Optimising a Better Fit
The first step is to expand the previous quarter-over-quarter (QOQ) and month-over-month (MOM) price changes versus months of inventory (MOI) scatter plots to include other time intervals and determine if there are other intervals with higher correlation coefficients than MOM and QOQ. This is simply done by computing “XMOXM” % changes in price, from 1 month to 12 months (YOY), and calculating and graphing the correlation coefficient. When this is done we can find the 4MO4M correlation is strongest, with a coefficient of -0.83, slightly better than the QOQ (3MO3M) coefficient of -0.78. Part of the reason the coefficient is weak is due to the variance in MOI in off season periods (December and January). The correlation can be improved significantly by taking the 3 month moving average of MOI. The resulting correlation coefficients are plotted below:
One can see here that the HOH (6MO6M) % change values have the highest correlation with the 3 month moving average of MOI. Plotting on the scatter plot gives a better idea of how the correlation matches a true linear regression:
Plotting HOH price changes and MOI 3 month MA allows us to “predict” a HOH price change in May of 1.4%±1.8% based upon % price change being dependent upon MOI:
The above analysis gives a slightly more certain result of price movements compared to the QOQ and MOM versus non-averaged MOI linear regressions.
Into the Future
The same method can be further expanded by performing cross correlations on the data. Here we experimented with various MOI moving averages but, as you will see, having an unfiltered MOI produces some neat results. The %XMOXM change in price is cross-correlated with raw MOI. The results are displayed in the contour graph:
One can see that 4MO4M % change is a maxima at an offset of 0 months, as expected. But notice a correlation maxima at -3 months offset at 9MO9M. The cool thing here is that we are effectively finding a correlation of current MOI with 9MO9M price changes 3 months into the future. The graph below better illustrates the relationship:
And versus time:
One can see the relationship is not as strong as the HOH-MOI correlation. However this level of accuracy is approximately the same as the QOQ plot versus MOI. The reason MOI must be raw is that any averaging will intuitively reduce the ability to predict farther into the future. Further work around using seasonal adjustments to produce better fitting is possible but I am neither versed in seasonal adjustment techniques nor do I want to fiddle with the data as it stands too much, no knock against Statscan or NAR implied.
We should note a few things about the analysis and data used here:
- Data is taken only from January 2005, well into the current price boom, meaning whatever memes that were driving prices over this period (interest rates, speculative behaviour, supply, etc.) are from the past 3+ years only. It is important to realise that the behaviours and events governing price changes may significantly change if prices start falling, meaning the correlation may become weaker in this case.
- It goes without saying this is merely a curve fitting exercise. There is some certainty that the % change prices, are to some degree, dependent upon MOI but it should not be taken as fact.
Interestingly I tried adding an inflation factor to the benchmark price and the data became less correlated. Draw your own conclusions here. mohican did a quick fit to FVREB data and got similar results. Further work could be done examining US markets (using CS HPI) to see how such analayis compares especially after 2 years of falling prices.