Louisiana Department of Transportation and Development

Forecasting Construction Cost Index

Values Using Auto Regression Modeling Charles Nickel, P.E.

Cost Estimate & VE Directorcharles.nickel@la.gov

(225) 379-1078

Auto Regression Modeling

Uses Linear Regression of a series’ own previous values to try and forecast future values.The series must be “stationary,” that is, the series values must range within a finite upper and lower bounds.

La. DOTD Construction Cost Index (CCI)

Based on Polynomial Linear Regression CurvesIndex values are not reliable at the extreme either ends of the series.Continues to Increase over time, therefore, it is not “stationary.”

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Construction Cost Index

Monthly Differences (CCI)

Does not continue to increase or decrease over time Remains with in +/- 0.04

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Monthly Differences

Monthly Differences (CCI)

Can be modeled using the following equation:

• Only data prior to January 1, 2011 was modeled• Forecasted Values beyond January 1, 2011 were

compared to Actual Values

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Forecasted & Actual CCI

Using the CCI to Obtain the CCI

Actual or Forecasted Monthly CCI values can be added back to obtain the CCI values.

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Forecasted & Actual CCI

Modeling CCI using Monte Carlo

• The amount of change from on month’s CCI to the next is assumed to be random

• Monthly changes in the CCI are assumed to be Normally Distributed.

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Distribution of CCI

Modeling CCI using Monte Carlo

• From the Cumulative Normal Distribution Curve a random probable CCI can be generated

• For example, if a number between 0% and 100% is chosen, say 25%, the corresponding probable CCI would be 0.007413866

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Cumulative Distributionof CCI

Modeling CCI using Monte Carlo

• Adding back all the randomly selected probable CCI values produces a probable CCI series or scenario.

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CCI Scenario 1

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CCI Scenario 2

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CCI Scenario 3

Modeling CCI using Monte Carlo

• 10,000 such scenarios were generated.• Standard deviations from the Forecasted CCI

were calculated for each month.

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Probable Deviations

Inflation• Suppose we want to forecast how much

construction costs will have inflated since December 1, 2010, to January 1, 2014.

• That is 37 months out.

Inflation

• The forecasted percent increase can be calculated from the Forecasted CCI as follows:

Inflation

• The CCI was forecasted to increase by 10.57%

Inflation

• An increase by 10.57% suggests an effective annual inflation rate of 3.31%

• But by how much could the actual increase in the CCI vary by?

Inflation Risk

• At 37 months out, one standard deviation above the forecasted CCI is 1.673201, which would be an 18.69% increase.

• This would suggest an effective annual inflation rate of 5.71%

Inflation Risk

• At 37 months out, one standard deviation below the forecasted CCI is 1.444326, which would only be a 2.45% increase.

• This would suggest an effective annual inflation rate of 0.79%.

Inflation Risk• At 37 months out, based on one standard

deviation, there is about a 68% chance that the effective annual inflation rate could be anywhere between 0.79% and 5.71%

• The Forecasted effective annual inflation rate is 3.31%

• The Actual effective annual inflation rate is 1.41%

Inflation Risks to a Program• Multiple projects can be modeled to reflect an

anticipated minimum, maximum, and most likely inflation rate.

• A Monte Carlo Simulation can be run to determine what the probable range in Program Level Risk is due to the inflation risks associated with each individual project.

Cointegrated Vector Auto Regression (VAR) Modeling

• Cointegrates the CCI series with other series, say like the West Texas Intermediate (WTI) Crude Oil Index.

Cointegrated Vector Auto Regression (VAR) Modeling

• May can take advantage of known lags.

Questions?

Charles Nickel, P.E.Cost Estimate & VE Directorcharles.nickel@la.gov(225) 379-1078