Time-Series Models by Hand: Stationarity, Differencing, Autocorrelation, AR & MA Terms, ARIMA Forecasts and Residual Checks
Build the classic time-series models without a black box. You will test a series for a stable mean and spread, difference it to remove trend and season, compute autocorrelations and the first partial autocorrelations from scratch, fit an AR(1) term with SLOPE, run an MA(1) recursion, forecast with a differenced model and turn it back into levels, check residuals and compare models by error and a simple information score, with every cell checked as you go.
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About this course
This course builds the classic time-series models in a spreadsheet without a black box. For a fictional lake ferry company you check a passenger series for a stable mean and spread with rolling windows, remove trend and season with first and seasonal differences, and compute autocorrelations at lags 1 to 6 with SUMPRODUCT. You derive partial autocorrelations, read the model order from ACF and PACF patterns, fit an AR(1) term with SLOPE and run an MA(1) residual recursion. You forecast a differenced ARIMA(1,1,0) model and integrate it back to levels, then test residuals with a Q statistic against a fictional table and compare models with an information score.
Lessons
- Stationarity by Numbers: Rolling Means, Rolling Spreads and a Simple Verdict Pro
- Differencing: First Differences, Seasonal Differences (Lag 12) and Both Together Pro
- Autocorrelation by Hand: ACF at Lags 1–6 with SUMPRODUCT and the ±2/√n Band Pro
- Partial Autocorrelation: φ₁₁, φ₂₂ and Reading the Model Order from ACF and PACF Pro
- AR(1) by Hand: Fit φ with SLOPE, Build the Constant and Forecast One Step Ahead Pro
- MA(1) by Hand: Residual Recursion with a Given θ, One-Step Forecasts and Shocks Pro
- ARIMA(1,1,0): Forecast the Differences and Integrate Back to Levels Pro
- Residual Checks & Model Choice: Residual ACF, Q Statistic, RMSE and an Information Score Pro