[R-SIG-Finance] Does R have a formal test for long vs short memory process?

[Spencer Graves]

      If it were my problem, I would start by writing probability models 
for long and short memory processes.  I would cast them in a Bayesian 
framework with plausible priors over the unknown parameters;  with 
multiple series, it should be easy enough to get plausible priors.  Then 
I would test one vs. the other using a likelihood ratio of simple 
hypothesis (i.e., the marginal with all the parameters integrated out 
using the posterior distribution) vs. simple alternative.  I could do 
that with Markov Chain Monte Carlo if I didn't feel comfortable with any 
other approximation. 

      The Neyman-Pearson lemma says that the most powerful test of 
simple vs. simple is the likelihood ratio.  I could get p-values by 
Monte Carlo if by nothing else. 

      I'd start with a literature search.  The references I know about 
that are in Tsay (2005) Analysis of Financial Time Series, 2nd ed. 
(Wiley):  Section 2.11 discusses long-memory models, and section 3.13 
describes long-memory stochastic volatility models.  The data sets 
described in that book are all available in the 'FinTS' package, and 
'scripts\ch02.R' includes R code to recreate the figures in chapter 2 
(including Figure 2.22 pertaining to section 2.11). 

      Hope this helps. 
      Spencer Graves

tom soyer wrote:
> Thanks Brian. I wanted to test if a data series has long memory or short
> memory. By short memory process, I meant that their acf declines
> exponentially. For long memory processes, their acf declines very slowly. I
> was thinking that if such a test is available, then one could use it to help
> determine how to model a series, e.g. ARMA vs. GARCH, etc. One could make
> the determination based on a visual examination of the acf correllogram, but
> the problem with this method is that it's not quantitative and therefore not
> automatable. Does that make sense?
>
>
> On 1/31/08, Brian G. Peterson <brian at braverock.com> wrote:
>   
>> tom soyer wrote:
>>     
>>> Does anyone know if there are formal tests for long vs short memory
>>> processes? i.e., quantitative tests instead of visual examination of
>>> corellograms produced by acf.
>>>       
>> Perhaps you could be a bit more specific about what you want?
>>
>> In addition to the ACF chart, the acf calculation calculates confidence
>> intervals for significance.  The summary() method on the results of an
>> acf will tell you what the values for these confidence intervals are.
>>
>> There are also several other quantitative methods that have been
>> proposed for measuring and dealing with acf and partial acf in financial
>> time series.  If you have one of these methods in mind, perhaps we can
>> see if they are either already implemented or could be implemented easily.
>>
>> Regards,
>>
>>    - Brian
>>
>>     
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