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Time Series. Techniques and an Example from Roger Simon’s The City Building Process. What is a Time Series?. Numerical data ordered by intervals of time in chronological order The analysis of a time series involves decomposing the series into its components, e.g., Trends
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Time Series Techniques and an Example from Roger Simon’s The City Building Process
What is a Time Series? • Numerical data ordered by intervals of time in chronological order • The analysis of a time series involves decomposing the series into its components, e.g., • Trends • Cyclical and Seasonal Fluctuations • Irregular Fluctuations
To Analyze a Time Series… • Identify the possible processes affecting the series: • Inflation or Deflation (for series of prices or expenditures) • Long term trend • Cyclical fluctuations • Seasonal fluctuations • Irregular fluctuations
Steps to Analyze Changing Construction Costs • Identify a measure: • Construction Cost? Or…. • Construction Cost Per Square Foot • Convert to Constant Dollars • Measure the Trend • Identify cyclical or seasonal factors • Identify irregular fluctuations
Adjusting for Inflation • if yrbuilt >887 and yrbuilt < 912 then let concost2=concost*20 • if yrbuilt >911 and yrbuilt < 916 then let concost2=concost/.06 • if yrbuilt = 916 then let concost2=concost/.065 • if yrbuilt = 917 then let concost2=concost/.077 • if yrbuilt = 918 then let concost2=concost/.090 • if yrbuilt = 919 then let concost2=concost/.104 • if yrbuilt = 920 then let concost2=concost/.120 • if yrbuilt = 921 then let concost2=concost/.107 • if yrbuilt = 922 then let concost2=concost/.103 • if yrbuilt = 923 then let concost2=concost/.102 • if yrbuilt = 924 then let concost2=concost/.102 • if yrbuilt = 925 then let concost2=concost/.105 • if yrbuilt = 926 then let concost2=concost/.106 • if yrbuilt = 927 then let concost2=concost/.104 • if yrbuilt = 928 then let concost2=concost/.102 • if yrbuilt = 929 then let concost2=concost/.102 • if yrbuilt=. then let concost2= concost *20 • if concost=. Then let concost2 =.
The Model: Cost per square foot = constant(a) + b1*year + b2*(last year’s cost per square foot)
Cost per square foot = $7.33 + .59 (last year’s cost) + .29 (year) Number of cases: 39 (1889-1928). 1889=1 Adjusted R Square: 77.2 The Model: Cost per square foot = constant(a) + b1*year + b2*last year’s cost per square foot
The Data:1.Year 2. Cost Per Square Foot3. Last Year’s Cost Per Square Foot4. Predicted Cost5. Residual