[R-SIG-Finance] LPPL model for bubble burst forcasting
Wind
windspeedo99 at gmail.com
Tue Sep 22 15:02:50 CEST 2009
No furthure progress. In July, I just calculate the model with genoud in
the rgenoud package, with the same codes for LPPL function I have shared in
the list. Today I just found the codes and run it against the S&P 500. I
run genoud ten times for about 20 minutes. Though the parameters may be
not within the range that LPPL papers defined, the curve fitting is OK. I
received your email while studying the graph. So the graph is attached.
It says that S&P would begin correction after Sept. Just for fun.
Actually the LPPL should be applied with rolling window, and parameters
meeting some creterion. It would be very time consuming for genoud.
wind
On Tue, Sep 22, 2009 at 3:23 PM, Mark Breman <breman.mark at gmail.com> wrote:
> Hello Wind,
> I was wondering if you made any progress on the R implementation of the
> model, and if you could/would be willing to share what you got so far?
>
> Regards,
>
> -Mark-
>
> 2009/7/24 Wind <windspeedo99 at gmail.com>
>
>> Since I am not good at coding or statistics, genetic algo has been used
>> instead of tabu search. Package rgenoud is great and idiot proof.
>>
>> Attached is the latest analysis on SSEC index, the equity market index of
>> mainland China. genoud() has been run for 10 times, generating 10 fits.
>> The residuals are all stationary according to ADF test from package urca.
>> But the time window setting is subjective and maybe some minor problems on
>> parameter conditions such as omega and C. So, just for fun.
>>
>> Thanks for all the encouragement and help from the list. And thanks for
>> the detailed instructions on statistics issues by one of the author on LPPL,
>> Dr. Lin.
>>
>> wind
>>
>> On Mon, Jul 20, 2009 at 9:22 PM, Brian G. Peterson <brian at braverock.com>wrote:
>>
>>> Glad to see you're making progress on this problem.
>>>
>>> This paper
>>> http://www.diegm.uniud.it/satt/papers/DiSc06b.pdf
>>>
>>> implements a tabu search in R, though they didn't publish their code.
>>> You might want to contact them for the implementation and permission to
>>> share their tabu search algorithm/code with the R community.
>>>
>>> They also reference an R package called RACE by this gentleman:
>>> http://iridia.ulb.ac.be/~mbiro/
>>> that they use for evaluating the solution.
>>>
>>> More generally, from my limited understanding, tabu search is an
>>> extension and refinement of simulated annealing approaches easily
>>> implemented in R. In brief the approach is to take your best 'n' solutions
>>> from a random space search, and then search "near" those solutions.
>>> Simulated annealing and its close cousins have a lot of benefits in
>>> finance, where a single true optima from a closed form problem is not likely
>>> to be available. I personally have rarely found 'optim' to be usable for my
>>> problem space, and have had to use other solvers for practical problems in
>>> finance.
>>>
>>> Regards,
>>>
>>> - Brian
>>>
>>>
>>> Wind wrote:
>>>
>>>> Some progress. The LPPL curve could be plotted with the following
>>>> codes.
>>>> The problem now is how to get the best fit parameters.
>>>> Some researchers use python or matlab for LPPL calibrating. It
>>>> seems that some of them prefer tabu search for optimums locating. It
>>>> seems that there's still no general function for tabu search in R.
>>>> At the end of codes, I give the possible parameter combinations to be
>>>> searched in, maybe there are other functions for optimum searching in
>>>> R.
>>>> Any suggestion would be appreciated.
>>>>
>>>>
>>>> ## Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the
>>>> Financial and Economic Crisis
>>>> ## http://arxiv.org/abs/0905.0220
>>>> ## Fig. 23 S&P500 index (in logarithmic scale)in Page 39
>>>>
>>>>
>>>> library(quantmod)
>>>>
>>>> LPPL1<-function(p,dtc=20,alpha=0.35,omega=0.1,phi=1)
>>>> {
>>>> #function in page 26 of http://arxiv.org/abs/0905.0220
>>>> #the basic form of LPPL
>>>> dtc=abs(floor(dtc))
>>>> tc<-length(p)+dtc
>>>> dt<-abs(tc-(1:length(p)))
>>>>
>>>> x1<-dt^alpha
>>>> x2<-(dt^alpha)*cos(omega*log(dt)+phi)
>>>>
>>>> f<-lm(log(p) ~ x1+x2)
>>>>
>>>>
>>>> f$para<-list(recno=dim(f$model)[1],dtc=dtc,alpha=alpha,omega=omega,phi=phi,sigma=summary(f)$sigma)
>>>> return(f)
>>>> }
>>>>
>>>> opt.lppl<-function(x)
>>>> {
>>>> #derived function for optim
>>>>
>>>> return(LPPL1(p,dtc=x[1],alpha=x[2],omega=x[3],phi=x[4])$para$sigma)
>>>> }
>>>>
>>>> LPPL1.x<-function(lpplf,pt=100)
>>>> {
>>>> #x axis for predicting
>>>> dt<-abs((lpplf$recno+lpplf$dtc)-(1:(lpplf$recno+lpplf$dtc+pt)))
>>>> dt[dt==0]<-0.5
>>>>
>>>> x1<-dt^lpplf$alpha
>>>> x2<-(dt^lpplf$alpha)*cos(lpplf$omega*log(dt)+lpplf$phi)
>>>> return(list(x1=x1,x2=x2))
>>>>
>>>> }
>>>>
>>>> #get the SP500 index
>>>>
>>>> pr<-getSymbols("^GSPC",auto.assign=FALSE,from="2003-10-1",to="2007-05-16")[,4]
>>>> p<-as.numeric(pr)
>>>>
>>>>
>>>> plot(p,type="l",log="y",xlim=c(0,length(p)+100),ylim=c(min(p),max(p)*1.2))
>>>> abline(v=length(p),col="green")
>>>>
>>>> #something like the Fig. 23 in Page 39 of
>>>> http://arxiv.org/abs/0905.0220
>>>> #but obviously the result is not calibrated well
>>>> #using optim like this can not calibrate the LPPL model
>>>> opts<-sapply(seq(1,50,10),function(x){
>>>> o<-optim(c(x,0.6,20,1),opt.lppl)
>>>>
>>>> f3<-LPPL1(p,dtc=o$par[1],alpha=o$par[2],omega=o$par[3],phi=o$par[4])
>>>> xp<-LPPL1.x(f3$para,200)
>>>> f3p<-predict(f3,data.frame(x1=xp$x1,x2=xp$x2))
>>>> lines(exp(f3p),col="blue")
>>>> lines(exp(fitted(f3)),col="red")
>>>> f3$para
>>>> })
>>>>
>>>>
>>>>
>>>> ##crash point after dtc days
>>>> dtc<-seq(1,100,1)
>>>>
>>>> ##appropraite range of the parametes of LPPL
>>>> ##according to Dr. W.X. Zhou's new book which is in Chinese
>>>> ##the increments of the sequences are added according to my own judement
>>>> alpha<-seq(0.01,1.2,0.1)
>>>> omega<-seq(0,40,1)
>>>> phi<-seq(0,7,0.1)
>>>>
>>>> ##millions possible combinations
>>>> #complete test would be difficult
>>>> para<-expand.grid(dtc=dtc,alpha=alpha,omega=omega,phi=phi)
>>>> dim(para)
>>>>
>>>> system.time(sigs<-apply(para[1:100,],1,function(x){LPPL1(p,dtc=x[1],alpha=x[2],omega=x[3],phi=x[4])$para$sigma}))
>>>>
>>>> ##methods for minimum sigma searching within the parameter combinations
>>>> ##not implemented yet
>>>>
>>>>
>>>> wind
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> On Thu, Jul 16, 2009 at 9:25 PM, Brian G. Peterson<brian at braverock.com>
>>>> wrote:
>>>>
>>>>
>>>>> So first, using your real name and ideally your professional identity,
>>>>> ask
>>>>> for the python code. Better yet, get an academic buddy to do it.
>>>>> Usually
>>>>> getting access to the code isn't too tough. Mention things like
>>>>> "repeatable
>>>>> research" and "collaboration" in your email. Two of the authors
>>>>> publish
>>>>> their email addresses in one of the papers you reference, so contacting
>>>>> them
>>>>> should be easy.
>>>>>
>>>>> Next port the python code to R.
>>>>>
>>>>> If you can't do that, then replicate the model in R "from scratch". A
>>>>> trivial scan of the paper in question lends several techniques that are
>>>>> well
>>>>> covered in R: AR, GARCH, power laws, linear regression, stochastic
>>>>> discount
>>>>> factor, Ornstein-Uhlenbeck, etc.
>>>>> There are volumes of information available on these topics from within
>>>>> R, in
>>>>> numerous books, and in the archives of this mailing list and r-help.
>>>>>
>>>>> You're going to have to do your replication in pieces, probably
>>>>> starting
>>>>> with their implementation of the log periodic power law (LPPL), for
>>>>> which I
>>>>> do not believe there is an existing direct analogue in R though all the
>>>>> component parts necessary to replicate it should be readily available.
>>>>>
>>>>> As you work on each step of the replication, share your code with this
>>>>> list
>>>>> and the problems you are having with a particular step. Ask specific,
>>>>> directed questions with code to back them up. Someone will likely help
>>>>> you
>>>>> solve the specific problem.
>>>>>
>>>>> In R generally, it is not necessary that you be able to *do* the math
>>>>> (think
>>>>> pencil and paper), but if you plan to replicate published work, it will
>>>>> be
>>>>> necessary to *understand* at least some of how the math works, and to
>>>>> be
>>>>> able to pick out the names of techniques that you can search for an
>>>>> utilize.
>>>>>
>>>>> Basically, I'm recommending that you (specifically) and others (more
>>>>> generally) should share the process of replicating a technique like
>>>>> this, as
>>>>> well as the final product, to give all the rest of us who are likely to
>>>>> be
>>>>> helping "you" get all this done. quid pro quo.
>>>>>
>>>>> Cheers,
>>>>>
>>>>> - Brian
>>>>>
>>>>>
>>>>> --
>>>>> Brian G. Peterson
>>>>> http://braverock.com/brian/
>>>>> Ph: 773-459-4973
>>>>> IM: bgpbraverock
>>>>>
>>>>>
>>>>>
>>>>> Wind wrote:
>>>>>
>>>>>
>>>>>> Prof. Sornette has spent years forcasting bubble burst with
>>>>>> "log-periodic power law". The latest paper gives "a
>>>>>> self-consistent model for explosive financial bubbles, which combines
>>>>>> a mean-reverting volatility process and a stochastic conditional
>>>>>> return which reflects nonlinear positive feedbacks and continuous
>>>>>> updates of the investors' beliefs and sentiments."
>>>>>>
>>>>>> And his latest predicting is the burst of Chinese equity bubble at
>>>>>> the end of July. http://arxiv.org/abs/0907.1827
>>>>>>
>>>>>> While waiting to see the result, I wonder whether it is possible to
>>>>>> replicate the forcast with R. The model is in the page 10 of the "A
>>>>>> Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing
>>>>>> Residuals", http://arxiv.org/abs/0905.0128 . The output chart is
>>>>>> in the page 3 of "The Chinese Equity Bubble: Ready to Burst",
>>>>>> http://arxiv.org/abs/0907.1827 . I guess the authors of the latter
>>>>>> paper use the same model as described in the first paper.
>>>>>>
>>>>>> Because statistics is still challenging for me though I could use R
>>>>>> for basic data manipulations, I wonder which package or function
>>>>>> would be necessary to implement the model in the paper. The model
>>>>>> seems more complicated than the models in the R tutorials for me.
>>>>>> By the way, the author of the paper used Python and the codes are
>>>>>> private.
>>>>>>
>>>>>> Any suggestion would be highly appreciated.
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>
>>> --
>>> Brian G. Peterson
>>> http://braverock.com/brian/
>>> Ph: 773-459-4973
>>> IM: bgpbraverock
>>>
>>>
>>
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>
>
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