1. IT Applications in Business Analytics
Business Analytics (M.Sc.)
IT in Business Analytics
IT Applications in Business Analytics
Lecture 09 – Time Series Regression
Thomas Zeutschler
IT Applications in Business Analytics Time Series Regression

2. „Prediction is very difficult, especially when it‘s about the future.“
Let’s get started…
„Prediction is very difficult,
especially when it‘s about the future.“
Niels Bohr
IT Applications in Business Analytics Time Series Regression

3. Regression Analysis
Regression analysis is a class of statistical methods, to describe the relation between one dependent and one or more independent variables.
Many economical time series have robust relations.
Oil price > fuel price
US 12m avg. fuel price > engine size (Hubraum) of US cars.
Average US income > engine size (Hubraum) of US cars.
IT Applications in Business Analytics Time Series Regression

4. Time Series Dependencies
IT Applications in Business Analytics Time Series Regression

5. Nonlinear Time Series
IT Applications in Business Analytics Time Series Regression

6. Nonlinear Time Series
A nonlinear time series (process) is any stochastic process that is not linear.
Nonlinear time series are generated by nonlinear dynamic equations. Their display features cannot be modelled by linear processes:
time-changing variance,
Asymmetric cycles,
higher-moment structures,
thresholds and breaks.
IT Applications in Business Analytics Time Series Regression

7. Time Series in R ASTSA R Package
A collection of time series analysis methods
A package containing some sample data sets
By David Stoffer, “Data sets and scripts for Time Series Analysis and Its Applications: With R Examples”,
IT Applications in Business Analytics Time Series Regression

8. Time Series – Use Case El Niño and the Fish
Southern Oscillation Index, or SOI, gives an indication of the development and intensity of El Niño or La Niña events in the Pacific Ocean.
The SOI is calculated using the pressure differences between Tahiti and Darwin.
SOI = 10 x
Pdiff   =   (average Tahiti MSLP for the month) - (average Darwin MSLP for the month), Pdiffav   =   long term average of Pdiff for the month in question, and SD(Pdiff)   =   long term standard deviation of Pdiff for the month in question.
(Pdiff – Pdiffav)
SD(Pdiff)
IT Applications in Business Analytics Time Series Regression

9. Time Series – Use Case
IT Applications in Business Analytics Time Series Regression

10. Time Series – Use Case El Niño and the Fish
Fish Recruitment A measure of the fish population in the southern hemisphere.
library(astsa) # R-Package with Data sets and scripts for Time Series Analysis
# Southern Oscillation Index (SOI) for a period of 453 months ranging # over the years
soi = scan("soi.dat")
soi = ts(soi)
# Fish recruitment (number of new fish) for a period of 453 months ranging # over the years
rec = scan("recruit.dat")
rec = ts(rec)
IT Applications in Business Analytics Time Series Regression

11. Time Series – Use Case El Niño and the Fish
Let’s Take a look at Auto-Covariance and Correlation…
What does it tell us?
# Auto-Covariance and -Correlation function estimation for REC
acf(rec)
# Partial Auto-Covariance and -Correlation function estimation for REC
pacf(rec)
# Cross-Covariance and -Correlation function estimation for REC & SOI
ccf(soi,rec)
IT Applications in Business Analytics Time Series Regression

12. Time Series – Use Case El Niño and the Fish
Let’s do a visual analysis of SOI and REC
# Visual coorelation analysis
lag2.plot(soi, rec, 10)
IT Applications in Business Analytics Time Series Regression

13. Time Series – Use Case El Niño and the Fish
Data preparation for the setup of a prediction model…
# create a table with shifted timeseries.
# Just keep periods where for all periods there is a value using 'ts.intersect()'
alldata = ts.intersect(rec, reclag1 = lag(rec,-1), reclag2 = lag(rec,-2), soilag5 = lag(soi,-5), soilag6 = lag(soi,-6), soilag7 = lag(soi,-7), soilag8 = lag(soi,-8), soilag9 = lag(soi,-9), soilag10 = lag(soi,-10))
# show the table
alldata
IT Applications in Business Analytics Time Series Regression

14. Time Series – Use Case El Niño and the Fish
Build a linear model based on SOI -5 to -10 (into the past)
# build a linear model (using 'lm()' function)
# 1st try a multiple regression in which the REC variable is a linear function
# of (past) lags 5, 6, 7, 8, 9, and 10 of the SOI variable
# info: lm(formula, data) -> format for formula := [response]~[terms] -> terms is
tryit1 = lm( formula = rec ~ soilag5 + soilag6 + soilag7 + soilag8 + soilag9 + soilag10, data = alldata)
summary(tryit1)
# Visual analysis of prediction model
plot(tryit1)
IT Applications in Business Analytics Time Series Regression

15. Time Series – Use Case El Niño and the Fish
Let’s take a look at the models residuals
# plot and print ACF (Auto Correlated Function) and PACF (partial ACF) of REC & the model
# info: residuals() is a generic function which extracts model residuals from objects returned by modeling functions
acf2(rec)
acf2(residuals(tryit1))
IT Applications in Business Analytics Time Series Regression

16. Time Series – Use Case El Niño and the Fish
PACF > high values for t-1 and t-2 indicates auto correlation
Adjust the model and introduce REC for t-1 and t-2…
# 2nd try a multiple regression in which the REC variable is a linear function
# of (past) lags 5, 6, 7, 8, 9, and 10 of the SOI variable + 2 past values from REC
tryit2 = lm(formula = rec ~ reclag1 + reclag2 + soilag5 + soilag6 + soilag7 + soilag8 + soilag9 + soilag10, data = alldata)
summary(tryit2)
acf2(residuals(tryit2))
IT Applications in Business Analytics Time Series Regression

17. Time Series – Use Case El Niño and the Fish
Can we optimize or simplify the model?
Remove variable without significance: SOI t-7, t-8, t-9 and t-10
# 3rd try a multiple regression in which the REC variable is a linear function
# of only 2 (past) lags 5 and 6 of the SOI variable + 2 past values REC
tryit3 = lm(formula = rec~reclag1+reclag2+ soilag5+soilag6, data = alldata)
summary(tryit3)
acf2(residuals(tryit3))
IT Applications in Business Analytics Time Series Regression

18. Time Series – Use Case El Niño and the Fish Congratulations !!!
We have build a reliable model over the supposed dependency between El Niño and the fish replication rate.
IT Applications in Business Analytics Time Series Regression

19. Lecture Summary & Homework
IT Applications in Business Analytics Time Series Regression

20. Homework
Take the course… „Applied Time Series Analysis“ by Pennsylvania State University
IT Applications in Business Analytics Time Series Regression

21. Literatur
Take a look at „Nonlinear time series modelling. An Introduction“
Take a look at “Nonlinear Time Series, Theory, Methods and Application with R Examples”
Books worth to spend money…
“Time Series Analysis: Forecasting and Control” Box, Jenkins 5th Ed
“New Introduction to Multiple Time Series Analysis”,
IT Applications in Business Analytics Time Series Regression

22. Any Questions?
IT Applications in Business Analytics Time Series Regression