Space-Time Getis-Ord Gi* Hot Spot Statistic
Also known as: ST-Gi*, space-time hot spot analysis, emerging hot spot analysis, space-time local autocorrelation statistic
The Space-Time Getis-Ord Gi* statistic extends the classic Gi* local hot spot measure into three dimensions — two spatial and one temporal — revealing not only where concentrations of high or low values cluster, but how those clusters evolve, intensify, or diminish over time. It is widely used in crime analysis, epidemiology, ecology, and urban studies.
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When to use it
Use Space-Time Gi* when you have repeated measurements of a variable at the same set of spatial units across multiple time periods and you want to know both where clusters occur and how they change over time — for example, tracking crime hot spots over months, monitoring disease incidence across years, or mapping wildlife sightings through seasons. The method requires a reasonably large number of spatial units (generally at least 30) and enough time steps (at least 10 are recommended for reliable trend classification). Do not use it when data are available for only one or two time periods (use ordinary Gi* instead), when the spatial units change size or shape over time (geometry must be consistent), or when the variable is continuous and sampled irregularly in space (use space-time kriging instead).
Strengths & limitations
- Identifies not just where hot spots exist but how they evolve — persistent, emerging, intensifying, or diminishing — providing actionable temporal context.
- Produces directly mappable z-scores and significance flags that are easy to communicate to non-specialist audiences.
- The cube-based framework explicitly accounts for both spatial and temporal autocorrelation, reducing false positives relative to repeated cross-sectional analysis.
- Widely supported in mainstream GIS software (ArcGIS Emerging Hot Spot Analysis, PySAL, spdep), lowering the technical barrier.
- Flexible neighbourhood definitions (distance band, fixed count of neighbours) accommodate different spatial data structures.
- Trend categories (persistent, emerging, sporadic, etc.) depend on the chosen significance threshold and the number of time steps; results can shift substantially when these settings change.
- Requires a consistent, regularly gridded or zoned spatial framework across all time periods; irregular or changing boundaries invalidate the cube structure.
- Like all local statistics, it is sensitive to the modifiable areal unit problem (MAUP): results change with spatial resolution and zone definition.
- No built-in covariate adjustment — confounders such as population density or socioeconomic factors are not controlled unless the input variable is pre-adjusted.
- Assumes stationarity of the underlying spatial process; strong non-stationarity may require geographically weighted alternatives.
Frequently asked
How many time steps do I need for reliable trend classification?
Esri recommends at least 10 time steps for meaningful trend categories. With fewer steps the Mann-Kendall trend test has low power, and categories such as 'oscillating' or 'sporadic' are difficult to distinguish reliably.
What is the difference between Space-Time Gi* and Space-Time Moran's I (LISA)?
Both are local statistics that extend to space-time, but they measure different things. Gi* detects clusters of high or low absolute values (hot and cold spots). LISA detects spatial association including both clustering of similar values and spatial outliers (high values surrounded by low, or vice versa). Use Gi* when you specifically want hot spot detection; use LISA when you also care about spatial outliers.
Does Space-Time Gi* account for temporal autocorrelation?
The statistic pools neighbours across a time window, which implicitly smooths temporal variation, but it does not explicitly model temporal autocorrelation as a time-series model would. The trend classification step applies the Mann-Kendall test to the Gi* time series for each location, capturing monotonic trends.
How do I choose the spatial and temporal neighbourhood sizes?
The spatial bandwidth is typically chosen based on the scale of the phenomenon (e.g., a 500 m radius for pedestrian-scale crime) and tested for sensitivity. The temporal bandwidth should match the periodicity of the process (e.g., monthly for seasonal disease). Incremental spatial autocorrelation analysis can help identify natural breaks in spatial dependence to guide bandwidth selection.
Can I apply this method to raster data?
Yes, if you aggregate the raster to a regular grid of polygons or points over consistent time steps. Continuous raster time series can be analysed by converting each cell to a space-time cube record, though very large rasters may require computational optimisation.
Sources
- Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189-206. DOI: 10.1111/j.1538-4632.1992.tb00261.x ↗
- Ord, J. K., & Getis, A. (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4), 286-306. DOI: 10.1111/j.1538-4632.1995.tb00912.x ↗
How to cite this page
ScholarGate. (2026, June 3). Space-Time Getis-Ord Gi* Hot Spot Statistic. ScholarGate. https://scholargate.app/en/spatial-analysis/space-time-getis-ord-gi-star
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Hot Spot AnalysisSpatial analysis↔ compare
- Local Getis-Ord Gi*Spatial analysis↔ compare
- Space-Time Local Indicators of Spatial AssociationSpatial analysis↔ compare
- Space-Time Spatial AutocorrelationSpatial analysis↔ compare