How do I test whether a given time series is just noise?

In NumXL, we can test whether a time series is a white noise or not using 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 $\log(T)$

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