[R] Hyperbolic code in R studio ?

[Rui Barradas]

Hello,

I agree with Jeff and also:

I don't want to be snarky but can't resit, the question's subject title 
is provocative.

A hyperbole is the figure of speech that consists of exaggeration of 
expression, enlarging the true dimension of things. In simplified terms, 
hyperbole is the overtly exaggerated expression of an idea.


*Minimal* reproducible examples must be, well, minimal.
Do you really need all that code to show you are finding the generation 
of a hyperbolic function difficult? If the question is on how to create 
a function, why several functions?

Às 15:45 de 21/12/19, Jeff Newmiller escreveu:
> It is not so much a question of "bother us" as it is of "following the Posting Guide" and "not interfering with an educational institution by helping to cheat".
> 
> Please read the Posting Guide (espm about homework help) and next time change your mail program settings so you send plain text to the list (HTML formatted email can become unreadable on our end of your transmission).
> 
> On December 21, 2019 1:33:16 AM PST, Aissata Kagnassi <tatikagnassi using gmail.com> wrote:
>> Good morning everyone,
>>
>>
>>
>> I don't want to bother you. I'm new at using R. :)
>>
>> 1. I was wondering if someone could help me figure out why I can't
>> generate
>> the code to get a hyperbolic function.
>>
>>
>>
>> 2. My second question is, I generated the code. I don't have any
>> problem
>> with other distributions but I still can't get the graphics displayed.
>>
>>
>>
>> Here are the instructions for my exercise and here is the code I used:
>>
>>
>>
>> **Instructions**
>>
>> Project: hereafter the series of financial returns will be refered to
>> as yt
>> and the series of fundamentals as xt. Here are the questions you need
>> to
>> raise and answer:
>>
>> Part 1: maximum likelihood estimation, student test and goodness of
>> fit.
>>
>> 1. Consider the following model:
>>
>> yt =μ+σεt, with εt a disturbance such that E[εt] = 0 and V[εt] = 1.
>>
>> *Estimate the parameters of the following distributions by maximum
>> likelihood using the Yt:*
>>
>> • Gaussian distribution N(0,1)
>>
>> • Student-t distribution with parameter ν
>>
>> • A mixture of Gaussian distribution MN(φ, μ1, σ1, μ2, σ2)
>>
>> • A generalized hyperbolic distribution GH(λ, α, β, δ, μ).
>>
>>
>>
>> 2. *Test the parameters for their significance using a Student test.
>> Are
>> all the parameters statistically significant?*
>>
>>
>>
>> **My code:**
>>
>> For the first three distributions, I answered well for questions one
>> and
>> two which are in italics. But I have a problem with the last one.
>>
>> library(readxl)
>>
>> Data <- read_excel("Data_project.xlsx", sheet = 2, skip = 5, col_names
>> =
>> FALSE)
>>
>> #y variable to explain, Nikkei 225 index
>>
>> y <- Data[16]
>>
>> # x variable explanatory variable, Australian Dollar vs. US Dollar
>>
>> x <- Data[30]
>>
>>
>>
>> returns_y = diff(as.matrix(log(y)),1)
>>
>> returns_x = diff(as.matrix(log(x)),1)
>>
>> returnsy_std = scale(returns_y)
>>
>>
>>
>> #1. Estimate the parameters by maximum likelihood
>>
>> #Gaussian distribution N(0, 1)
>>
>>
>>
>> mu=0
>>
>> sigma=0.1
>>
>> para0 = c(mu,sigma)
>>
>>
>>
>> loglikG<-function(para,returns_y)
>>
>> {
>>
>>   mu = para[1]
>>
>>   sigma =  para[2]
>>
>>   print(para)
>>
>> logl=sum(log(dnorm((returns_y-mu)/sigma, 0, 1)/sigma))
>>
>>   return(-logl)
>>
>> }
>>
>>
>>
>> loglikG(para0,returns_y)
>>
>> fit <- optim(para0, loglikG, gr=NULL, returns_y,
>> method="BFGS",hessian=T)
>>
>>
>>
>> paraopt<- fit[["par"]]
>>
>>
>>
>> Hessian = fit$hessian
>>
>> invh = solve(Hessian)
>>
>>
>>
>> t1= sqrt(invh[1,1])
>>
>> t2=sqrt(invh[2,2])
>>
>> testzmu = paraopt[1]/t1
>>
>> testzvar = paraopt[2]/t2
>>
>> print(testzmu)
>>
>> print(testzvar)
>>
>>
>>
>>
>>
>> #T-student
>>
>>
>>
>> para_t=c(0,0.012,5)
>>
>>
>>
>> loglikt <- function(para,returns_y){
>>
>>   mut=para[1]
>>
>>   sigmat=para[2]
>>
>>   nu=para[3]
>>
>> m=-sum(log(dt((returns_y-mut)/sigmat, df=nu)/sigmat))
>>
>>
>>
>>   return(m)
>>
>> }
>>
>>
>>
>> loglikt(para_t,returns_y)
>>
>>
>>
>> output_t= optim(para_t, loglikt, gr=NULL, returns_y, method="BFGS",
>> hessian=TRUE)
>>
>> paraopt_t <- output_t[["par"]]
>>
>>
>>
>> Hessian_t = output_t$hessian
>>
>> invh_t = solve(Hessian_t)
>>
>>
>>
>> t1_t= sqrt(invh_t[1,1])
>>
>> t2_t=sqrt(invh_t[2,2])
>>
>> t3_t= sqrt(invh_t[3,3])
>>
>> testzmu_t = paraopt_t[1]/t1_t
>>
>> testzvar_t = paraopt_t[2]/t2_t
>>
>> testznu_t = paraopt_t[3]/t3_t
>>
>> print(testzmu_t)
>>
>> print(testzvar_t)
>>
>> print(testznu_t)
>>
>>
>>
>> #Mixture of Gaussian finding initial values
>>
>> library(LaplacesDemon)
>>
>> eps = 0.001
>>
>> tolerance = 0.95
>>
>> paraMG = c(-0.02,0.03,0.6,0.8,0.7)
>>
>>
>>
>> likehoodMG <- function(para,returnsy_std)
>>
>> {
>>
>>   muM12 = para[1:2]
>>
>>   sigmaM12 = para[3:4]
>>
>>   phi = para[5]
>>
>>   p = c(phi,1-phi)
>>
>> LM=sum(log(dnormm(returnsy_std,muM12,sigmaM12,p=p)))
>>
>>   mean_w = p[1]*muM12[1] + p[2]*muM12[2]
>>
>>   var_w = p[1]*sqrt(sigmaM12[1]) + p[2]*sqrt(sigmaM12[2])
>>
>> if((abs(mean_w)>tolerance) || (abs(var_w-1)>tolerance)){
>>
>>     return(NaN)
>>
>>   }
>>
>>   return(-LM)
>>
>> }
>>
>>
>>
>> likehoodMG(paraMG,returnsy_std)
>>
>>
>>
>> outputMG = optim(paraMG, likehoodMG, gr=NULL, returnsy_std, method =
>> "L-BFGS-B", hessian=TRUE,
>>
>>                   lower = c(eps,eps,-Inf,-Inf,eps), upper =
>> c(Inf,Inf,Inf,Inf,1-eps))
>>
>>
>>
>> paraoptMG = outputMG[["par"]]
>>
>>
>>
>> #Mixture of Gaussian
>>
>> #(0.000345,0.023306)
>>
>> paraM
>> =c(0.000345,0.023306,0.0253514,0.0010000,0.8715856,2.7857329,0.9659020)
>>
>>
>>
>> likehoodM <- function(para,returns_y)
>>
>> {
>>
>>   muM1 = para[1]
>>
>>   sigmaM = para[2]
>>
>>   muM12 = para[3:4]
>>
>>   sigmaM12 = para[5:6]
>>
>>   phi = para[7]
>>
>>   p = c(phi,1-phi)
>>
>> LM=sum(log(dnormm((returns_y-muM1)/sigmaM,muM12,sigmaM12,p=p)/sigmaM))
>>
>>   return(-LM)
>>
>> }
>>
>>
>>
>> likehoodM(paraM,returns_y)
>>
>>
>>
>> outputM = optim(paraM, likehoodM, gr=NULL, returns_y, method =
>> "L-BFGS-B",
>> hessian=TRUE,
>>
>>                 lower = c(-Inf,eps,eps,eps,-Inf,-Inf,eps), upper =
>> c(Inf,Inf,Inf,Inf,Inf,Inf,1-eps))
>>
>>
>>
>> paraoptM = outputM[["par"]]
>>
>>
>>
>> HM = outputM[["hessian"]]
>>
>> invHM = solve(HM)
>>
>>
>>
>> tm1 = sqrt(invHM[1,1])
>>
>> tm2 = sqrt(invHM[2,2])
>>
>> tm3 = sqrt(invHM[3,3])
>>
>> tm4 = sqrt(invHM[4,4])
>>
>> tm5 = sqrt(invHM[5,5])
>>
>> tm6 = sqrt(invHM[6,6])
>>
>> tm7 = sqrt(invHM[7,7])
>>
>>
>>
>> testtmum = (paraoptM[1]-0)/tm1
>>
>> testtsigmam = paraoptM[2]/tm2
>>
>> testtmum1 = (paraoptM[3])/tm3
>>
>> testtmum2 = paraoptM[4]/tm4
>>
>> testtvarm1 = paraoptM[5]/tm5
>>
>> testtvarm2 = paraoptM[6]/tm6
>>
>> testtphi = paraoptM[7]/tm7
>>
>> print(testtmum)
>>
>> print(testtsigmam)
>>
>> print(testtmum1)
>>
>> print(testtmum2)
>>
>> print(testtvarm1)
>>
>> print(testtvarm2)
>>
>> print(testtphi)
>>
>>
>>
>> #A generalized hyperbolic distribution GH(??, ??, ??, ??, ?).
>>
>> library(readxl)
>>
>> Data <- read_excel("Data_project.xlsx", sheet = 2, skip = 5, col_names
>> =
>> FALSE)
>>
>> #y variable to explain, Nikkei 225 index
>>
>> y <- Data[16]
>>
>> # x variable explanatory variable, Australian Dollar vs. US Dollar
>>
>> x <- Data[30]
>>
>>
>>
>> returns_y = diff(as.matrix(log(y)),1)
>>
>> returns_x = diff(as.matrix(log(x)),1)
>>
>> returnsy_std = scale(returns_y)
>>
>>
>>
>>
>>
>> #A generalized hyperbolic distribution GH(??, ??, ??, ??, ?).
>>
>>
>>
>> library(ghyp)
>>
>>
>>
>> para_gh= c(-0.00002,0.005,1,0,1,0.1,0.1) # mu,delta,alpha,beta,lambda
>>
>>
>>
>> loglikGH <- function(para,returns_y){
>>
>>   mugh=para[1]
>>
>>   sigmagh=para[2]
>>
>>   alpha=para[3]
>>
>>   beta = para[4]
>>
>>   delta=para[5]
>>
>>   chi=para[6]
>>
>>   lamda=para[7]
>>
>>   if(delta < abs(chi)){
>>
>>     return(10000)
>>
>>   }else{
>>
>>    return(-sum(log(dghyp(((returns_y-mugh)/sigmagh),object =
>> ghyp(alpha,beta,delta,chi,lamda))/sigmagh)))
>>
>>   }
>>
>> }
>>
>>
>>
>>
>>
>> loglikGH(para_gh,returns_y)
>>
>>
>>
>> eps = 0.001
>>
>>
>>
>> outputGH= optim(para_gh, loglikGH, gr=NULL, returns_y, method =
>> "L-BFGS-B",
>> hessian=TRUE,
>>
>>                 lower = c(-Inf,eps,eps,eps,-Inf,-Inf,eps), upper =
>> c(Inf,Inf,Inf,Inf,Inf,Inf,Inf))
>>
>>
>>
>> paraoptGH = outputGH[["par"]]
>>
>>
>>
>> HGH = outputGH[["hessian"]]
>>
>> invHGM = solve(HGH)
>>
>> tm1_H = sqrt(invHGM[1,1])
>>
>> tm2_H = sqrt(invHGM[2,2])
>>
>> tm3_H = sqrt(invHGM[3,3])
>>
>> tm4_H = sqrt(invHGM[4,4])
>>
>> tm5_H = sqrt(invHGM[5,5])
>>
>> tm6_H = sqrt(invHGM[6,6])
>>
>> tm7_H = sqrt(invHGM[7,7])
>>
>>
>>
>> testtmuH = (paraoptGH[1]-0)/tm1_H
>>
>> testtsigmaH = paraoptGH[2]/tm2_H
>>
>> testtalpha = (paraoptGH[3])/tm3_H
>>
>> testtbetha = paraoptGH[4]/tm4_H
>>
>> testtdelta = paraoptGH[5]/tm5_H
>>
>> testtvchi = paraoptGH[6]/tm6_H
>>
>> testtlambda = paraoptGH[7]/tm7
>>
>>
>>
>> print(testtmuH)
>>
>> print(testtsigmaH)
>>
>> testtalpha
>>
>> testtbetha
>>
>> testtdelta
>>
>> testtvchi
>>
>> testtlambda
>>
>> 	[[alternative HTML version deleted]]
>>
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>