Statistics Field Guide

Time and Sampling

Check cadence, memory, seasonality, and candidate boundaries before modeling or monitoring a series.

1. CadenceHow regular is the observation schedule, and are gaps, duplicates, or mixed intervals large enough to change downstream time-series conclusions?

   Use withCoefficient of VariationResamplingNyquist and Aliasing

2. Rolling StatisticsHow does a local summary of the recent past change as the time window moves through an ordered series?

   Use withMoving AverageChange-point SketchesHampel Filter

3. Change-point SketchesWhere should a practitioner inspect first for possible changes before fitting a formal change-point model?

   Use withCUSUMRolling StatisticsPELT

4. Kernel Scores for Distributional ChangeAt a proposed boundary, do the observations on its two sides differ in a feature represented by the chosen kernel even when their means agree?

   Use withChange-point SketchesPELTWasserstein Distance

5. CUSUMIs a small but persistent deviation accumulating into enough evidence to call a process shift?

   Use withChange-point SketchesRolling StatisticsAnomaly Thresholds

6. Bayesian Online Change-Point DetectionAs each observation arrives, how should posterior mass move between a new boundary and the possible continuing run lengths?

   Use withChange-point SketchesCUSUMBayesian Workflow and Posterior Predictive Checks

7. StationarityCan one baseline, variance, and lag structure be reused across this time window?

   Use withAugmented Dickey-FullerKPSSDifferencing and Detrending

8. Augmented Dickey-FullerIs this series a wandering level, or is there evidence that shocks pull back toward a stable level or trend?

   Use withStationarityKPSSDifferencing and Detrending

9. KPSSIs this series still credible as level-stationary or trend-stationary after accounting for short-run dependence?

   Use withStationarityAugmented Dickey-FullerDifferencing and Detrending

10. Differencing and DetrendingShould trend be removed by differencing or by subtracting an estimated trend before reading dependence or fitting a time-series model?

    Use withStationarityAugmented Dickey-FullerSTL Decomposition

11. Autocorrelation FunctionAt which lags does a series retain linear memory of its own past?

    Use withPartial Autocorrelation FunctionStationarityPeriodogram

12. Partial Autocorrelation FunctionWhich lag relationships remain after the shorter lag relationships have already been accounted for?

    Use withAutocorrelation FunctionPeriodogramLomb-Scargle Periodogram

13. Power Spectral DensityAt which frequencies is variance concentrated, after accounting for sampling rate, smoothing, and spectral scaling?

    Use withPeriodogramCoherenceNyquist and Aliasing

14. PeriodogramWhich Fourier frequencies look unusually strong in this finite, regularly sampled series?

    Use withPower Spectral DensityLomb-Scargle PeriodogramAutocorrelation Function

15. Lomb-Scargle PeriodogramWhich sinusoidal frequencies explain unevenly sampled observations without first forcing them onto a regular grid?

    Use withPeriodogramAutocorrelation FunctionNyquist and Aliasing

16. STL DecompositionHow much of a regular seasonal series can be separated into trend, seasonal pattern, and remainder?

    Use withStationarityPeriodogramMoving Average

17. Nyquist and AliasingCan this sampling design distinguish the highest frequencies that matter, or will faster variation masquerade as slower structure?

    Use withCadenceResamplingPower Spectral Density

18. ResamplingWhat assumptions enter when observations are moved from their recorded timestamps onto a different time grid?

    Use withCadenceLinear InterpolationNyquist and Aliasing

19. Moving AverageWhat local level is implied by averaging a fixed-width neighborhood of the series?

    Use withRolling StatisticsExponential Moving AverageSavitzky-Golay Filter

20. Exponential Moving AverageWhat smoothed level results when recent observations receive exponentially more weight than older observations?

    Use withMoving AverageRolling StatisticsSavitzky-Golay Filter

21. Savitzky-Golay FilterHow can a local polynomial smooth a regularly sampled series while preserving peaks and curvature better than a flat average?

    Use withMoving AverageResamplingSTL Decomposition