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Module · 5 lessons
Autocorrelation: ACF and PACF
Read ACF and PACF plots to tell an AR process from an MA process, know which lags are actually significant, and turn that reading into candidate ARIMA orders for Cyclepath.
At a glance
Level
Intermediate
Lessons
5 lessons
Time to complete
1 week
Cost
Free forever · no sign-up
Welcome to Autocorrelation: ACF and PACF, the fourth module of the course. Module 3 stationarized Cyclepath — seasonal differencing, confirmed with the ADF test — but stationarity alone doesn’t tell you how to build a model on top of it. ARIMA, which Module 5 introduces, needs two specific numbers: how many autoregressive (AR) terms and how many moving-average (MA) terms to include. This module is where those numbers come from.
You’ll start with what the autocorrelation function (ACF) and partial autocorrelation function (PACF) actually measure, and why you need both rather than either alone. You’ll learn the classic signatures that separate an AR process from an MA process — one tails off while the other cuts off sharply, and which is which tells you the process type. You’ll learn to read a significance band properly, including the real risk of chasing a spike that’s just noise. And you’ll apply all of it to Cyclepath’s stationary series from Module 3, turning a plot into a genuine shortlist of ARIMA orders to try next.
Every plot in this module is generated from real data — synthetic AR and MA processes with known, verifiable structure, and the actual seasonally-differenced Cyclepath series — computed with statsmodels.tsa.stattools.acf and pacf. Start with Lesson 1 on what these two functions are actually measuring.
Lessons in this module
1
What ACF and PACF Measure
The ACF measures raw correlation between a series and its own past; the PACF measures the same relationship with the effect of every intermediate lag stripped out. The difference between them is what tells an AR process from an MA process.
2
Reading the Signatures: AR vs MA
An AR process's ACF tails off gradually while its PACF cuts off sharply; an MA process is the mirror image. Demonstrated on synthetic AR(1) and MA(1) series with known structure, the textbook signatures show up exactly as advertised.
3
Confidence Bands and Multiple Testing
The ±1.96/√n band marks which ACF/PACF bars are statistically significant against pure white noise — but testing many lags at once means some bars cross that line by chance alone. A simulation shows 42% of pure noise series trip at least one 'significant' spike out of 15 lags.
4
Reading Cyclepath's ACF and PACF
Applied to Cyclepath's stationary series, the ACF and PACF are flat everywhere except two lags: 7 and 12. One has a story behind it — the seasonal period — and one doesn't, which is exactly the discipline the last three lessons built toward.
5
Guided Project: Choosing ARIMA Orders for Cyclepath
Turn the ACF/PACF reading into an actual shortlist of candidate orders, then use a quick preview fit to see which one is leading — and an honest residual check to show the shortlist isn't the finish line.
Achievement
Complete all 5 lessons to finish the Autocorrelation: ACF and PACF module.