Zillow expects new home sales and existing home sales to move in opposite directions in December.  New home sales are expected to decrease 1.8 percent to a seasonally adjusted annual rate (SAAR) of 430,000, down from 438,000 units (SAAR) in November.  Existing home sales, on the other hand, are expected to increase 2.3 percent to 5.04 million units (SAAR), up from 4.93 million units in November. Below we provide greater detail about the models and assumptions that went into our December 2014 forecast.

As in previous months, Zillow’s new and existing home sales forecasts use two models:

• A “structural” model that estimates new and existing home sales as a function of other economic data common to both types of home sales.
• A “historical” model for both types of home sales:
  • New home sales are estimated as a function of past movements in new home sales as well as recent single family housing starts data.
  • Existing home sales are estimated as a function of past movements in existing home sales as well as recent pending home sales data.

However, this month we have added several new techniques and inputs to our models.

Methodology

Structural Model

The structural model typically provides greater insight than the historical model into the broader economic forces that drive home sales.  However, depending on the month, some of these fundamental data will only be available with a lag.  To avoiding making too many assumptions about how these variables have moved since their last release, we make use of the relationship between past movements of these variables and current sales to forecast sales for the most recent month.

The fundamental data we use to forecast new and existing home sales include:

• The 30-year mortgage fixed interest rate and the median sale price of new or existing homes sold
  • Intended to capture pricing effects
• The Kansas City Federal Reserve Financial Stress Index and the percent of loans in foreclosure
  • Intended to capture credit conditions
• The number of households, the homeowner vacancy rate, the homeownership rate, and the median family income
  • Intended to capture consumer characteristics
• Qualitative tax credit variables
  • Intended to capture the effects of the 2010 first-time homebuyer tax credits
• Existing home sales are also used as an input to new home sales and vice versa
  • Intended to capture housing demand effects

The relative effects of these variables are expected to differ between new and existing home sales.  New and existing homes are different in many ways, and homebuyers will generally have differing preferences for them.

The 30-year mortgage fixed rate is available without a lag. However, all the other variables that go into our model are published with a lag.  The median sales price of new and existing homes and the Kansas City Federal Reserve Financial Stress Index are always available with a one-month lag.  The number of households, the homeownership rate, the homeowner vacancy rate and the percent of loans in foreclosure are available at a one- to three-month lag depending on the month, since they are based on quarterly data.  (At the time of this writing, they are available at a three-month lag.)  Median family income is available with a lag of anywhere between one and six months, depending on the month.  (At the time of this writing, it is available with a six-month lag.)

Historical Model

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

For existing home sales, the historical model uses past values of existing home sales as well as past values of pending home sales.  We model the number of existing home sales in each month from April 2001 to November 2014 as an ARIMAX(2,1,1) process, with three (one, two and three month) lags of pending home sales.

Each of the historical models is chosen to minimize the Akaike and Bayesian Information criteria among various combinations of external lags tested.  For new homes sales, various combinations of one to five month lags were tested.  For existing home sales, various combinations of one to three month lags were tested.

Combined Forecast

It is difficult to identify a single best forecast from the models we use since it is unlikely that only one will dominate over time.  In order to obtain a point forecast for new and existing home sales from the information provided from the structural and historical models, we use a best-fit technique. This method makes our forecast more robust to model misspecification through diversification gains by extracting information from both models.

To obtain forecast errors, each model is estimated over an expanding window, starting from one-fourth of the data set.  Once the model is estimated, a one-period-ahead forecast is obtained.  One period is then added to the data set and the process is repeated until the full sample is estimated.  The forecasts from the two models are then combined to minimize the squared forecast error.

For new home sales, the forecasts are combined with a weight of about two-thirds on the structural model and one-third on the historical model. For existing home sales, the forecasts are combined with a weight greater than one on the historical model and a small negative weight on the structural model to offset some of the prediction error of the historical model.