In many books, articles and comments on this website I read that the variance of the autocorrelation of a white noise process is $\frac{1}{T}$ when T is sufficiently large. Often this characteristic is used to calculate the confidence bounds in an ACF plot, where the bounds are calculated by: $b = \pm 1.96 \frac{1}{\sqrt{T}}$, which is the confidence interval of a normally distributed value having zero mean and variance $\frac{1}{T}$.

The question is where the $\frac{1}{T}$ is coming from. Why is the variance of the autocorrelation $r_h$ of a white noise process equal to $\frac{1}{T}$?


1 Answer 1


Hill, 2011:p.349; Chatfield, 2009:p.56; Kendall, 1983 answer the question properly.

Hill, R.C., Griffiths, W.E., Lim, G.C. (2011). Principles of Econometrics, 4.ed., Wiley, USA. https://www.wiley.com/en-us/Principles+of+Econometrics%2C+4th+Edition-p-9780470626733

Chatfield, C. (2009). The Analysis of Time Series: An Introduction, 6.ed., London, Chapman and Hall/CRC. https://www.crcpress.com/The-Analysis-of-Time-Series-An-Introduction-Sixth-Edition/Chatfield/p/book/9781584883173

KENDALL Stuart Ord 1983 The Advanced Theory of Statistics Vol3 4E.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.