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I'm not sure about the presence of a GARCH effect in this first differenced series. What do you suggest? I've fitted an ARIMA(0,1,0), so the original series is a random walk. I'm working with eurusd exchange rates.

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Here you can found the initial plots https://ibb.co/m80N8H and here the squadre residuals of ARIMA(0,1,0) plus Mcleod Li test. https://ibb.co/dOgdbS . I've tried also an ARIMA(3,1,0) but it seems the original series is a random walk.

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    $\begingroup$ There is not enough information to answer your question. But why don't you run an ARCH-LM test which is specifically suited for identifying presence of ARCH effects? $\endgroup$ – Richard Hardy Feb 21 '18 at 18:47
  • $\begingroup$ I've add other plots above. However, I ve tried the test but I have problem to interpret it. The test must be run on the differenced series or on its residuals $\endgroup$ – Kimira Feb 22 '18 at 10:10
  • $\begingroup$ You run the test directly on the data you are examining. If you care about the original series, run it on the original series. If you care about residuals, run it on residuals. The plots in the second link indicate no ARCH patterns. $\endgroup$ – Richard Hardy Feb 22 '18 at 10:22
  • $\begingroup$ I never understood this aspect. Summing up, there is no serial correlation in my squared residuals, so there is no Arch effect. But there is no arch effect in the residuals or in the differenced time series? What's the procedure that i have to follow? 1. I fitted an ARIMA(0,1,0) because data seems to be a random walk 2. Squared residuals have no correlation so no arch effect. What s the next step? Thanks very much $\endgroup$ – Kimira Feb 22 '18 at 10:37
  • $\begingroup$ Next step? If there are no GARCH effects, then there is no need for a GARCH model. More precisely, there is no need to add a GARCH-type conditional variance equation to your current model. Keep the model you have now. $\endgroup$ – Richard Hardy Feb 22 '18 at 13:40
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For the residuals plotting there seems to be a pattern. Have you tried higher order of AR and MA? A first glance for Arch effect is testing non correlation over squared residuals (ljung-box)

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  • $\begingroup$ I put above other plots. The squared residuals seems to go well, do you think so? $\endgroup$ – Kimira Feb 22 '18 at 10:07
  • $\begingroup$ What do you mean in your second sentence? $\endgroup$ – Richard Hardy Feb 22 '18 at 10:25

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