Moments calc by different methods do not match?

[dynare_usr]

Hello,

I am running Dynare 4.4.3 stoch_simul with option periods.
Then I compare correlation between two variables calculated with data in oo_.var
and compare the corr coef with that calculated with oo_.endo_simul.

For example:

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oo_.var(2,1)/(sqrt(oo_.var(2,2)) * sqrt(oo_.var(1,1)))

and

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corrcoef(oo_.endo_simul(2,:),oo_.endo_simul(1,:))

Since I am using periods option, both oo_.var & oo_.endo_simul contain simulated data but I obtain significantly different results (for some series the difference is about 0.2).

Am I missing anything?

[jpfeifer]

Please provide the full codes.

[dynare_usr]

I think I figured out what went wrong.

I used stoch_simul with option periods AND option hp_filter.
oo_.var saves filtered statistics, while
oo_.endo_simul saves simulated series before the HP filter.

Can you confirm, please?

A corollary question, after I run

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stoch_simul(hp_filter = 100, order = 1, irf = 1000, periods=10000)

the moments I obtain via

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oo_.var

are the same regardless of the number of periods, whereas the moments obtained via

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corrcoef(oo_.endo_simul(2,:),oo_.endo_simul(1,:))

vary with the number of periods. I tried from the range from 100 to 10^4. The difference can be as high as 0.04

Does it mean that oo_.var gives theoretical moments? I thought the manual says to the contrary:

oo_.var Contains theoretical variance if the periods option is not present (or an approximation thereof for
order=2), and empirical variance otherwise.

[jpfeifer]

1. Yes, if you specify a filter, the moments will be filtered, while the simulated series will be unfiltered
2. No, this should not be the case. Please provide the file to replicate the issue.

[dynare_usr]

I attached the files with minimal working examples

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stoch_simul(order=1, periods=1000);

and

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stoch_simul(order=1, periods=1000, hp_filter=100);

In this version, the difference between the correlations of C & Y are around 0.006 but it decreases with the length of the simulated series.

Also, for the HP-filtered version, I was wondering how Dynare filters the simulated series (with hp_filter option) so fast. If I conduct HP filtering of endo_simul by hand with periods=10000, it takes my computer to filter the series and to calculate the moments significantly longer than if I use Dynare's hp_filter option.
With periods = 100000, my PC runs into the curse of dimensionality.
I attached the HP filter code I use as well.

Thanks.

[jpfeifer]

When switching from 10000 to 1000 periods,

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oo_.var

goes from

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ans =

   0.000326615664192   0.000035416548315   0.000224502764851   0.000139894628857   0.000075319264576   0.000071830808337
   0.000035416548315   0.000021236903551   0.000049779041118   0.000027336117315   0.000001851174164  -0.000020538216304
   0.000224502764851   0.000049779041118   0.001170764900180   0.000081945259818   0.000042536905984   0.000075228986918
   0.000139894628857   0.000027336117315   0.000081945259818   0.000069473878539   0.000027843140250   0.000008756607555
   0.000075319264576   0.000001851174164   0.000042536905984   0.000027843140250   0.000019662155193   0.000026849167137
   0.000071830808337  -0.000020538216304   0.000075228986918   0.000008756607555   0.000026849167137   0.000066544587358
   

to

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ans =

   0.000334544718752   0.000039518537012   0.000239060495493   0.000145415558713   0.000075970615395   0.000068595256611
   0.000039518537012   0.000021475606432   0.000061794114533   0.000028638576743   0.000002871940263  -0.000018648095685
   0.000239060495493   0.000061794114533   0.001217896764845   0.000094765000760   0.000042104863384   0.000062938707817
   0.000145415558713   0.000028638576743   0.000094765000760   0.000072069499163   0.000028860770924   0.000009374071833
   0.000075970615395   0.000002871940263   0.000042104863384   0.000028860770924   0.000019467398574   0.000025289415214
   0.000068595256611  -0.000018648095685   0.000062938707817   0.000009374071833   0.000025289415214   0.000061267383943


showing that the simulation correctly works.

Regarding your second question: you are using the most inefficient version of the HP-filter you can program. It does not make use of the sparsity of HP-filter matrix and uses an explicit inverse. You might want to use Dynare's

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sample_hp_filter.m

instead

[dynare_usr]

Thank your for pointing my attention to sample_hp_filter.m, Johannes.

Per oo_.var. Please correct me if I am wrong but I think the comparison of oo_.var from simulations with different # of periods shows that empirical moments vary with the length of the series. Which is fine.

However, I am trying to understand why, given a certain number of periods, the values correlations calculated from oo_.var and oo_.endo_simul do not coincide.
for example, after

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stoch_simul(order=1, periods=1000);

I obtain the following correlations between the first two variables:

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OOVar =
    0.8910
CorrCoef =
    1.0000    0.8847
    0.8847    1.0000
difference between oo_.var & oo_.endo_simul:
ans =
    0.0063

[jpfeifer]

That's because Dynare drops

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options_.drop

periods of burnin when computing the moments

[dynare_usr]

Great, thanks.