Wikipedia:Reference desk/Archives/Mathematics/2006 August 17

Please be aware that this

statistical hypothesis testing is not uniformly accepted as based on firm ground. --Lambiam^Talk 00:28, 18 August 2006 (UTC)[reply

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Thanks. If I had a large number of ratios between many different cities, and I wanted to put them in order of the strength of the oscillations, would it make any sense to do a fourier analysis on each of the ratios and calculate a figure of merit for it by dividing the amplitude of the frequency of the largest amplitude by the average amplitude of all the other frequencies of that ratio?

Sorry, no, that doesn't feel right. It might put very weak oscillations ahead of strong ones. I'd actually work with the log of the ratios, and look at the absolute size of the amplitude of oscillations for ordering by "strength". This is logically independent of the statistical significance, which is not meant to assess strength, but rather signal as opposed to noise. A weak signal can be less noisy than a strong one. If the strength is very low, the question whether it is significant becomes moot. --Lambiam^Talk 09:19, 18 August 2006 (UTC)[reply]

Hmmmmmmn. "I'd actually work with the log of the ratios" - why would this be any better please?, "and look at the absolute size of the amplitude of oscillations for ordering by "strength"." - do you just mean the amplitude between the peaks and troughs of the raw data?

I have been thinking about this as a possible investment strategy - move back and forth between cities A and B by moving house from one city to the other when you expect house prices in the other city to rise more than the city you are in. This should mean that you can buy a more and more expensive house each time.

If you have a number of pairs of cities to choose from, then you want to choose a pair whose ratio has a high amplitude of cycle, and one that has a clear cycle without what you've seen in the past merely being random fluctuations. Any ideas as to how to best choose these from a large number of different ratios please?

I'm rather skeptical that the whole idea is going to pan out, but if you get rich this way, remember me. Why the log? Well, if you compare Ansby to Blackbury, and also Blackbury to Ansby, shouldn't these two be essentially the same except that they are each other's mirror images? That's what the log gives you. I meant the amplitude of the idealized "waves" as determined by the optimal fit. For the selection, I'd discard the statistically non-significant pairs and order the rest by amplitude. I expect that after the initial culling very few significant pairs if any will be left; that is why I am skeptical. --Lambiam^Talk 10:49, 19 August 2006 (UTC)[reply]

Thanks. But I don't understand why log(A/B) would be equal to log(B/A) anymore than A/B would be equal to B/A. And could you measure the amplitude just by calculating the RMS of the ratio?

log(B/A) = – log(A/B), so you get the same graph flipped over the horizontal axis. I don't see why the RMS would give the same results as the amplitude.

On second thoughts, you may be better off looking a time-lagged

sunspot cycle, do you? And perhaps you do not so much want to correlate the prices themselves, but the trends. Ah, the possible variations are endless. --Lambiam^Talk 19:30, 19 August 2006 (UTC)[reply

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I believe he suggested working with logarithms because logarithms turn exponential growth into linear growth. Evidentally he expects housing costs or whatever this is to be exponential. I would think there's an exponential inflation component, maybe, but the oscillation part? I wouldn't presume... but it's often good to take a look at both graphs. - Rainwarrior 22:44, 19 August 2006 (UTC)[reply]

Thanks again. I was interested in considering the ratios because, firstly, when you've made money from speculation in property (UK) or real estate (US) then there isnt much else to do with it apart from buying a bigger house, often in a nicer area. Looked at it that way, the important thing is not the absolute rise in prices, but changes in the ratio of prices from where you are to where you want to move to.

Secondly, my guess is that an ARMA forecast of such a ratio may be more reliable than ARMA forecasts of the market in two seperate cities, since aspects of the market that apply to both cities will cancel out. My guess is that the ratio would have less variance than just the price in either city.

Thirdly, you could in theory make a lot more money by moving between two places than just staying in one place, as you could benefit from the best price rises in each city when the other city's prices are rising less.

Due to inflation in the UK being much lower now at around 2 1/2 % per year compared to the 25% of the 1970's, then I'm not sure that plain exponential growth will be as powerful a consideration as it was in the past.

I have looked at time lags between London and different parts of the UK. They suggest that it could be the case that price rises start in London and spread out like a ripple in a pond to other parts of the UK, with the lag between London and northern england being about two or three years.

Every few years there are emotive reports in the UK press about how rising prices in the south of England mean that people from the North cannot afford to move down here, but I think this is mostly due to a cycle in the ratios of prices arising from the lag of property price rises in different areas rather much of a pernament change. When prices are stable or falling slightly in London they always seem to be still rising in the north. I do not know if the same kind of thing happens in the US or other countries.

What would be thrilling would be to 'surf' the wave that (may) spread out from London, moving up Britain from London to

I am interested in seeing price changes in the housing market as being like a spatial wave moving through a medium rather than just something that happens at points, but my understanding of the maths of this is currently very limited. Price rises in one area have a knock-on effect in adjacent areas, as people living in one area where prices have risen buy in an adjacent area with cheaper prices, causing prices in that area to rise also; and similarly with any price falls.

I do wonder how this process could be modelled mathematically - I wonder if there is any physical process that would be analogous, perhaps with the energy of individual molecules in a homogenous medium being analogous to price, such as sound moving through still air, or heat from a point-source in a thin sheet? Or like

Some models, like that for weather are destined to be chaotic (and thus aren't predictable in the long term). There are things like the

Lorenz attractor, which while flipping between two usual positions, is not an oscillation because its timing is unpredictable. I don't know much about housing prices, but I suspect there is more going on than a simple oscillations... there is probably some sort of oscillating component with a period of one year, as there is probably a seasonal change in the houses people sell, but other than that, I wouldn't know. - Rainwarrior 16:31, 20 August 2006 (UTC)[reply

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As another comment, anything can be modelled - but you have to be judicious about which aspect of the housing market you really want to capture. The model may give precise answers, but if it is not created in a way to capture all the fundamentals, the model would not be useful. Some modellers like to approach this problem from a

stochastic processes point of view. --HappyCamper 04:55, 21 August 2006 (UTC)[reply

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