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Posted: **Mon Jun 08, 2015 7:36 am**

Hi

I'm interested in estimating time varying variances and covariances using a simple two sided gaussian/normal kernel function. However it is not one of the built-in options.

Can anyone direct me towards how to specify the "User Kernel Vector" in order to do this if possible? Or pointers on how to implement a program that may do it.

In my case I'm using daily data and want a Gaussian Kernel with a bandwidth of 250days.

Best regards,
Thomas

Posted: **Wed Jun 10, 2015 8:30 am**

I have tried to come up with a program to calculate the time varying standard deviation of a return series. Code is below.

It seems to do the job pretty good, however it's incredibly inefficient. I have over 9000 observations leading to around 170 million iterations. Execution time is around 10-12mins on my laptop per series and ultimately I have hundreds of series I need to run.

Is there no other way to do this more efficiently? I've been trying to think of a way to weight each observation by a full normal distribution from the built-in function, but can't come up with a solution.

Code: Select all

stom(g_r, ret)

!obs = @rows(ret)
!h = 250/!obs
vector(!obs) kernelvec

for !i = 1 to !obs
	!tau = !i / !obs
	!sum = 0
	!kerndev = 0
	for !j = 1 to !obs
		
		!z = !j/!obs - !tau
		!kernel = (1 / sqr(  2 * @acos(-1)  ) * exp( - (  !z  /  !h  )  ^  2  /  2)) / (!h*!obs)
		!sum = !sum + !kernel
	next !j
	for !j = 1 to !obs
		!z = !j/!obs - !tau
		!kernel = (1 / sqr(  2 * @acos(-1)  ) * exp( - (  !z  /  !h  )  ^  2  /  2)) / (!h*!obs) / !sum
		!kerndev = !kerndev + !kernel * ret(!j) ^2
	next !i

	kernelvec(!i) = sqr(!kerndev)
next !i

mtos(kernelvec, kernel250)

Posted: **Wed Jun 10, 2015 1:10 pm**

Without commenting on the desired calculations...

Here's a snippet which simulates data for 10000 observations, performs the desired calculations, and times the process. Note that where possible I use the series generation tools rather than observation loops. Looking at it right now, are a couple of other optimizations we could do, but this should be good enough to hold you over.

Code: Select all


rndseed 1
workfile u 10000
series ret = nrnd
series ret2 = ret^2

tic

!obs = @obs(ret)
!h = 250/!obs

series rollstd

for !i=1 to @obs(ret)
	series z = (@trend+1-!i)/!obs
	series w = @dnorm(z/!h)
	!kernel = @inner(w, ret2) / @sum(w)
	smpl if (@trend+1=!i)
	rollstd = @sqrt(!kernel)
	smpl @all
next

!elapsed = @toc
table(1,1) time
time(1,1) = !elapsed

The original code with the same simulated data process and a timer

Code: Select all


rndseed 1
workfile u 10000
series g_r = nrnd


tic
stom(g_r, ret)

!obs = @rows(ret)
!h = 250/!obs
vector(!obs) kernelvec


for !i = 1 to !obs
   !tau = !i / !obs
   !sum = 0
   !kerndev = 0
   for !j = 1 to !obs
   
      !z = !j/!obs - !tau
      !kernel = (1 / sqr(  2 * @acos(-1)  ) * exp( - (  !z  /  !h  )  ^  2  /  2)) / (!h*!obs)
      !sum = !sum + !kernel
   next !j
   for !j = 1 to !obs
      !z = !j/!obs - !tau
      !kernel = (1 / sqr(  2 * @acos(-1)  ) * exp( - (  !z  /  !h  )  ^  2  /  2)) / (!h*!obs) / !sum
      !kerndev = !kerndev + !kernel * ret(!j) ^2
   next !i

   kernelvec(!i) = sqr(!kerndev)

next !i

mtos(kernelvec, kernel250)
!elapsed = @toc
table(1,1) time

Timings will obviously vary, but on my computer the former took 9.1 seconds, while the original took 267.6 seconds.

Posted: **Wed Jun 10, 2015 3:40 pm**

Thanks a bunch Glenn! Took a bit to figure out how it worked, but its a genious solution.

Reduced my complete execution time by a factor 115.

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