Time-Series Models by Hand: Stationarity, Differencing, Autocorrelation, AR & MA Terms, ARIMA Forecasts and Residual Checks

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Test 24 months of ferry passengers for a stable mean and spread with rolling windows, measure how far the mean has moved between the two halves and turn that into a verdict.
• Remove trend and season from three years of monthly passengers with first, seasonal and combined differences and chart the original series against its seasonal difference.
• Compute the autocorrelations of 20 differenced passenger values from centred sums of products and mark which lags lie outside the ±2/√n band.
• Turn the autocorrelations of four Wrenfield series into partial autocorrelations, compare them with the ±2/√n band and read off which model each series suggests.
• Fit an AR(1) model to 25 weeks of average waiting times at the ferry pier, compute the in-sample one-step forecasts and forecast week 26.
• Run the MA(1) recursion for 24 weeks of café covers on the ferry, measure the mean absolute residual and forecast week 25.
• Fit an AR(1) to the monthly changes in season-pass holders, forecast six changes ahead and add them back up to a six-month level forecast.
• Test the residuals of two candidate passenger models for leftover structure with a portmanteau Q statistic, score both models and chart their residuals.