Coruscation

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 ‘spurious regressions’ 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.