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While reading this page on time series I found this sentence:

The Ljung-Box test showed that there is little evidence of non-zero autocorrelations in the in-sample forecast errors, and the distribution of forecast errors seems to be normally distributed with mean zero. This suggests that the simple exponential smoothing method provides an adequate predictive model for London rainfall, which probably cannot be improved upon. Furthermore, the assumptions that the 80% and 95% predictions intervals were based upon (that there are no autocorrelations in the forecast errors, and the forecast errors are normally distributed with mean zero and constant variance) are probably valid

Why does the evidence that the residual are similar to white noise means that the simple exponential smoothing (tested in the web page) should be considered valid and over all why can't we improve upon it?

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The Ljung-Box test assumes that there are no pulses/level shifts/seasonal pulses/local time trends AND that the model parameters and model error variance are constant over time. If these assumptions are true or at least can't be rejected then and only then would there be "proof" that any specified model would be sufficient.

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