Time Series
Observations indexed by time, where the sequence itself is data. Trend, seasonality, cycles and noise — and the distinction most summaries get wrong.
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Causal Impact
The estimate is the gap between what happened and a forecast of what would have happened. Everything depends on that forecast being right.
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Temporal autocorrelation (Serial Correlation)
Serial dependence changes the information in a time series. Positive and negative dependence can affect uncertainty in opposite directions.
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Blocked Splits (Single Holdout)
Moving one cut point across a series changed the MAE from 1.19 to 3.18 — same data, same model, nine defensible splits.
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Sliding Window (Rolling Window) Cross-Validation
After a regime change, the sliding window recovers to an MAE of 0.43 while the expanding window stalls at 2.79.
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Expanding Window Validation
The first fold trained on 200 rows scores 1.77 and the last on 1,000 scores 0.87. Their mean summarizes this sequence of historical evaluations.
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Forecasting Benchmarks
Mean, naive, seasonal naive, drift: the simple methods a model has to beat on the same test set, origins, and horizons before its complexity is justified.
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Seasonal Lag
The value from the same season one period ago. Where it appears in the ACF, what seasonal differencing does with it, and why it is expensive in data.
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Simple Baseline Methods
On a trend the mean method scored MAE 15.8737 against drift’s 2.2367. On a seasonal series, seasonal naive won at 1.7016 against naive’s 3.0688.
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Time Series Forecasting
Predicting the next values of a series. The benchmarks any method has to beat, and the evaluation that decides whether it did.
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Seasonality
A repeating pattern tied to the calendar. What separates it from a cycle, and why confusing the two produces forecasts the data never supported.
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Upsampling
Interpolating a daily series to hourly makes the 18:00 value exactly 0.250 x today plus 0.750 x tomorrow. Forward fill stays at 1.000 x today.
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Downsampling
Keeping every 4th sample of a 300 Hz tone turned it into a 50 Hz tone. Averaging each group of four left the same 50 Hz at a fifth of the amplitude.
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Time-Based Splits
On a random walk, the level scores R² 0.83 under a chronological split and 0.97 when shuffled, while the change scores below zero. A high level R² alone does not show skill over a naive baseline.
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Time-Series Forecasting
The rows are not exchangeable and the baseline is strong.