Majority observations outside confidence interval

2
votes

I have a time series (called sigma.year), with a length of 100. Its histogram and qqplot shows strong evidence for normality.

I am calculating confidence interval (in R) for sample mean as follows:

exp.sigma<-mean(sigma.year)
sd.sigma<-sd(sigma.year)
se.sigma=sd.sigma/sqrt(length(sigma.year))
me.sigma=qt(.995,df=length(sigma.year)-1)*se.sigma
low.sigma=exp.sigma-me.sigma
up.sigma=exp.sigma+me.sigma

My problem is 83/100 observations falls outside the confidence interval. Do you have any idea why I have this so? Is this because I have time-series, rather than cross section data? Or, am I calculating conf interval in a wrong way?

Thanks.

1
rtime-seriesconfidence-interval

1 Answers

3
votes

It's hard to evaluate completely without knowing all of your inputs (for example, a dput of sigma.year), but your confidence interval appears to be a confidence interval for the mean. So it is not unexpected that 83/100 observations are outside of a 99% confidence interval about the mean.

To clarify. If sd.sigma is the standard deviation of your sample, then you have correctly calculated the 99% confidence interval about the mean.

And again, your data are behaving as you'd expect for a sample of 100 observations drawn from a population with a normal distribution. Here's some code to check that:

x <- rnorm(100)
exp.x <- mean(x)
se.x <- sd(x)/sqrt(length(x))
q.x <- qt(0.995, df = length(x)-1)
interval <- c(exp.x - se.x*q.x, exp.x + se.x*q.x)
sum(x > interval[1] & x < interval[2])
# will vary, because I didn't set the seed on purpose, but try this
# you'll get a value around 20