https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/Recent content in Autocorrelation: ACF and PACF on DATATWEETSHugoenCopyright (c) 2025 DatatweetsFri, 03 Jul 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-1-what-acf-and-pacf-measure/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-1-what-acf-and-pacf-measure/The autocorrelation function (ACF) at lag k is the correlation between y_t and y_t-k, including any indirect relationship carried through the lags in between. The partial autocorrelation function (PACF) at lag k is that same relationship with the intermediate lags’ effects removed — the direct connection only. This lesson defines both precisely, computes the first few lags on Cyclepath’s stationary series from Module 3, and explains why needing both is what makes AR/MA order selection possible.https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-2-reading-the-signatures-ar-vs-ma/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-2-reading-the-signatures-ar-vs-ma/The classic Box-Jenkins identification rule: an AR(p) process has an ACF that decays gradually (geometrically, or as a damped wave) and a PACF that cuts off sharply after lag p; an MA(q) process is the mirror image, with the ACF cutting off after lag q and the PACF tailing off. Built on a known AR(1) process (phi=0.7) and MA(1) process (theta=0.7), both signatures show up exactly as the theory predicts, giving you a reference to compare any real series against.https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-3-confidence-bands-and-multiple-testing/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-3-confidence-bands-and-multiple-testing/The conventional ACF/PACF significance band is ±1.96/√n, the 95% confidence interval under the null hypothesis that the series is white noise. But testing 15 lags at a 5% significance level each means chance alone produces a false alarm surprisingly often — a real simulation on pure white noise shows 42% of series trip at least one spurious ‘significant’ lag. This lesson teaches the band’s formula and the discipline of treating an isolated spike with suspicion unless it has independent backing.https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-4-reading-cyclepaths-acf-and-pacf/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-4-reading-cyclepaths-acf-and-pacf/Cyclepath’s seasonally-differenced series shows only two lags crossing the significance band on both ACF and PACF: lag 7 (-0.22 / -0.273) and lag 12 (-0.417 / -0.483). Everywhere else, both functions sit inside the band — the signature of essentially no regular AR or MA structure. Lag 12 has independent corroboration from Module 3’s known seasonal echo; lag 7 doesn’t, and the multiple-testing math from Lesson 3 says an isolated spurious spike like it is expected roughly 42% of the time anyway.https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-5-guided-project-choosing-arima-orders-for-cyclepath/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/autocorrelation-acf-and-pacf/lesson-5-guided-project-choosing-arima-orders-for-cyclepath/The Module 4 capstone. From the ACF/PACF table, you’ll conclude the non-seasonal order is essentially (0,0) and shortlist three seasonal candidates at lag 12. A preview fit with statsmodels’ SARIMAX shows the seasonal-AR(1) candidate winning on AIC (1123.93) by a wide margin — but a Ljung-Box residual check shows even the leader still has significant leftover autocorrelation, an honest signal that this shortlist is a starting point for Module 5 and 6, not a finished model.