https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/Recent content in AR, MA, ARMA, ARIMA on DATATWEETSHugoenCopyright (c) 2025 DatatweetsFri, 03 Jul 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-1-the-autoregressive-ar-model/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-1-the-autoregressive-ar-model/The autoregressive model AR(p) writes today’s value as a constant plus weighted contributions from the previous p values plus a random shock. This lesson fits an AR(1) to a synthetic series built with a known phi of 0.7, recovers the coefficient as 0.701, and shows the defining forecast behavior: an AR forecast decays geometrically back toward the series mean, remembering the past with ever-weakening influence.https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-2-the-moving-average-ma-model/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-2-the-moving-average-ma-model/The moving-average model MA(q) writes today as a constant plus weighted contributions from the last q random shocks. This lesson fits an MA(1) to a synthetic series with known theta of 0.7, recovers it as 0.716, and shows the defining forecast behavior: an MA(q) forecast goes flat at the mean after exactly q steps, because beyond q steps there are no observed shocks left to inform it — a sharp contrast with AR’s gradual mean reversion.https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-3-arma-and-arima-combining-and-differencing/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-3-arma-and-arima-combining-and-differencing/ARMA(p,q) combines autoregressive and moving-average terms in a single model for stationary data. ARIMA(p,d,q) adds an integration order d — d rounds of differencing applied internally before the ARMA part is fit — which is exactly the differencing from Module 3 built into the model. This lets ARIMA fit a trending series like raw Cyclepath directly, with no manual differencing step, unifying the whole workflow into one order tuple.https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-4-fitting-and-forecasting-arima-with-statsmodels/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-4-fitting-and-forecasting-arima-with-statsmodels/A fitted ARIMA object exposes a full summary: the coefficient table with standard errors and p-values, and fit scores like AIC and BIC. This lesson reads an ARIMA(1,1,1) summary on Cyclepath’s training set, interprets which coefficients are significant, then produces a 12-step forecast with confidence intervals that widen from about 3,200 wide at step 1 to nearly 30,000 wide at step 12 — an honest, and here revealingly large, quantification of forecast uncertainty.https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-5-guided-project-an-arima-forecast-for-cyclepath/Fri, 10 Apr 2026 09:00:00 +0200https://datatweets.com/courses/time-series-forecasting/ar-ma-arma-arima/lesson-5-guided-project-an-arima-forecast-for-cyclepath/The Module 5 capstone. You’ll fit a range of non-seasonal ARIMA candidates to Cyclepath’s training set and score their 12-month forecasts against the seasonal-naive baseline (5.9% MAPE) from Module 1. The honest result: the best stable non-seasonal model manages only 16% MAPE, AIC and test error disagree about which candidate is best, and the one model that beats the baseline (ARIMA(2,1,2) at 1.9%) does so via a degenerate unit-root solution faking a 12-month cycle. The conclusion — non-seasonal ARIMA is structurally blind to seasonality — is exactly why SARIMA exists.