[R] arma: what is the meaning of Pr(>|t|)?

[Alberto Monteiro]

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.

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)

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