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If the EACF of my TS suggests ARMA(0,0) and the Box-Ljung test does not suggest my TS has correlation, can I conclude that my TS is white noise or merely that there is no reason to suspect that it is not white noise?

Conversely, if my TS is white noise, will I necessarily get ARMA(0,0) from EACF, ACF, PACF, etc?

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If you truly knew that your data generating process (DGP) is ARMA(0,0): $x_t=c+\varepsilon_t$, then, yes, it is, basically, a white noise.

The problem is that you do not know the DGP, usually. So, all you can say is that you don't see the serial correlation, and thus conclude that it's a constant with a noise.

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  • $\begingroup$ By "So, all you can say is that you don't see the serial correlation, and thus conclude that it's a constant with a noise.", do you mean "So, if the suggested model is ARMA(0,0), all you can say is that you don't see the serial correlation, and thus conclude that it's a constant with a noise." ? $\endgroup$ – BCLC May 8 '14 at 14:49
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    $\begingroup$ @BCLC, yes your version will work too. Let's be reasonable here, you are looking for a descriptive model, but sometimes you simply give up when it's impossible to find an acceptable model to describe the data. If I asked you to give me a model of waiting time on a bus station, it's likely you'd come up with something very simple like a constant, say "15 minutes". $\endgroup$ – Aksakal May 8 '14 at 14:53

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