Hello, R users:
 
I am interested in nonparametric estimation of time-varying beta using additive model, 
following "Estimating Beta-Coefficients of German Stock Data: A Non-Parametric Approach" 
European Journal of Finance, September 2007.
 
Authors suggest using gam in library(mgcv) to estimate time varying beta 
of i-th stock (= beta_i + beta_i (t) ) in the following model:
 
R_it = alpha_i + beta_i * R_Mt + beta_i (t) * R_Mt + e_it
 
They show some codes used for tables and graphs of the paper 
in the appendix as follows:
 
> output &lt;- gam(Rj бн RM + s(t, by=RM))
 
where t is the time trend. My questions about this code are:
 
1. When I use their code and plot the time varying smooth s(t) by "plot(output)", 
It plots only beta_i (t), not beta_i + beta_i (t). 
 
But when I am using "output &lt;- gam(Rj бн s(t, by=RM))", It plots OK.
Is this the correct beta?
 
2. I cannot plot varying beta with x-axis of year.
(I am using zoo object of monthly stock returns) 
How do I set up the time trend t for this?
 
3. How do I retrieve the fitted time-varying beta?
 
4. Do you have any recommendation of R nonparametric function
for estimating time-varying market beta?
 
Thanks in advance.
SW KIM
 

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