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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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    $\begingroup$ 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"! $\endgroup$
    – whuber ♦
    Commented Dec 12, 2023 at 19:08
  • $\begingroup$ I remember this question, with mixing up the critical region with the confidence region, being asked before. $\endgroup$
    – Sextus Empiricus
    Commented Dec 12, 2023 at 21:10
  • $\begingroup$ stats.stackexchange.com/questions/518786 $\endgroup$
    – Sextus Empiricus
    Commented Dec 12, 2023 at 21:11
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    $\begingroup$ 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. $\endgroup$
    – Stephan Kolassa
    Commented Dec 12, 2023 at 21:21
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    $\begingroup$ 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. $\endgroup$
    – Stephan Kolassa
    Commented Dec 12, 2023 at 21:23

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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.

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