Zillow expects new home sales for November to fall by 1 percent, to a seasonally adjusted annual rate (SAAR) of 453,500 units, down from 458,000 units in October. But the models we use and the assumptions that underlie them are not always as definitive as we would like.

Below, we provide greater detail about the assumptions that went into our November 2014 forecast.

Zillow’s new home sales forecasts uses two models:

• A “structural” model that estimates home sales as a function of other economic data.
• A “historical” model that estimates home sales as a function of past movements in new home sales as well as recent pending home sales data.

More information about the models and adjustment made this month can be found in the Methodology section below.

According to the historical model, when housing starts increase, new home sales tend to rise in the subsequent months. But when new home sales increase one month, they are expected to fall in the next.

For November, our historical model suggests that new home sales will fall by 1 percent to a seasonally adjusted annual rate (SAAR) of 453,500 units. The decline is mostly because of October’s increase in home sales, but can also partly be attributed to a decrease in housing starts in June. Homes started in June are those homes most likely to be completed and ready for sale in November.

The structural model typically provides greater insight than the historical model into the broader economic forces that drive new home sales. However, depending on the month, it can rely heavily on forecasts of explanatory variables. In particular, our forecasts of the homeownership rate and homeowner vacancy rate – which we must forecast anywhere from one to four months ahead because they are only released quarterly – can have important effects on the model estimates. For November, we must forecast these variables two months ahead. Median family, which is also important and was last made available in June, must be forecast five months ahead.

A very naïve forecast is done assuming the variables listed above will not change from the last time they were made available. These assumptions predict a slight increase in new home sales of 0.5 percent, to 460,100 units (SAAR). However, these variables have exhibited trends that suggest the naïve forecast is not very realistic.

Median family income has shown a strong tendency to move with the Consumer Price Index (CPI) for Services. Thus, for the following scenarios, median family income is assumed to increase at a rate consistent with services CPI.

The homeownership rate has been steadily declining. Holding all else constant, if it continues to decline through November at its month-over-month average over the past year, new home sales could fall by 1.9 percent to 449,400 units (SAAR).

The homeowner vacancy rate has shown slight increases over the past two months, in contrast to its steady decline throughout the recovery. If nothing else were to change, but the homeowner vacancy rate were to rise in October at a rate consistent with Zillow’s for-sale inventory series, then sales could fall by 1.5 percent to 451,000 units (SAAR).

If both of these predictions were to come true, then new home sales would decline by 2 percent, to the forecasted 449,000 units (SAAR).

Our model is less sensitive to other assumptions, including the following:

• We estimate that the median sales price of new homes sold in November will increase to $292,500 – the result of a best-fit ARIMA model, an ARIMA(1,1,4) in this instance.
• We estimate that median family income will increase to $66,900 in November, from $66,300 in June, in line with growth in the Consumer Price Index (CPI) for Services.
• We estimate that the number of households will increase to 116.1 million in November, the result of a best-fit ARIMA model – an ARIMA(1,2,2), in this instance.
• We estimate the share of loans in foreclosure in November will fall to 2.29 percent, the result of a best fit ARIMA model – an ARIMA(3,15), in this instance – consistent with recent with its downward trend since 2012.

Methodology

Structural Model

The structural model estimates new home sales as a function of key macroeconomic fundamentals, including: The contemporaneous homeownership rate; the homeowner vacancy rate; home sales prices; interest rates; family incomes; loans in foreclosure; and the total number of households.

The adjustment made to this month’s forecasting model was to estimate monthly changes in new home sales as a function of monthly differences in the fundamental variables. The original model estimated new home sales as a function of levels of some fundamental variables, and yearly percent changes on others. This adjustment improved the mean average percent error by about 50 percent.

Historical Model

The historical model uses past new home sales data and past values of housing starts. We model the number of new home sales in each month from January 1963 to June 2014 as an ARIMAX(4,1,2) process, with three lags of housing starts as external regressors, from four, five and six months prior.

In 2013, it took an average of five months to complete a new home, according to the U.S. Census Bureau’s Survey of Construction. We use this observation as a starting point for lag-length selection for housing starts. Choosing four, five and six month lags of housing starts minimized the Akaike and Bayesian information criteria among various combinations of two-to-six lags tested.