Time-Series Forecasting (ARIMA & Prophet)

Predict the future from the past. Learn to spot trend and seasonality, make a series stationary, and use ARIMA, SARIMA, and Prophet — without ever shuffling your data.

Learn Time-Series Forecasting (ARIMA & Prophet) in our free AI & Machine Learning course — a beginner-friendly interactive lesson with worked examples, a…

Part of the free AI & Machine Learning course at LearnCodingFast — hands-on lessons with examples you run in your browser, plus practice exercises and a quick quiz.

What You'll Learn in This Lesson

🎯 Real-World Analogy: Reading the Tide

A sailor reading the sea separates three things: the slow rise of the tide (the trend), the regular daily ebb and flow (the seasonality ), and the random splash of individual waves (the noise ). Predicting the water level means modelling each part.

Time-series forecasting does exactly this: pull apart trend, seasonality, and noise, model the predictable parts, and project them forward. And just like the sea, you can only learn from the past to predict the future — never the other way around.

1 Trend, Seasonality & Stationarity

Every time series mixes a few components. Trend is the long-term direction. Seasonality is a pattern that repeats over a fixed period (weekly, yearly). Noise is the random leftover.

Classic models assume the series is stationary — its mean and variance stay roughly constant over time. Most real series aren't, so we apply differencing (subtract the previous value) to strip out the trend and bring the series closer to stationary.

• Plot the series; identify trend and seasonality.
• Difference (and/or transform) to reach stationarity.
• Fit a model (ARIMA / SARIMA / Prophet).
• Evaluate on a held-out recent period — no shuffling.

2 Decomposing a Series

Let's pull a tiny series apart. A moving average smooths the seasonal wiggle to reveal the trend, and differencing strips the trend out so the seasonal pattern stands clear. Run it and watch.

3 ARIMA, SARIMA & Prophet

ARIMA(p, d, q) is the classic statistical model. p is the autoregressive order (how many past values), d is the differencing order (how many times you difference to reach stationarity), and q is the moving-average order (how many past errors).

• SARIMA: ARIMA plus explicit seasonal terms — use it when the data repeats over a fixed period.
• Prophet (Meta): a robust, low-effort model that decomposes trend, multiple seasonalities, and holiday effects automatically and tolerates missing data — popular for business forecasting.

🌍 Worked Example: The Real Tools (statsmodels & Prophet)

Here's ARIMA via statsmodels and a Prophet forecast. Study it (it isn't runnable in the in-browser sandbox) and notice the train/test split is done by time order , never shuffled.

Prophet wants two columns named ds (date) and y (value); ARIMA takes the raw series and an order=(p, d, q) tuple.

4 Splitting & Evaluating Forecasts

The cardinal rule of time series: train on the past, test on the future . Never shuffle. Hold out the most recent slice and evaluate the forecast on it, mimicking real deployment.

Three metrics tell you how good a forecast is:

• MAE — average absolute error, in the original units.
• RMSE — like MAE but punishes large misses more.
• MAPE — error as a percentage of the actual value, easy to compare across scales.

🎯 Your Turn 1: First-Order Differencing

Fill in the blank so difference() subtracts the previous value at each step. The expected output is in the comments.

🎯 Your Turn 2: Compute MAE

Finish the MAE function by dividing the total error by the number of points. The expected output is in the comments.

🎯 Mini-Challenge: Time-Aware Split + RMSE

Split a series by time (no shuffling) and compute RMSE on the held-out period. Only a comment outline is provided.

5 Common Errors (And How to Fix Them)

These are the mistakes that quietly ruin time-series projects. Watch for them.

A random split puts future points in the training set — the future leaks into the past.

Trend or changing variance breaks ARIMA's assumptions and the forecast drifts.

✅ Fix: difference (raise d) to reach stationarity:

A monthly series with a yearly cycle needs seasonal terms, or it forecasts a flat line through the peaks.

✅ Fix: use SARIMA (or Prophet) with a seasonal period:

📋 Quick Reference

Concept

What It Is

Key Point

Trend

Long-term direction

Removed by differencing

Seasonality

Repeating cycle

Fixed period (e.g. yearly)

Stationarity

Stable mean and variance

ARIMA assumes it

ARIMA(p, d, q)

AR + differencing + MA

d = differencing order

SARIMA

Seasonal ARIMA

Adds seasonal terms

Prophet

Trend + seasonality + holidays

Robust, low-tuning

Train/test split

Past trains, future tests

Never shuffle

MAE / RMSE / MAPE

Error metrics

MAPE is a percentage

❓ Frequently Asked Questions

🎉 Lesson Complete!

You can now separate trend and seasonality , make a series stationary with differencing, read ARIMA(p, d, q) , reach for SARIMA or Prophet when needed, and evaluate forecasts with MAE, RMSE, and MAPE — without ever shuffling.

🚀 Up next: Anomaly Detection — finding the rare points that don't fit the pattern.

Practice quiz

Continue this course

• Previous: Feature Engineering & Selection
• Next: Anomaly Detection