Applying bootstrap methods to time series and regression

Applying bootstrap methods to time series and regression models “An Introduction to the Bootstrap” by Efron and Tibshirani, chapters 8 -9 M. Sc. Seminar in statistics, TAU, March 2017 By Yotam Haruvi 1

The general problem • 2

Unknown probabilistic model Observed data Estimated probabilistic model Bootstrap sample We will focus on this part today Statistic of interest 3 Bootstrap replication

Agenda We wish to extend the bootstrap method to other, more complexed data structures: • Time series • Regression We will review several, ad-hoc bootstrap methods, for each of the structures above. But we’ll start with a simple example - Two-sample problem. 4

Two-sample problem – the framework • 5

Two-sample problems – a bootstrap solution • 6

Two-sample problems – a bootstrap solution • 7

Time series • 8

Time series - illustration lutenizing hormone 4 Hormone level 3. 5 3 2. 5 2 1. 5 1 Time point Diggle, 1990: 48 measurements taken from a healthy woman, every 10 minutes 9

Time series – the problem • 10

Time series – a bootstrap solution • 11

Time series – a bootstrap solution • 12

Time series – moving blocks bootstrap • Original sample 13 Bootstrap sample

Time series – moving blocks bootstrap • 14

Time series – discussion of two methods • 15

Regression – the framework • 16

Regression – the problem • 17

Regression – Bootstrap solutions We will cover two different ways in which we can generate bootstrap samples: • Bootstrapping pairs • Bootstrapping residuals 18

Regression - Bootstrapping pairs • 19

Regression - Bootstrapping residuals • 20

Regression – discussion of two methods • 21

Conclusion • 22

Thank you! 23