I am trying to predict the long term residual value of a product with only the releasing price. I have collected some data off the Internet related with one phone type, and it is pretty obvious that the residual value (say eBay and Amazon used pricing) of a used electronic product (say iphone) is decreasing exponential. Like the plot below:
par(mfrow=c(3,1)) x <- 1:100 y <- exp(-0.03 * x) * (2 + rnorm(100)) plot(x, y, main="raw data", ylim=c(0, 4)) plot(diff(y), main="diff", pch=4, ylim=c(-2, 2)) plot(y ~ as.factor(as.integer(x/10)))
Clearly, the derivative is not constant and also decreasing. So I think exponential model might be a good fit.
However, one interesting thing here is the longer the time goes since the release.. the less dispersive the data is. In another way, when phone first released. People started selling used phones, and since the value is the highest, say $700.
They can possibly sell at 600 USD or even 300 USD if they want. But 3 years later, the phone value is much lower, say even a new phone is only $200, then when they sell old phones, the prices are probably at the range of 100~200, a much narrowed band.
In my scenario, I am more interested in the residual value in a longer term, which is at the narrowed band.
Here is my question:
- should I only look at the attenuation coefficient, the b from
Exp(b*x)for different types of phones... and predict the new b for the phone that I am going to predict based on all the data that I have.
PhoneModel b iPhone3 -0.04 iPhone4 -0.05 iPhone5 -0.03 iPhone6 TBD
- or should I only look at the time period that I am interested in. say 2 ~ 3 years (or 36 months time point) and do the modeling in that range since the data is much narrowed.. To avoid the dispersion brought by the 0 ~ 2 years data..
PhoneModel residualRatio iPhone3 20% iPhone4 25% iPhone5 30% iPhone6 TBD
Again, I am trying to predict the long term residual value of a product with only the releasing price.