### House Price CAPM

Cointegration and Error Correction Mechanism Approaches:

Estimating a Capital Asset Pricing Model (CAPM) for House

Price Index Returns with SAS

Many researchers erroneously use the framework of linear

regression models to analyze time series data when predicting

changes over time or when extrapolating from present conditions

to future conditions. Caution is needed when interpreting the results

of these regression models. Granger and Newbold (1974) discovered

the existence of â€˜spurious regressionsâ€™ that can occur when the

variables in a regression are nonstationary. While these regressions

appear to look good in terms of having a high R2 and significant

t-statistics, the results are meaningless. Both analysis and modeling

of time series data require knowledge about the mathematical model

of the process.

This paper introduces a methodology that utilizes the power

of the SAS DATA STEP, and PROC X12

and REG procedures. The DATA STEP uses the SAS LAG and

DIF functions to manipulate the data and create an additional

set of variables including Home Price Index Returns (HPI_R1), first

differenced, and lagged first differenced. PROC X12 seasonally

adjusts the time series. Resulting variables are manipulated

further (1) to create additional variables that are tested for

stationarity, (2) to develop a cointegration model, and (3) to

develop an error correction mechanism modeled to determine

the short-run deviations from long-run equilibrium. The relevancy

of each variable created in the data step to time series analysis is

discussed. Of particular interest is the coefficient of the error

correction term that can be modeled in an error correction mechanism

to determine the speed at which the series returns to equilibrium. The

main finding is that Metropolitan Statistical Areas (MSAs) with very

slow shortrun acceleration paths to the equilibrium have higher

returns and risk associated with house price returns than

MSAs with very rapid speed-of-adjustment coefficients.

-- Ismail Mohamed and Theresa R. DiVenti, PDF.