





Hi,

I have a time series (say "x") of 13 years showing an evident increase. I want to exclude two observations (the fourth and 10th), so I do:

> trend.test(x[-c(4,10)])

where:

> x[-c(4,10)]
 [1]    7   37   79   72  197  385  636  705  700 1500 1900

and I get:

    Spearman's rank correlation rho

data:  x[-c(4, 10)] and time(x[-c(4, 10)]) 
S = 4, p-value < 2.2e-16
alternative hypothesis: true rho is not equal to 0 
sample estimates:
      rho 
0.9818182 

Very strong positive correlation! the "x" is increasing

Now, I would like to resample this time series because I have others time series where the trend is more "uncertain" and the sample size is still small.
I read "Resampling Methods in R: The boot Package (ISSN 1609-3631)" and I believe that a way of doing it is by a block bootstrap that allows to deal with the autocorrelation (I know that some of my time series show autocorrelation, lag=1).

I used "trend.test" function (library=pastecs) and I did:

>trend.x=trend.test(x[-c(4,10)],R=999)
>trend.x
>trend.x$p.value
>plot(trend.x)
 
And I get:

> trend.x=trend.test(x[-c(4,10)],R=999)
> trend.x

BLOCK BOOTSTRAP FOR TIME SERIES

Fixed Block Length of 1 

Call:
tsboot(tseries = x, statistic = test.trend, R = R, l = 1, sim = "fixed")


Bootstrap Statistics :
     original     bias    std. error
t1* 0.9818182 -0.9844001   0.3272114
> trend.x$p.value
[1] 0

I suppose that the problem arises from the length of the block (1) and in this way I get a rho=0, (nevertheless I don't understand how it is significant).
I would like to change the block length but I am not able to (I tried in several different ways but unsuccessfully).
So, two questions:
1) How can I change the block length?
2) In terms of block length and type of simulation (sim="fixed" or "geom"), what is the best way of doing it? 


Thanks in advance for any suggestion,
Best wishes

Simone

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