This course is part of the Bayesian Statistics Specialization

Raquel Prado

2,371 already enrolled

Offered By

Bayesian Statistics SpecializationUniversity of California, Santa Cruz

About this Course

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This course for practicing and aspiring data scientists and statisticians. It is the fourth of a four-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, Techniques and Models, and Mixture models. 
Time series analysis is concerned with modeling the dependency among elements of a sequence of temporally related variables. To succeed in this course, you should be familiar with calculus-based probability, the principles of maximum likelihood estimation, and Bayesian inference. You will learn how to build models that can describe temporal dependencies and how to perform Bayesian inference and forecasting for the models. You will apply what you've learned with the open-source, freely available software R with sample databases. Your instructor Raquel Prado will take you from basic concepts for modeling temporally dependent data to implementation of specific classes of models

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Course 4 of 5 in the

Bayesian Statistics Specialization

Intermediate Level

Familiarity with calculus-based probability, the principles of maximum likelihood estimation, and Bayesian inference.

Approx. 22 hours to complete

English

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Skills you will gain

Bayesian Statistics
Forecasting
Dynamic Linear Modeling
Time Series
R Programming

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Course 4 of 5 in the

Bayesian Statistics Specialization

Intermediate Level

Familiarity with calculus-based probability, the principles of maximum likelihood estimation, and Bayesian inference.

Approx. 22 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Raquel Prado

Professor

Statistics

2,371 Learners

1 Course

Offered by

University of California, Santa Cruz

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Syllabus - What you will learn from this course

Week1

Week 1

6 hours to complete

Week 1: Introduction to time series and the AR(1) process

6 hours to complete

9 videos (Total 94 min), 12 readings, 5 quizzes

9 videos

Welcome to Bayesian Statistics: Time Series 7mStationarity 6mThe autocorrelation function (ACF) 8mACF, PACF, Differencing and Smoothing: Examples 11mThe AR(1) 15mSimulating from an AR(1) process 8mMaximum likelihood estimation in the AR(1)22mBayesian inference in the AR(1)10mBayesian inference in the AR(1): Conditional likelihood example 3m

12 readings

Introduction to R10mList of References 4mThe partial autocorrelation function (PACF)15mDifferencing and Smoothing 10mR Code: Differencing and filtering via moving averages10mR Code: Simulate data from a white noise process10mThe PACF of the AR(1) process 15mR Code: Sample data from AR(1) processes10mReview of maximum likelihood and Bayesian inference in regression 15mR code: MLE for the AR(1), examples15mR Code: AR(1) Bayesian inference, conditional likelihood example 12mBayesian inference in the AR(1), full likelihood example 10m

4 practice exercises

Objectives of the course 20mStationarity, the ACF and the PACF 30mThe AR(1) definitions and properties 30mMLE and Bayesian inference in the AR(1) 30m

Week2

Week 2

5 hours to complete

Week 2: The AR(p) process

5 hours to complete

9 videos (Total 96 min), 8 readings, 3 quizzes

9 videos

Definition and state-space representation20mExamples 17mACF of the AR(p)7mSimulating data from an AR(p)11mBayesian inference in the AR(p): Reference prior, conditional likelihood 8mModel order selection6mExample: Bayesian inference in the AR(p), conditional likelihood 12mSpectral representation of the AR(p)5mSpectral representation of the AR(p): Example 5m

8 readings

Rcode: Computing the roots of the AR polynomial 5mRcode: Simulating data from an AR(p)15mThe AR(p): Review 15mRcode: Maximum likelihood estimation, AR(p), conditional likelihood 10mRcode: Bayesian inference, AR(p), conditional likelihood 10mRcode: Model order selection 10mRcode: Spectral density of AR(p) 10mARIMA processes10m

2 practice exercises

Properties of AR processes 30mSpectral representation of the AR(p)30m

Week3

Week 3

5 hours to complete

Week 3: Normal dynamic linear models, Part I

5 hours to complete

10 videos (Total 114 min), 7 readings, 3 quizzes

10 videos

NDLM: Definition 16mPolynomial trend models13mRegression models 8mThe superposition principle 6mFiltering 19mFiltering in the NDLM: Example 14mSmoothing and forecasting 11mSmoothing in the NDLM: Example6mSecond order polynomial: Filtering and smoothing example7mUsing the dlm package in R 8m

7 readings

Summary of polynomial trend and regression models 10mSuperposition principle: General case10mSummary of the filtering distributions10mRcode. Filtering in the NDLM: Example 10mSummary of the smoothing and forecasting distributions10mRcode: Smoothing in the NDLM, Example10mRcode: Using the dlm package in R10m

2 practice exercises

The Normal Dynamic Linear Model30mNDLM, Part I: Review 30m

Week4

Week 4

4 hours to complete

Week 4: Normal dynamic linear models, Part II

4 hours to complete

7 videos (Total 103 min), 4 readings, 3 quizzes

7 videos

Fourier representation17mBuilding NDLMs with multiple components: Examples8mFiltering, Smoothing and Forecasting: Unknown observational variance10mSpecifying the system covariance matrix via discount factors17mNDLM, Unknown Observational Variance: Example13mEEG data 17mGoogle trends17m

4 readings

Fourier Representation: Example 110mSummary: DLM Fourier representation 12mSummary of Filtering, Smoothing and Forecasting Distributions, NDLM unknown observational variance 10mRcode: NDLM, Unknown Observational Variance Example 10m

2 practice exercises

Seasonal Models and Superposition30mNDLM, Part II20m

About the Bayesian Statistics Specialization

This Specialization is intended for all learners seeking to develop proficiency in statistics, Bayesian statistics, Bayesian inference, R programming, and much more. Through four complete courses (From Concept to Data Analysis; Techniques and Models; Mixture Models; Time Series Analysis) and a culminating project, you will cover Bayesian methods — such as conjugate models, MCMC, mixture models, and dynamic linear modeling — which will provide you with the skills necessary to perform analysis, engage in forecasting, and create statistical models using real-world data.

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When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
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Bayesian Statistics: Time Series Analysis

About this Course

Skills you will gain