Sunday, March 14, 2010

Noise and sign

When I put the day before yesterday my graph on the volume of credit granted for the mortgages on housing registered until November, I did not realize that the fact of this month had been published that one on the same morning, accompanied by the corresponding press release of the INE (it is for what he has to ask the friends to order you the last updated file).
So in the night I took a surprise on having seen that precisely the news was speaking about this statistics, and they were emphasizing that in November, for the first time from 2007, more mortgages had been constituted on housing that in the same month of the previous year (one more 1,8 % to be precise).
Since I was concentrated on the topic of the volume of the credit, it had not paid a lot of attention to the number of loans, but in effect, in November, for the first time from April, 2007, they were granted more than one year earlier.
The interesting question that appears here is that of the difficulty to detect changes of tendency and to distinguish them from mere saw teeth (those that I have called other times anecdatos). I explain myself: in most of the social phenomena that we observe across the time, and that count (per days, weeks, months, years...) there will be tendencies of fund (stability, growth, decrease) and teeth of saw (in an erratic way the fact of every concrete period of time does not continue exactly the tendency, but it is anything higher or anything more down than it would be necessary to wait). If the saw teeth are pronounced, and we concentrate very much on them, cover the danger of spending every month (or week, or period that is) from the panic to the optimism, and vice versa, in an erratic way, according to the deviation of the tendency that touches this time, without realizing that we are reacting to oscillations concerning the tendency, and do not see the tendency itself.
How to know if the last fact of a series is a tooth of saw or a change of tendency? Definitely speaking, we will not be able to know it until we see those who come later. But what yes we can find out easily is if the information at the level of temporary disintegration that we are using is given or not to the saw teeth. For example, the fact that has just be published is that in November a 1,8 more % of mortgages registered on housing than in November, 2008. Let's see the trajectory of this indicator in the last years (click to extend):

We can see that yes, there are saw teeth, and they are in some considerable cases (even forgetting the showiest, in March and April, which is seen affected by the dances of the holy week). We can illustrate it simply with the values of last seven months (rounded to the unit):-25,-10,-19,-6,-6,-18, +2.
With this oscillation grade concerning the tendency, it is a difficult knowledge if the November fact is a saw tooth more, or a real change was doing positive levels. But yes we can know that this statistics, when he joins per months, is given to produce saw teeth. A remedy for these situations is to "smooth" the curve, so that the peaks up and down they are compensated, and let's see the fund tendency. How to do that? Very simple, instead of looking at the fact per months, we can see it for major periods. That we analyze the temporary information per days, per weeks, per months or per years it is a relatively arbitrary convention. But one of the good reasons to modify the convention is precisely that if the grade of aggregation that I use produces a statistics with many saw teeth, perhaps it is that I am disintegrating too much, that I am putting the magnifying glass too much close to the information, and the oscillations concerning the tendency confuse me.
We can see, therefore, the evolution of this indicator for perodos, for example, of three months. Instead of using finished and successive trimesters, trimesters can be used deslizantes, that some are overlapping with others (just as we do, for example, with the inflation, when we give the value of last twelve months, and we check it every month). This way, every fact of the series would be ene+feb+mar, feb+mar+abr, mar+abr+may, abr+may+jun...
In the following graph we see the result for the last years (in blue) superposed to the monthly fact (in red) that we have seen earlier (click to extend):

The new statistics scarcely has saw teeth, what is a good indication of which it is a question of an aggregation level more adapted to distinguish the tendency of the oscillations with regard to the same one. I dress like that, the last fact (September - oct-nov) is not a too important change, but simply he confirms the process of soft braking in the fall that has been happening throughout 2009: from a maximum fall of-41 % (in the trimester finished in ene-09), the descents have been smoothed in a quite uniform way during the whole year, and in the last period the decrease is already "only" of-8 %. Logical thing, on the other hand: after falling down for one year, 30-40 % is difficult that the same turns to fall down.
I imagine that it is great to ask a newspaper that to decide what it imports is not the monthly fact, but the quarterly fact, which needs proper making, to separate from the press release of the INE, and it is explained to the readership. But: would not be this the type of things for that we would ask to a few means to which it likes thinking that they serve to us to distinguish the real information of the mere information, to separate the sign of the noise?.

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