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Time Series
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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
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Cross-Sectional: Many Variables, One-Time
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Longitudinal: Measurements over Time
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No
YesNo
Yes
Longitudinal
Cro
ss-S
ecti
onal PEW Mobile Phone
Galton Children Height
Tracking Studies
Census
Stock Market
Historical River Levels
Old Faithful
Web Analytics
Titanic Survivors
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Forecasting: Qualitative Data
•Used when situation is vague & little data exist• New products• New technology
• Involve intuition, experience• “Expert” Opinion•Directional: Up / Down•Uncertainty
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•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
Forecasting: Quantitative Methods
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Time Series Components
1. Trend2. Cyclical3. Seasonal
A. WeatherB. Customs
4. Event-Based
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Time Series Forecasting
Time Series
Moving Average
Smoothing
ExponentialSmoothing
Trend Analysis
Auto-Regressive
Linear Exponential
Quadratic
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• Upward or Downward Swings• May Vary in Length• Usually Lasts 2 - 10 Years
Outcome
Time
Cycle
Cyclical Component
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• Regular pattern of up & down fluctuations• Weather• Customs etc.
• Retail Sales
Seasonal Component
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Moving Average Method
• Series of arithmetic means • Used for smoothing• Provides overall impression of data over time
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hist(beer,prob=T,col="red")lines(density(beer),lwd=2)
beer<-read.csv("beer.csv",header=T,dec=",",sep=";")beer<-ts(beer[,1],start=1956,freq=12)plot(beer,type="l")
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plot(stl(beer,s.window="periodic"))
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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
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# 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)
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Summary
• Described what forecasting is• Explained time series & its components• Smoothed a data series
• Moving average• Exponential smoothing
• Forecasted using trend models