# White noise ACF - PACF

I found PACF and ACF like the following table . But, how can I decide whether there exists white noise? And what is white noise? If there is no white noise, can I say being stationary?

• These are all pretty elementary questions and are normally covered in introductory time series courses. Have you tried looking them up in a textbook? If you have and still do not understand, please specify in more detail what is unclear. – Richard Hardy Mar 2 '15 at 19:09
• i only know that i need to look at first two blocks to decide white noise. @RichardHardy – user315 Mar 2 '15 at 19:38
• but i dont know how to decide. this point is unclear @RichardHardy – user315 Mar 2 '15 at 19:39
• The bars at lag 1 and lag 4 in both ACF and PACF plots stick out quit a lot beyond the confidence bound (the dashed line). The confidence bound is defined as follows. There is only 5% probability that the bar would stick out beyond the bound if the underlying data generating process had zero ACF/PACF. Hence, it is quite unlikely (only 5% chance) that the underlying process has zero ACF/PACF. That is, it is quite likely (95% chance) that the ACF/PACF is real and not just a matter of coincidence. That is, there is almost surely a pattern in the data $\rightarrow$ your data is not white noise. – Richard Hardy Mar 2 '15 at 19:50
• okay thank you so much:). what i want to learn is that! @RichardHardy – user315 Mar 2 '15 at 19:52

## 2 Answers

What is white noise? Time series data that shows no auto correlation is called white noise.

How do I know whether it is white noise? A general assumption is that if 95% of the spikes in the Auto-correlation Function lie within (+/-)2/sqrt(T), where T being the length of the time series.

So, by the above mentioned formula, one can infer whether the series/data is white noise or not.

A white noise process would not be correlated with its own values at any lag.Its mean is zero, variance is constant and autocovariance(using which the autocorrelation plots like acf and pacf are figured out) is also zero. Thus, your results are clearly indicative of the fact that its not a white noise process.