Techniques and an Example from Roger Simon’s The City Building Process

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Presentation transcript:

Techniques and an Example from Roger Simon’s The City Building Process 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

Example of a Time Series 1888 2 1889 29 1890 33 1891 40 1892 56 1893 43 1894 39 1895 21 1896 38 Etc… 31

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

Raw Construction Cost over Time

Properties Built over Time

Size of Buildings Built over Time

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 =.

Construction Cost Adjusted for Inflation

Comparing Raw and Inflation Adjusted Construction Costs

Construction Cost per Square Foot (Inflation Adjusted)

Construction Cost per Square Foot (Inflation Adjusted)

The Model: Cost per square foot = constant(a) + b1. year + b2 The Model: Cost per square foot = constant(a) + b1*year + b2*(last year’s cost per square foot)

The Model: Cost per square foot = constant(a) + b1. year + b2 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

Trend and Residuals

The Data: 1. Year 2. Cost Per Square Foot 3 The Data: 1.Year 2. Cost Per Square Foot 3. Last Year’s Cost Per Square Foot 4. Predicted Cost 5. Residual