Does R have a formal test for long vs short memory process?

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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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

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