On Wed, 20 Aug 2008, Prof Brian Ripley wrote:
On Wed, 20 Aug 2008, Alberto Monteiro wrote:
In the summary of the output of arma, there's a number Pr(>|t|), however, I
don't know what is its meaning - at least, it doesn't _seem_ to be a
Student's t distribution.
It is using asymptotic normality. There is no exact theory. Who mentioned
Student's t?
Reproducible test case:
x <- c(0.5, sin(1:9))
reg <- arma(x, c(1,0))
summary(reg)
<output>
Call:
arma(x = x, order = c(1, 0))
Model:
ARMA(1,0)
Residuals:
Min 1Q Median 3Q Max
-0.9217 -0.4915 0.2254 0.4580 0.7481
Coefficient(s):
Estimate Std. Error t value Pr(>|t|)
ar1 0.6089 0.2490 2.446 0.0145 *
intercept 0.0790 0.1815 0.435 0.6634
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Fit:
sigma^2 estimated as 0.3348, Conditional Sum-of-Squares = 2.68, AIC =
21.44
</output>
Now, 2.446 is 0.6089 / 0.2490, but 0.0145 is not
2 * (1 - pt(2.446, df = 7))
(I think there are seven degrees of freedom: the first value of
the series x is deterministic, and two degrees are lost in the
estimation of ar1 and intercept)
Why is the first value deterministic? This is not a conditional mle (see the
help page).
It is a conditional SSq, so perhaps you meant 'held constant'?
What am I misunderstanding?
BTW, a similar example:
x <- 1:10
y <- sin(x)
reg <- lm(y ~ x)
summary(reg)
will give a t-value for 'x' = 0.704 with P(>|t|) = 0.501,
which is 2 * (1 - pt(0.704, df=8))
Alberto Monteiro
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--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
