Bayesian Statistics: Time Series Analysis

This course is part of Bayesian Statistics Specialization

Instructor: Raquel Prado

Sponsored by Louisiana Workforce Commission

4,809 already enrolled

5 modules

Gain insight into a topic and learn the fundamentals.

4.3

(15 reviews)

Intermediate level

Recommended experience

22 hours to complete

3 weeks at 7 hours a week

Flexible schedule

Learn at your own pace

5 modules

Gain insight into a topic and learn the fundamentals.

4.3

(15 reviews)

Intermediate level

Recommended experience

22 hours to complete

3 weeks at 7 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Build models that describe temporal dependencies.
Use R for analysis and forecasting of times series.
Explain stationary time series processes.

Skills you'll gain

Mathematics

Details to know

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Assessments

10 assignments

Taught in English

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There are 5 modules in this course

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

This module defines stationary time series processes, the autocorrelation function and the autoregressive process of order one or AR(1). Parameter estimation via maximum likelihood and Bayesian inference in the AR(1) are also discussed.

What's included

9 videos12 readings4 assignments1 peer review

9 videosTotal 93 minutes

Welcome to Bayesian Statistics: Time Series 7 minutesPreview module
Stationarity 6 minutes
The autocorrelation function (ACF) 8 minutes
ACF, PACF, Differencing and Smoothing: Examples 11 minutes
The AR(1) 15 minutes
Simulating from an AR(1) process 8 minutes
Maximum likelihood estimation in the AR(1)22 minutes
Bayesian inference in the AR(1)10 minutes
Bayesian inference in the AR(1): Conditional likelihood example 3 minutes

12 readingsTotal 136 minutes

Introduction to R10 minutes
List of References 4 minutes
The partial autocorrelation function (PACF)15 minutes
Differencing and Smoothing 10 minutes
R Code: Differencing and filtering via moving averages10 minutes
R Code: Simulate data from a white noise process10 minutes
The PACF of the AR(1) process 15 minutes
R Code: Sample data from AR(1) processes10 minutes
Review of maximum likelihood and Bayesian inference in regression 15 minutes
R code: MLE for the AR(1), examples15 minutes
R Code: AR(1) Bayesian inference, conditional likelihood example 12 minutes
Bayesian inference in the AR(1), full likelihood example 10 minutes

4 assignmentsTotal 110 minutes

Objectives of the course 20 minutes
MLE and Bayesian inference in the AR(1) 30 minutes
Stationarity, the ACF and the PACF 30 minutes
The AR(1) definitions and properties 30 minutes

1 peer reviewTotal 20 minutes

MLE and Bayesian inference in the AR(1) 20 minutes

This module extends the concepts learned in Week 1 about the AR(1) process to the general case of the AR(p). Maximum likelihood estimation and Bayesian posterior inference in the AR(p) are discussed.

What's included

9 videos8 readings2 assignments1 peer review

9 videosTotal 95 minutes

Definition and state-space representation20 minutesPreview module
Examples 17 minutes
ACF of the AR(p)7 minutes
Simulating data from an AR(p)11 minutes
Bayesian inference in the AR(p): Reference prior, conditional likelihood 8 minutes
Model order selection6 minutes
Example: Bayesian inference in the AR(p), conditional likelihood 12 minutes
Spectral representation of the AR(p)5 minutes
Spectral representation of the AR(p): Example 5 minutes

8 readingsTotal 85 minutes

Rcode: Computing the roots of the AR polynomial 5 minutes
Rcode: Simulating data from an AR(p)15 minutes
The AR(p): Review 15 minutes
Rcode: Maximum likelihood estimation, AR(p), conditional likelihood 10 minutes
Rcode: Bayesian inference, AR(p), conditional likelihood 10 minutes
Rcode: Model order selection 10 minutes
Rcode: Spectral density of AR(p) 10 minutes
ARIMA processes10 minutes

2 assignmentsTotal 60 minutes

Properties of AR processes 30 minutes
Spectral representation of the AR(p)30 minutes

1 peer reviewTotal 60 minutes

Bayesian analysis of an EEG dataset using an AR(p) 60 minutes

Normal Dynamic Linear Models (NDLMs) are defined and illustrated in this module using several examples. Model building based on the forecast function via the superposition principle is explained. Methods for Bayesian filtering, smoothing and forecasting for NDLMs in the case of known observational variances and known system covariance matrices are discussed and illustrated.

What's included

10 videos7 readings2 assignments1 peer review

10 videosTotal 113 minutes

NDLM: Definition 16 minutesPreview module
Polynomial trend models13 minutes
Regression models 8 minutes
The superposition principle 6 minutes
Filtering 19 minutes
Filtering in the NDLM: Example 14 minutes
Smoothing and forecasting 11 minutes
Smoothing in the NDLM: Example6 minutes
Second order polynomial: Filtering and smoothing example7 minutes
Using the dlm package in R 8 minutes

7 readingsTotal 70 minutes

Summary of polynomial trend and regression models 10 minutes
Superposition principle: General case10 minutes
Summary of the filtering distributions10 minutes
Rcode. Filtering in the NDLM: Example 10 minutes
Summary of the smoothing and forecasting distributions10 minutes
Rcode: Smoothing in the NDLM, Example10 minutes
Rcode: Using the dlm package in R10 minutes

2 assignmentsTotal 60 minutes

The Normal Dynamic Linear Model30 minutes
NDLM, Part I: Review 30 minutes

1 peer reviewTotal 60 minutes

NDLM: sensitivity to the model parameters 60 minutes

What's included

7 videos4 readings2 assignments1 peer review

7 videosTotal 102 minutes

Fourier representation17 minutesPreview module
Building NDLMs with multiple components: Examples8 minutes
Filtering, Smoothing and Forecasting: Unknown observational variance10 minutes
Specifying the system covariance matrix via discount factors17 minutes
NDLM, Unknown Observational Variance: Example13 minutes
EEG data 17 minutes
Google trends17 minutes

4 readingsTotal 42 minutes

Fourier Representation: Example 110 minutes
Summary: DLM Fourier representation 12 minutes
Summary of Filtering, Smoothing and Forecasting Distributions, NDLM unknown observational variance 10 minutes
Rcode: NDLM, Unknown Observational Variance Example 10 minutes