Time Series Regression in R: A Hands-On Interactive Course
Every time series can be explained the way you would explain any outcome: with a regression. This six-lesson interactive course takes the ordinary linear model you already know and shows exactly which of TSLM()'s extra tools, and dangers, show up once the predictor is time itself.
TSLM() looks like lm() and fits the same way, but it understands trend() and season() as time-aware predictors, forecasts forward with new_data(), and inherits two assumptions, independent errors and a stable relationship, that time series breaks more often than not. This course works through the regression toolkit end to end: fitting and reading a trend line, building seasonal predictors two different ways, adding lags and calendar effects, selecting predictors honestly, and catching the classic trap of spurious regression before it costs you a real forecast.
Each lesson is a guided, interactive experience: you run real R code in the page, answer checkpoints, and work with one real dataset per idea. No setup, no installs.
The six lessons
Lesson 1: Fitting a trend line with TSLM
Fit an ordinary regression line to 48 months of a SaaS company's user growth with TSLM(), read what the slope and intercept mean, forecast ahead with new_data(), and see the two assumptions ordinary regression borrows and time series breaks.
Start Lesson 1: Fitting a trend line with TSLM
Lesson 2: Trend and seasonal dummy variables
Add season() alongside trend() in TSLM(y ~ trend() + season()), avoid the dummy variable trap, fit a piecewise linear trend with knots, read seasonal coefficients against a baseline period, and see why a linear trend is a dangerous tool to extrapolate far beyond the data.
Start Lesson 2: Trend and seasonal dummy variables
Lesson 3: Fourier terms for seasonality
Replace a long run of seasonal dummies with a compact sine and cosine basis. Use fourier(K = ) inside TSLM, choose K by AICc, and see why Fourier terms beat dummies once a series has a long or multiple seasonal period.
Start Lesson 3: Fourier terms for seasonality
Lesson 4: Useful predictors: lags, calendar and holidays
Add lagged predictors, and learn why the lag has to be known at forecast time. Build calendar, holiday and intervention dummies, and separate an ex-ante forecast from an ex-post one when a predictor's own future path is only a scenario.
Start Lesson 4: Useful predictors: lags, calendar and holidays
Lesson 5: Selecting predictors with cross-validation
Compare adjusted R-squared, AICc and BIC as selection criteria, see why a predictor's p-value is the wrong tool for choosing it, and use cross-validated error as the honest test. Walk through best-subset versus stepwise selection, and the leakage trap of selecting a model on the same window you test it on.
Start Lesson 5: Selecting predictors with cross-validation
Lesson 6: Spurious regression and how to avoid it
Regress two completely unrelated trending series against each other and watch r climb near 0.97. See why non-stationary regressors produce huge t-statistics and an autocorrelated residual ACF, use that residual ACF as the alarm, and learn the three cures: difference the data, model the errors directly, or move to dynamic regression.
Start Lesson 6: Spurious regression and how to avoid it
Who this is for
Anyone who has already worked through Time Series Foundations and is comfortable holding a tsibble and reading a series' trend and season by eye. You do not need any prior regression modeling experience beyond lm(). By the end you will be able to fit and read a TSLM() model end to end, build seasonal predictors two different ways, add lags and calendar effects correctly, select predictors without leaking the test window, and recognize spurious regression before it reaches a client.
What you will be able to do
- Fit
TSLM(y ~ trend())and read the slope, intercept and forecast it implies - Build seasonal predictors with dummy variables and with Fourier terms, and choose between them
- Add lagged, calendar and holiday predictors without breaking the forecast horizon
- Tell an ex-ante forecast from an ex-post one when a predictor's future is a scenario
- Select predictors with AICc, BIC and cross-validated error instead of p-values
- Spot spurious regression from a high r and an autocorrelated residual ACF, and fix it
This course is part of the Forecaster track.