence (Optional)
- Reading: Autoregressive Processes- Definition and First Examples
- Video: Autoregressive Processes - Definition, Simulation, and First Examples
- Reading: Autoregressive Processes - Backshift Operator and the ACF
- Video: Autoregressive Processes - Backshift Operator and the ACF
- Video: Difference equations
- Video: Yule - Walker equations
- Reading: Yule - Walker equations - Slides
Graded: Stationarity
Graded: Series, Backward Shift Operator, Invertibility and Duality
Graded: AR(p) and the ACF
Graded: Difference equations and Yule-Walker equations
WEEK 4
Week 4: AR(p) processes, Yule-Walker equations, PACF
In this week, partial autocorrelation is introduced. We work more on Yule-Walker equations, and apply what we have learned so far to few real-world datasets.
8 videos, 3 readings
- Video: Week 4 Welcome Video
- Reading: Partial Autocorrelation and the PACF First Examples
- Video: Partial Autocorrelation and the PACF First Examples
- Reading: Partial Autocorrelation and the PACF: Concept Development
- Video: Partial Autocorrelation and the PACF - Concept Development
- Reading: All slides together for the next two lessons
- Video: Yule-Walker Equations in Matrix Form
- Notebook: AR(2) Simulation (Parameter Estimation)
- Video: Yule Walker Estimation - AR(2) Simulation
- Notebook: AR(3) Simulation (Parameter Estimation)
- Video: Yule Walker Estimation - AR(3) Simulation
- Notebook: Recruitment - model fitting
- Video: Recruitment data - model fitting
- Notebook: Johnson & Johnson-model fitting
- Video: Johnson & Johnson-model fitting
Graded: Partial Autocorrelation
Graded: Yule-Walker in matrix form and Yule-Walker estimation
Graded: 'LakeHuron' dataset
WEEK 5
Week 5: Akaike Information Criterion (AIC), Mixed Models, Integrated Models
In Week 5, we start working with Akaike Information criterion as a tool to judge our models, introduce mixed models such as ARMA, ARIMA and model few real-world datasets.
7 videos, 6 readings
- Video: Week 5 Welcome Video
- Reading: Akaike Information Criterion and Model Quality
- Video: Akaike Information Criterion and Model Quality
- Reading: ARMA Models and a Little Theory
- Video: ARMA Models (And a Little Theory)
- Reading: ARMA Properties and Examples
- Video: ARMA Properties and Examples
- Reading: All slides together for this lesson
- Video: ARIMA Processes
- Notebook: ARIMA(2,1,1) Simulation
- Video: Q-Statistic
- Video: Daily births in California in 1959
- Reading: Daily birth dataset
- Notebook: Daily birth - R code
- Reading: Daily female birth (R file)
Graded: AIC and model building
Graded: ARMA Processes
Graded: ARIMA and Q-statistic
Graded: 'BJsales' dataset
WEEK 6
Week 6: Seasonality, SARIMA, Forecasting
In the last week of our course, another model is introduced: SARIMA. We fit SARIMA models to various datasets and start forecasting.
10 videos, 6 readings
- Video: Week 6 Welcome Video
- Reading: All slides together for the next two lessons
- Video: SARIMA processes
- Video: ACF of SARIMA models
- Reading: SARIMA simulation (code block)
- Video: SARIMA fitting: Johnson & Johnson
- Reading: SARIMA code for J&J (code block)
- Video: SARIMA fitting: Milk production
- Notebook: SARIMA code for Milk production
- Video: SARIMA fitting: Sales at a souvenir shop
- Notebook: SARIMA code for Sales at a souvenir shop
- Reading: Forecasting using Simple Exponential Smoothing
- Video: Forecasting Using Simple Exponential Smoothing
- Reading: Forecasting Using Holt Winters for Trend (Double Exponential)
- Video: Double Exponential Smoothing
- Reading: Forecasting Using Holt Winters for Trend and Seasonality (Triple Exponential)
- Video: Triple Exponential Smoothing Concept Development
- Video: Triple Exponential Smoothing Implementation
Graded: SARIMA processes
Graded: 'USAccDeaths' dataset
Graded: Forecasting
FAQs
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Ratings and Reviews
Well built class. I especially enjoyed the inclusion of written material, which I find easier, faster and more enjoyable than videos usually. The material itself is well constructed and the professors are clear. The low point for me comes with the intended audience of the class. At first glance, it is directed toward professionals that have already some familiarity with time series. While I could follow the course independently, I had to rely on other resources to gain intuitions on the concepts. I still don't consider that I could explain the material that I learned as well as I wish I would.
Excellent course ! Great instructors !....Especially Dr Sadigov... Will prove very useful to me to analyze and forecast medical and public health time series :-)
Very nice and pedagogical introduction to time series analysis. By the end of the course you feel like you know how to analyse and model time series.
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DP
I think I need support on the very last week, namely, week 6, on the very first quiz. I don't understand the answers on how they were derived but I was able to get the answers by repeating the quiz.