## Question:

How do I verify the presence of significant serial correlation(s) in a given time series - i.e., time series is not white noise?

## Answer:

In NumXL, we can test whether a time series is white noise or not using the WNTest function. WNTest examines the data series for evidence of any serial correlation using Ljung-Box statistical test and modified Q*(m) statistics:

$$H_{o}: \rho_{1}=\rho_{2}=...=\rho_{m}=0$$ $$H_{1}: \exists \rho_{k}\neq 0$$ $$1\leq k \leq m$$

Where:

- $H_{o}$ is the null hypothesis.
- $H_{1}$ is the alternate hypothesis.
- $\rho_k$ is the population autocorrelation function for lag k
- $m$ is the maximum number of lags included in the white-noise test.

The user can specify the upper lag order for the test, but we recommend using the value of ${\left\lceil \log(T) \right\rceil}$

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