Statistics Quest

Time Series and Forecasting

Describe, model and forecast data that change over time.

Trend and seasonality, moving averages, exponential smoothing and Holt–Winters, forecast errors (MAE, RMSE, MAPE), holdouts and time-series cross-validation, decomposition, autocorrelation, stationarity and autoregressive models, and the limits of forecasts.

Lessons

  1. 1Time-indexed dataRecognise what makes data a time series, prepare a single regular series from raw records, and describe change over time correctly.25 minFree
  2. 2Trend, seasonality and cyclesIdentify the trend, seasonal, cyclical and irregular components of a series and decide whether seasonality is additive or multiplicative.30 minMembers
  3. 3Moving averagesCompute trailing and centred moving averages, choose the window, and explain the delay, the lost end values and why a moving average is a poor forecast for a trending series.30 minMembers
  4. 4Simple exponential smoothingUpdate and forecast with simple exponential smoothing, interpret the smoothing parameter α, and choose α honestly on held-out data.35 minMembers
  5. 5Holt and Holt–WintersExtend exponential smoothing with a trend (Holt) and a seasonal component (Holt–Winters), compute their forecasts, and choose between additive, multiplicative and damped versions on a holdout.40 minMembers
  6. 6Measuring forecast errorCalculate and interpret ME, MAE, MSE, RMSE, MAPE and MASE on held-out data, and choose a measure that fits the decision and the data.35 minMembers
  7. 7Holdouts and time-series cross-validationEvaluate forecasting methods honestly with a final holdout and with rolling-origin cross-validation, and recognise look-ahead leakage.35 minMembers
  8. 8DecompositionCarry out a classical additive or multiplicative decomposition, interpret seasonal indices and seasonally adjusted values, and recognise the method's limits.35 minMembers
  9. 9AutocorrelationCalculate and read autocorrelation (ACF) and partial autocorrelation (PACF) plots, recognise the signatures of trend, seasonality and white noise, and test for white noise with the Ljung–Box test.35 minMembers
  10. 10Stationarity and autoregressive modelsJudge whether a series is stationary, make it stationary by differencing, and fit, interpret and forecast with autoregressive AR(p) models; describe ARIMA models conceptually.40 minMembers
  11. 11Forecast uncertainty and limitsCompute approximate prediction intervals for simple forecasting methods, check them on held-out data, explain what they leave out, and communicate forecast uncertainty and structural breaks honestly.35 minMembers