1. Time Series 1

2. Learning Objectives Cross-sectional vs. Longitudinal
Describe what is forecasting
Explain time series & its components
Smooth a data series
Moving average
Exponential smoothing
Forecast using trend models
Simple Linear Regression
Auto-regressive 2

3. Cross-Sectional: Many Variables, One-Time

4. Longitudinal: Measurements over Time

5. Cross-Sectional Longitudinal Galton Children Height PEW Mobile Phone
Titanic Survivors
Yes
Census
Tracking Studies
Cross-Sectional
Stock Market
Web Analytics No
Old Faithful
Census
Historical River Levels No
Yes
Longitudinal

6. Forecasting: Qualitative Data
Used when situation is vague & little data exist
New products
New technology
Involve intuition, experience
“Expert” Opinion
Directional: Up / Down
Uncertainty 5

8. Forecasting: Quantitative Methods
Used when situation is ‘stable’ & historical data exist
Mature Market
Mathematical techniques
Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values
Assumes that factors influencing past, present, & future will continue 6

9. Time Series Components
Trend
Cyclical
Seasonal
Weather
Customs
Event-Based

10. Time Series Forecasting
Smoothing
Trend Analysis
Moving Average
Exponential
Smoothing
Linear
Exponential
Auto-Regressive
Quadratic 33

11. Cyclical Component Cycle Upward or Downward Swings May Vary in Length
Usually Lasts Years
Outcome
Time

13. Seasonal Component Regular pattern of up & down fluctuations
Weather
Customs etc.
Retail Sales 24

14. Moving Average Method Series of arithmetic means Used for smoothing
Provides overall impression of data over time 34

16. beer<-read.csv("beer.csv",header=T,dec=",",sep=";")
beer<-ts(beer[,1],start=1956,freq=12)
plot(beer,type="l")
hist(beer,prob=T,col="red")
lines(density(beer),lwd=2)

17. plot(stl(beer,s.window="periodic"))

18. Exponential Smoothing Method
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant (W)
Ranges from 0 to 1
Subjectively chosen
Involves little record keeping of past data 58

19. # Holt-Winters exponential smoothing with trend
# and additive seasonal component.
beer.hw<-HoltWinters(beer)
predict(beer.hw,n.ahead=12)
plot(beer,xlim=c(1956,1999))
lines(predict(beer.hw,n.ahead=48),col=2)

20. Summary Described what forecasting is
Explained time series & its components
Smoothed a data series
Moving average
Exponential smoothing
Forecasted using trend models
121