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I am trying to forecast electricity consumption using hourly consumption data over a span of 4 years. However, when I plot the ACF and PACF graphs, the confidence interval turns out to be very narrow, rendering the graphs seemingly meaningless. I have experimented with various alternatives for the frequency (e.g., 24, 365*24, 1, 12), but the narrow confidence interval persists. What could be the reason for this? I appreciate your assistance. enter image description here

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Richard Hardy
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Sila Sefer
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    These are not confidence intervals: they are approximate critical points for testing the hypotheses that a coefficient is zero. This is the very opposite of "meaningless"! – whuber Dec 12 '23 at 19:08
  • I remember this question, with mixing up the critical region with the confidence region, being asked before. – Sextus Empiricus Dec 12 '23 at 21:10
  • https://stats.stackexchange.com/questions/518786/ – Sextus Empiricus Dec 12 '23 at 21:11
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    Note that ACF/PACF plots are hard to interpret for the non-expert; in particular, you cannot simply read off the "correct" SARIMA model. "The" Box-Jenkins model building process is iterative, with taking differences, fitting models, plotting the ACF/PACF on residuals, and repeating until the ACF/PACF does not show a signal any more. I would strongly recommend you use an established auto-ARIMA tool instead. – Stephan Kolassa Dec 12 '23 at 21:21
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    Plus you very probably have multiple seasonalities: hour of day, as visible in your ACF plot, but also hour of week, since electricity consumption usually varies by weekday vs. weekend, and hour of year, with different patterns in summer vs. winter. SARIMA cannot deal with these. The tag wiki contains pointers to more appropriate models. – Stephan Kolassa Dec 12 '23 at 21:23
  • First of all thank you very much about your answers. I looked up auto-ARIMA tools for use but still I have to understand ACF and PACF graphs before analyzing. As I understand these graphs tell me about test is significant but the problem is if there is not a range how can I estimate coefficients (p,q)? – Sila Sefer Dec 21 '23 at 07:41

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You have a long time series (one with great many observations), so you are able to estimate the ACF and PACF very precisely. This is why your "confidence interval" (actually, critical points for testing the hypotheses that a coefficient is zero, as @whuber notes in his comment) is so narrow. You should be quite happy to have such great estimation precision! It grants you quite some confidence in choosing a model for replicating these patterns.

Richard Hardy
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