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Time Series

Time Series

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Time Series

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  1. Time Series

  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

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

  4. Longitudinal: Measurements over Time

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

  7. 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

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

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

  10. Cyclical Component Cycle • Upward or Downward Swings • May Vary in Length • Usually Lasts 2 - 10 Years Outcome Time

  11. Seasonal Component • Regular pattern of up & down fluctuations • Weather • Customs etc. • Retail Sales

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

  13. 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)

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

  15. 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

  16. # 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)

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