Time Series Analysis and Forecasting
Core concepts
Know the components of a time series: trend, seasonal, cyclical, and irregular. Understand stationarity, autocorrelation and partial autocorrelation functions, and the classical models: moving average, exponential smoothing (simple, Holt, Holt–Winters), and ARIMA (autoregressive, integrated, moving average). Be able to identify orders from ACF and PACF patterns, understand differencing to achieve stationarity, and know how to evaluate forecasts with MAE, MSE, RMSE, and MAPE. Understand white noise, random walks, and the dangers of spurious regression.
Traps
- Differencing a series that is already stationary, introducing unnecessary MA structure.
- Reading ACF/PACF plots without considering seasonality.
- Using MAPE when actual values are near zero, producing explosive values.
- Fitting a model to the whole series and evaluating on the same data (no holdout).
- Confusing an AR term (PACF cuts off, ACF tails off) with an MA term (the reverse).
- Regressing two trending series on each other without checking for cointegration.
Worked example
A series with a clear linear trend and no seasonality is first-differenced once, giving a stationary series. If the differenced series has a significant spike at lag 1 in both ACF and PACF, an ARIMA(1,1,0) or ARIMA(0,1,1) may be considered, and model choice should be confirmed with information criteria such as AIC. Rule of thumb: for AR(p), the ACF tails off and the PACF cuts off after lag p; for MA(q), the ACF cuts off after lag q.