Forecasting demand for 20 SKUs, each with a year and a half of history containing gaps and promotional spikes. The model shows a MAPE of 8% on the backtest, you happily hand it over to procurement planning, and a quarter later it turns out that it systematically underestimates peaks and fails to see a trend shift after the product mix changes. Sound familiar? This is the typical point where "textbook" time series analysis ends and real work begins.
Let's break down how the two most common classes of models — Prophet and the ARIMA/SARIMA family — are structured, what data each honestly works on, where it breaks, and why validation accuracy is almost always more optimistic than production accuracy.
How it actually works
ARIMA rests on three ideas: stationarity (a series without trend and changing variance), autoregression (the value depends on previous values), and moving average (on the residuals of previous forecasts). The parameters p, d, q are the orders of AR, differencing, and MA. Differencing is a way to remove trend: instead of levels, we model increments.
Prophet is structured differently: it decomposes the series into trend (piecewise linear or logistic with changepoints), seasonalities (Fourier series), and holiday effects, and estimates component weights in a Bayesian way — that is, with prior distributions and confidence intervals. This makes it more robust to gaps and "human" calendar effects, but the price is lower sensitivity to fine autocorrelation structure.
One walkthrough instead of a list of skills
Take daily sales with clear weekly seasonality and an annual cycle, with 2 years of history. A practitioner proceeds as follows:
- Plots the data and looks for gaps and outliers. Interpolates gaps carefully — otherwise differencing will produce false jumps.
- Checks stationarity (Dickey-Fuller test). A series with trend is non-stationary — takes d=1.
- Examines ACF/PACF to estimate p and q, then fits SARIMA with seasonal orders (P, D, Q, m), where m=7 for weekly seasonality.
- Does time series feature engineering: lags, moving averages, day of week, promo and holiday flags. This often yields more accuracy gain than switching models.
- Evaluates on a backtest — rolling origin, not a random train/test split. A random split in time series is a gross error: the model "peeks" into the future.
Now what goes wrong with a different order. If you don't check stationarity and feed a raw trending series into ARIMA, the model will extrapolate the trend linearly and fly off into absurdity. If you take d=2 "just in case" — you over-difference the series, get noise, and lose signal. If you evaluate on a single hold-out rather than multiple windows, the metric will turn out accidentally good.
Where the scheme itself breaks
Short series. Fewer than two or three seasonal cycles — seasonal components are estimated unreliably. Prophet will produce wide intervals (honestly), SARIMA — unstable parameters. Spot it in advance: look at the width of confidence intervals and the stability of parameters under a rolling window. If it's already too late — switch to simpler models or aggregate the series.
Trend shift. Promotions, product mix changes, external shocks — a model trained on the past continues the old trend. In Prophet, changepoints are set a priori; if they aren't updated, the model lags. A sign: systematic bias of residuals in one direction after an event.
Multiple seasonality. Weekly and annual simultaneously — classical SARIMA handles this poorly. Prophet copes better thanks to multiple seasonal components, but requires careful tuning. Anomaly detection also becomes harder: an anomaly against the backdrop of two seasonalities gets masked.
The tool stopped working. Models degrade due to data drift. Without drift monitoring and automatic retraining, the pipeline quietly loses accuracy. You can spot it by rising error on fresh data and by changes in the distribution of input features.
Learning paths and their trade-offs
| Path | Time | Money | Outcome |
|---|---|---|---|
| Self-study from documentation | Months | Minimal | Flexible, but no feedback and easy to cement mistakes |
| Structured course | Weeks | Moderate | Faster, with review of decisions |
| On-the-job practice | Depends on tasks | — | Real experience, but narrow context |
The self-study path hits a barrier: there's no one to check your backtest and model selection logic. Validation mistakes are costly and surface late. A course addresses exactly this — structure and feedback on decisions.
Who it suits and who it doesn't
Suits analysts and data specialists working with forecasts, metrics, and monitoring. Doesn't suit those looking for "a model that will just predict": without understanding the data and validation, any model will give false confidence.
The Time Series Analysis course works through these calculations with examples — from model selection to drift monitoring and retraining in a pipeline — and provides feedback on your decisions. Details and enrollment — on the course page.