Full_Name: Stan Miles
Version: 1.5.0.
OS: Windows 2000 Server
Submission from: (NULL) (130.63.74.220)
Short Description of the Problem:
I use R to simulate a random variable, with mean 0.14 and variance 0.2 . I
simulate 20 sets, 30000 realizations/set.
I take the average of each set, and all 20 of the averages are
much higher than 0.14. In fact, they are All about 2-3 stdev higher.
It seems that R is not generating the random variable with the mean I ask for.
The Details:
I simulate Prices [Pt] and Returns that are defined as
Rt = [P(t)-P(t-1)]/P(t-1). The returns have Normal distribution
=> Rt is has N(mu=0.14, sigmaSquared=0.2) distribution.
To do the task above, I use the following files:
c:\ProgramFiles\R\rw1050\Code1.txt
consists of the following text:
===================gpsim1_function(t,runs,mu,delta,stdev){
jold=0
xx_rep(0,t*runs)
for(i in 1:runs){
ind=(i-1)*t
xx[ind+1]=1
for(j in 2:t) {
xx[ind+j]_xx[ind+j-1]*
exp(rnorm(n=1,mean=mu*delta*delta,sd=stdev*delta))
}
}
xx
}
======================
File "experiment4commands.txt" has text:
source("code1.txt")
aa=gpsim1(30000,1,0.14,0.052342392,0.4472135955)
sink("experiment4mu14z20Path1.txt")
for(i in 1:length(aa)){print(aa[i])}
sink()
source("code1.txt")
aa=gpsim1(30000,1,0.14,0.052342392,0.4472135955)
sink("experiment4mu14z20Path2.txt")
for(i in 1:length(aa)){print(aa[i])}
sink()
:
:
:
source("code1.txt")
aa=gpsim1(30000,1,0.14,0.052342392,0.4472135955)
sink("experiment4mu14z20Path20.txt")
for(i in 1:length(aa)){print(aa[i])}
sink()
========================{Above, 0.052342392 = 1/365, it is my discretization
factor.}
I paste the text from the "experiment4commands.txt" file into R.
I now open each of the resulting 20 files in Excel. The output [with
variable Pt] is located in column B. To get back Rt, I paste
the following formula into cells C2:C30000 -
Ci = [B(i)-B(i-1)]/B(i-1).
My discretization factor was 1/365, thus, when I take the Average
[and the Variance] of cells C2:C30000, I also have to multiply this
number by 365, to get back the annual Rt.
I then made a table of the resulting 365*Average(C2:C30000), for each
of the 20 Sets that I have simulated using the methodology described above.
Set 365*Average(C2:C30000) for the set
1 0.284948
2 0.238827892
3 0.176492
4 0.242007
5 0.263882
6 0.211672
7 0.203536
8 0.19211
9 0.225185
10 0.234478
11 0.272792
12 0.205158
13 0.189349
14 0.222317
15 0.220652
16 0.165553
17 0.294211
18 0.333488
19 0.147971
20 0.290742
The average of the realizations of mu [true value = 0.14] over
20 paths, each with 30000 observations, is about 0.23.
For this case, daily mu = mu over each algorithm step
is 0.14/365 = 0.0003835616438
The daily variance is 0.2/365 = 0.0005479452055
However, according to statistics, as the number of observations increases
variance will fall. In particular, for 30,000 observations, the
StDev is calculated as follows:
SQRT(0.2/365)/SQRT(30000) = 0.0001351474 = {1 STDEV}
The average of the values in the table above, 0.23, is
[(0.23/365) - (0.14/365)]/0.0001351474 = 1.824 StDeviations above the mean.
As you can see Most of the 20 sets had realized values about 2-3 StDeviations
higher than the mean.
Something is wrong.
Thank you for considering this bug report.