Time Series Fundamentals

• Describe trend, seasonality and residual components
• Explain stationarity and why models assume it
• Frame a forecasting problem (horizon, frequency, as-of date)

• Ordering means standard i.i.d. assumptions are wrong — shuffling corrupts the signal.
• Trend and seasonality are modelable structure that naive methods ignore.
• Stationarity determines which statistical machinery (ARIMA, spectral, etc.) is even applicable.
• Choosing the wrong setup (horizon, forecast vs nowcast) silently invalidates results.

Each footprint (observation) says something about the one before and after — direction, stride, momentum. You can't 'shuffle' a trail and still read where it goes. Time series reading is about extrapolating from a pattern, not comparing independent samples.

• Establish the sampling frequency, horizon (h steps ahead) and the exact prediction-time view.
• Plot and split components: moving-average trend, seasonal effect by period, and residuals.
• Check stationarity (constant mean/variance over time) with the Augmented Dickey-Fuller test or visual inspection.
• Estimate autocorrelation (ACF/PACF) to see which lags carry signal.
• Choose modeling family by the components: trend/seasonal → decomposition+exponential/ARIMA; rich calendar features → ML.

• An e-commerce planner forecasts daily sales with a weekly seasonality at a 14-day horizon to set inventory buffers.
• An SRE team forecasts error-spike days by decomposing hourly 5xx count into weekly traffic cycles plus incident noise.
• A demand-sensing team retrains nightly so the seasonal effects always reflect last month's calendar.

• Pin the horizon and frequency up front; forecast targets drift if either changes.
• Validate on future-only windows (walk-forward), never shuffled folds.
• Inspect ACF/PACF before choosing a model family — the lags say which dependency structure is real.
• Always compare against the best trivial baseline (last value, seasonal naive).

• Ignoring the calendar (holidays, weekends) treated as uniform seasonality.
• Fitting models on raw trending data without differencing, then complaining about non-stationarity.
• Predicting far-future levels with a 'nowcast' model trained on short memory.
• Holding out a random test slice instead of the most recent — leaks future into training windows.

• Plot residuals vs fitted and vs time: a pattern in the residual line = missing component or decree.
• If ACF decays slowly at large lags, the series is trending — difference it and re-inspect.
• Forecast too smooth? Your model overdamps seasonality; verify the seasonal period matches the data.
• Two-step: fix the horizon and 'as-of' timestamp, then rerun — the test setup is usually the bug, not the model.