Housing Data and Stationarity

Eugenio,

As a follow-up to our meeting yesterday, a series of evaluations was conducted on the housing starts data to insure that the time series response variable was stationary (recall our brief discussion of results based on non-stationary time series). Dickey-Fuller and Augmented Dickey-Fuller (accounting for autocorrelation in the error term) unit root tests were used in the evaluation process. Given the limited number of observations for certain potentially important explanatory variables (e.g., %population change, etc.), we tested the housing starts variable over 3 historical periods. The results are provided below:

Period 1: 1959 through 2001 (obs=503)

TEST TEST STATISTIC CRITICAL VALUE (p=0.05)

DF -6.712 -1.95
ADF (5 lags) -2.436 -1.95
ADF (1 lag) -4.689 -1.95

Period 2: 1984 through 2001 (obs=201)

TEST TEST STATISTIC CRITICAL VALUE (p=0.05)

DF -3.140 -1.95
ADF (5 lags) -1.158 -1.95
ADF (1 lag) -2.053 -1.95

Period 3: 1996 through 2001 (obs=62)

TEST TEST STATISTIC CRITICAL VALUE (p=0.05)
DF -6.354 -1.95
ADF (5 lags) -2.100 -1.95
ADF (1 lag) -3.954 -1.95

**Time series stationary if TEST STATISTIC < CRITICAL VALUE

Based on the results above, the housing starts time series are stationary, with the possible exception of 1984 through 2001 data. Since you are likely to use the entire data series in an AR framework, the assumption of stationarity holds. Let us know if you have any further questions.

Nelson