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Time Series. 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

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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**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**Forecasting: Qualitative Data**• Used when situation is vague & little data exist • New products • New technology • Involve intuition, experience • “Expert” Opinion • Directional: Up / Down • Uncertainty**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**Time Series Components**• Trend • Cyclical • Seasonal • Weather • Customs • Event-Based**Time Series Forecasting**Time Series Smoothing Trend Analysis Moving Average Exponential Smoothing Linear Exponential Auto-Regressive Quadratic**Cyclical Component**Cycle • Upward or Downward Swings • May Vary in Length • Usually Lasts 2 - 10 Years Outcome Time**Seasonal Component**• Regular pattern of up & down fluctuations • Weather • Customs etc. • Retail Sales**Moving Average Method**• Series of arithmetic means • Used for smoothing • Provides overall impression of data over time**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)**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**# 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)**Summary**• Described what forecasting is • Explained time series & its components • Smoothed a data series • Moving average • Exponential smoothing • Forecasted using trend models

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