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I want to know if I have data of house prices of an area in time, what mathematical function will best fit it's graph?

Or in other word, what function I could use that in time $t$, $f(t)$ will be a good estimate for house price?

Is it like $f(t) = at + b$, or $f(t) = at^2 + bt + c$, or $f(t) = a\ln(t) + b$, or $f(t) = a\exp(t) + b$ or ...

I know it depends on many things, but please consider that I just want to get a estimate a regression, and coefficients like $a$, $b$, $c$, ... can be found with analyzing some big data of house prices in past few years.

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  • $\begingroup$ If you just want to get an estimate you can use any form you want. If you want to get a good estimate you should probably add variables other than just time. $\endgroup$
    – Giskard
    Feb 21, 2017 at 11:18
  • $\begingroup$ What makes this question even more bizarre is that time clearly has several possible units of measurement, not to mention start dates. These choices would probably affect which functional form is best. $\endgroup$
    – Giskard
    Feb 21, 2017 at 11:20
  • $\begingroup$ I'm voting to close this question as off-topic because it belongs to Cross-Validated site. $\endgroup$
    – luchonacho
    Feb 22, 2017 at 16:21

2 Answers 2

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There is no such function. The reason is that time itself is not really driving house prices at all.

Time can be used as a proxy: An older house is more likely to be designed in a way that was modern at the time of construction and has outdated technical standards (heating etc.), which influences the price; Usually economies face inflation, so the nominal price at the time of purchase is likely to be lower; An older house is more likely to cost more in terms of renovation; An older house may have been build in a location that by now turned out to be great resulting in a value increase, but it could have gone the other way too; and so on. The relationship between time and value depends on the underlying characteristics of the house. To estimate the evolution of your house price you need to give much more information.

To illustrate, consider two houses build at the same time. House A is small, House B is huge. House A in Aleppo, House B is in cental Tokyo. I think you see the point. Just considering time does not seem to be a smart idea to determine the value of a house.

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This is not an answer, just to complement @Bayesian reply.

All variables that will affect the housing price

  • Money supply
  • housing supply
  • housing demands
  • house type
  • location
  • Property related policies(Taxes, regulation, incentive,etc)
  • Employment rates
  • Salaries
  • Bank interest rates
  • household debts
  • Innovations
  • human sentiments

Ironically, what drive above is the flow of "time". But time itself has little effect to the value of the house. TIMING will cause various incidents that cause variance in housing price, e.g. financial crisis.

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