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Correlation Analysis
Simple correlation metric for time Δt from t
- Plus 1 when t+Δt changes in the same direction as t
- Minus 1 when t+Δt changes in the opposite direction
Cross correlation identifies cause and effect
Auto correlation identifies periodic components
Use smoothing to select long or short term
Variable window to match Δt to sample period
Notes:
This kind of correlation function identifies the most consistent relationships in the data. If samples are smoothed above the period of an effect, its influence on the correlation function will be reduced. Applying a smoothing interval exactly equal to the period of an effect will cancel it out completely and allow longer term periodicity to emerge.
The metric is the relative probability of correlated change. A value of zero indicates that there's an equal probability of a change in either direction N years after an arbitrary change. A value of 100 means that a change in the same direction always occurs N years later and a value of -100 indicates that the correlated change is always in the opposite direction.
To identify short term periodicity, a window selecting only recent samples is used, since only the recent samples are close enough together to identify short period effects.