Bartlett's Test for ACF

Definition

Bartlett’s test tests the significance of individual sample autocorrelations $r_k$ one at a time.

Hypotheses

$$\begin{array}{rl}{H}_0& :{\rho }_k=0\\ H_1& :{\rho }_k\ne 0\end{array}$$

Test Statistic

For white noise with large $n$:$r_k\sim N\left(0,\frac{1}{n}\right)$

Decision Rule

Reject $H_0$ at significance level $\alpha$ if:

$|r_k|>\frac{z_{\alpha /2}}{\sqrt{n}}$

For $\alpha =0.05$, reject if $|r_k|>\frac{1.96}{\sqrt{n}}$

If all $|r_k|<\frac{1.96}{\sqrt{n}}$, we conclude the series may be White Noise (no significant autocorrelation).

Related

• Sample Autocorrelation (ACF)
• Correlogram
• White Noise