Folks,
I have a time-series of 875 readings of the weekly returns of a stock
market index (India's Nifty). I am interested in the AR(1)
coefficient. When I do arima(r, order=c(1,0,0)) I get a statistically
significant AR1 coefficient.
If we apply the ordinary bootstrap to this problem, this involves
sampling with replacement, which destroys the time-series
structure. Hence, if we do bootstrap inference (using the ordinary
bootstrap) we ought to get a 95% confidence interval which is roughly
symmetric about zero. Yes?
The program:
---------------------------------------------------------------------------
library(boot)
AR1.boot <- function(x, d) { arima(x[d], order=c(1,0,0))$coef[1] }
load(url("http://www.mayin.org/ajayshah/A/nifty_weekly_returns.rda"))
arima(r, order=c(1,0,0))
b <- boot(r, AR1.boot, R=5000)
boot.ci(b, type="basic")
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gives me:
---------------------------------------------------------------------------> arima(r, order=c(1,0,0))
Call:
arima(x = r, order = c(1, 0, 0))
Coefficients:
ar1 intercept
0.0718 0.3061
s.e. 0.0337 0.1392
sigma^2 estimated as 14.61: log likelihood = -2414.86, aic =
4835.72> b <- boot(r, AR1.boot, R=R)
> boot.ci(b, type="basic")
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 5000 bootstrap replicates
CALL :
boot.ci(boot.out = b, type = "basic")
Intervals :
Level Basic
95% ( 0.0760, 0.2109 )
Calculations and Intervals on Original Scale
---------------------------------------------------------------------------
I find it very strange that the 95% confidence interval runs from
0.076 to 0.2109. I had expected that it should be symmetric about
0. What am I missing?
As an aside, how would you set about using tsboot() to obtain
inference for this AR(1) coefficient?
--
Ajay Shah http://www.mayin.org/ajayshah
ajayshah at mayin.org
http://ajayshahblog.blogspot.com
<*(:-? - wizard who doesn't know the answer.
