This is my first time at stack exchange, hence please pardon me if I miss something. I have multiple questions and I am tearing myself as curve-fitting and estimation is foreign land to me, I am ready to learn given directions and ideas.
I am trying to model liquidity (ease of trading) of a security. In my case the security has very sparse trading. Once it is issued, trading is quite active and dies out then. After some years it may again have some hectic trading and becomes inactive for the rest of its life. Typically trading marketshare of the security depends on its age and outstanding amount. A sample datafile can be found here. In the data file ms_vol is the marketshare based on volume, ms_trds is the marketshare based on number of trades, osd is the outstanding amount and age is the age of the security. A pdf of ms_vol vs age plot can be found here.
A research note has modeled such relationship as
$$ MS = \beta_1 \exp[-\beta_2 (Age-\beta_3)^2] + \beta_4 \beta_5^{Age} $$
All the $\beta$'s are > 0. This models only one hump, not two. I tried to use nls in R unsuccessfully with the following code and error message
dfX = read.csv("trading.csv")
mod_msV = nls(
ms_vol ~ beta1*exp(-beta2*(age-beta3)^2) + beta4*beta5^age,
start=list(beta1=0.3, beta2=0.83, beta3=0.55, beta4=0.5, beta5=0.5),
data=dfX, trace=T)
29310.88 : 0.30 0.83 0.55 0.50 0.50
Error in numericDeriv(form[[3L]], names(ind), env) :
Missing value or an infinity produced when evaluating the model
Following are my questions:
How do I extend the above model to incorporate two humps which may occur some age apart?
The above model has only one independent variable, age. In my case osd is another variable I would like to incorporate. ms_vol behaves with osd just like age, though it may not show 2 humps.
How do I estimate teh parameters? The error message by nls baffles me completely. My hunch is it may be because of the starting values. I have tried several sets but all of them lead to same error message.
Somewhere I read about "Flowering Curve" and it may be a curve of choice. I have tried unsuccessfully locating info on it, but without success. Is there any other curve I can try out.
Also how do I begin learning about this topic being a non-statistician?
I am sorry for asking too many questions. I am at the edge of sanity. Please help me with this.