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