This is a great question! Thanks for asking it.
Sometimes I think these tools should be called hot regions, rather than hot spots. Conceptually, they work by visiting each bin in the cube and computing the mean value for that bin and all it's space-time neighbors. It then compares that local mean to the global mean (the mean for all bins in the cube since you used Entire Cube for the Global Window parameter). So even if there aren't any points in a New Hot Spot bin, if the local mean for that bin and it's space-time neighbors is hot, you can still have a new hot spot.
Let me try to put it into the context of your analysis. It looks like you used Create Space Time Cube by Aggregating Points. You said you wanted each fishnet bin to be about 1/4 square mile by 4 weeks. Great. Then you ran Emerging Hot Spot Analysis and defined the spatial-temporal neighborhood to extend 1/2 mile around each bin and one time step previous (so the current time step plus the previous time step... encompassing 8 weeks).
Several bins in your graphic are sporadic hot spots, so sometimes the mean for those bins and their space time neighbors were hot spots and sometimes they weren't, but they WERE hot for the last (most recent) time step. One of the bins is a consecutive hot spot, so for the last time step and at least one other immediately previous time step (fewer than 90%, though), it was a statistically significant hot spot (the local mean was significantly higher than the global mean). For the new hot spot bins, only the last (most recent) time step is hot. Even though there aren't any points in those bins (according to the graphic), the local neighborhoods have points that apparently make those bins hot. Maybe look at the 3D version of the cube columns. I don't know what the points represent, but the pattern might suggest a spreading process to the east ??
Also, I'm not sure if your image is showing ALL points in one part of your study area or just points for the last 4 weeks. If it is ALL points, you will clearly have a LOT of zero bins in your cube. In that case, the global mean is zero and it doesn't take many points in a neighborhood to create a hot spot (since finding a point is soooo very rare). My own feeling is that a ton of zeros (the vast majority) makes the analysis unstable. Perhaps you can increase bin size so you have fewer zero bins? I'm not sure what your points represent but I might have other ideas if indeed you are dealing with a cube that is almost entirely zeros.
I hope this helps! Thanks again for your question, Stephen!
Lauren Griffin, Esri
