Time Series Techniques and an Example from Roger Simon’s The City Building Process
Dec 18, 2015
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*(last year’s cost per square foot)
Dep Var: COSTPER N: 39 Multiple R: 0.885 Squared multiple R: 0.784 Adjusted squared multiple R: 0.772 Standard error of estimate: 4.143 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT 7.330 3.100 0.000 . 2.364 0.024LAGCOSTP 0.589 0.148 0.540 0.325 3.974 0.000YEAR2 0.293 0.103 0.387 0.325 2.851 0.007
Analysis of VarianceSource Sum-of-Squares df Mean-Square F-ratio P Regression 2244.126 2 1122.063 65.375 0.000Residual 617.887 36 17.164
Dep Var: COSTPER N: 39 Multiple R: 0.885 Squared multiple R: 0.784 Adjusted squared multiple R: 0.772 Standard error of estimate: 4.143 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT 7.330 3.100 0.000 . 2.364 0.024LAGCOSTP 0.589 0.148 0.540 0.325 3.974 0.000YEAR2 0.293 0.103 0.387 0.325 2.851 0.007
Analysis of VarianceSource Sum-of-Squares df Mean-Square F-ratio P Regression 2244.126 2 1122.063 65.375 0.000Residual 617.887 36 17.164
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
YearCost Per
Square FootLast Year's Cost
Per Sq. Ft.PredictedCost PerSq. Ft.
Residual
889 $21.91 $22.67 $20.99 0.92890 $20.42 $21.91 $20.83 -0.41891 $17.27 $20.42 $20.25 -2.98892 $17.40 $17.27 $18.68 -1.29893 $19.21 $17.40 $19.05 0.16894 $19.76 $19.21 $20.41 -0.65895 $20.85 $19.76 $21.03 -0.19896 $19.36 $20.84 $21.96 -2.60897 $20.73 $19.36 $21.38 -0.65898 $20.54 $20.73 $22.48 -1.94899 $25.83 $20.54 $22.66 3.17900 $28.09 $25.83 $26.08 2.01901 $28.80 $28.09 $27.70 1.10902 $28.63 $28.80 $28.41 0.22903 $33.00 $28.63 $28.61 4.40904 $31.60 $33.00 $31.48 0.12905 $34.47 $31.60 $30.94 3.53906 $32.93 $34.47 $32.93 0.00907 $35.72 $32.93 $32.32 3.40908 $37.37 $35.72 $34.25 3.12909 $37.97 $37.37 $35.52 2.45910 $34.66 $37.97 $36.17 -1.51911 $35.13 $34.66 $34.51 0.63912 $30.27 $35.13 $35.08 -4.81913 $37.89 $30.27 $32.51 5.38914 $28.78 $37.89 $37.29 -8.51915 $38.23 $28.78 $32.22 6.01916 $37.99 $38.23 $38.08 -0.09917 $40.33 $37.99 $38.23 2.10918 $23.85 $40.33 $39.91 -16.06919 $30.15 $23.85 $30.49 -0.34920 $33.45 $30.15 $34.49 -1.04921 $34.19 $33.45 $36.73 -2.54922 $34.37 $34.19 $37.46 -3.09923 $36.37 $34.37 $37.86 -1.49924 $36.81 $36.37 $39.33 -2.53925 $42.96 $36.81 $39.88 3.08926 $49.20 $42.96 $43.80 5.40928 $53.59 $49.20 $48.07 5.52
. $53.59 . .
The Data:1.Year 2. Cost Per Square Foot3. Last Year’s Cost Per Square Foot4. Predicted Cost5. Residual