Case-Shiller Housing Index: Seasonal Effects

2nd in the series examining the S&P Case-Shiller housing index. You may want to read the previous post first.

The plot on the right shows the Case-Shiller 10-city Housing index since 1987. When you look at any time series of data collected over time one key question is whether there are any seasonal effects. The most common type of seasonal effect is one that occurs every 12 months for obvious reasons. Seasonal effects don't have to occur on a 12 month or 24 hour basis but commonly they do. So when you look at the Case-Shiller you see some wobble but is that just random wobble or is it due to a systematic seasonal effect? From this graphical perspective it is hard to be sure.

Monthly Change a.k.a "1st Difference"

A common data transformation done on time series data is to take the 1st difference which simply means to calculate the net difference between successive data points. Then you can examine what the monthly change looks like. I won't go into the details here but if we do a monthly change on the log of the Case-Shiller index value, it is easy to convert that back to % change each month.

Here is a graph of the monthly % change of the Case-Shiller plotted with the solid blue line. In this graph, there appears to be a much more obvious seasonal effect. It looks like it peaks in June and hits a low in about November. If you look close enough you will see that the same pattern appears almost every year. Also plotted in the red dashed line is the 12 month rolling average. IF there is indeed a 12 month seasonal effect, then a 12 month rolling average is a quick and easy way to average out that seasonal effect to get a feel for what the monthly change is doing over the longer time perspective. Looking at the red dashed line you can see how it matches up with the long term trend up and then down in the Case-Shiller index itself in the plot above.

Summarizing the Case-Shiller Seasonal Effect

We can examine the average seasonal effect by taking the monthly change and subtracting the 12 month rolling average which will give us the net seasonal effect each month. Then if we average this net effect for January we get the average January effect, do the same for Feb, March, etc. Here is a plot showing the average seasonal effect for the Case-Shiller since '87. So from this you can see the typical monthly change over the prior month. May, June, and July each year see the largest monthly increases and Nov, Dec, and Jan see the biggest monthly decreases in price. Keep in mind that this does not mean that June will always have 0.5% increase over May every year. Just that it will on average have 0.5% additional increase in price compared to what the 12 month rolling average is doing. So when the 12 month rolling average is dropping fast like it is lately, this 0.5% seasonal effect in June is not enough necessarily to ensure prices will increase in June, they may just not drop as far as they would without this seasonal effect helping out. Where in December, the seasonal effect will add to the overall dropping trend and make it drop even faster.

This has been a quick look (believe it or not) at the seasonality in the Case-Shiller. And I haven't at all touched whether this seasonality is statistically significant (real) or not. Seasonality is one of the most interesting things when looking at time series data and it is something I will surely talk about more in the future. But the key take-home for the common caveman trying to understand housing prices is to understand that this seasonality exists and that it will have an influence on the Case-Shiller month to month. So if the Case-Shiller starts to look better come June this year and the press is telling everyone to run to their real estate agent and buy, remember that it should look better in June and that does not necessarily mean the down cycle in housing prices is over!