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Long‐Range Forecasting as a Past Value Problem: Untangling Correlations and Causality With Scaling
Author(s) -
Del Rio Amador L.,
Lovejoy S.
Publication year - 2021
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2020gl092147
Subject(s) - teleconnection , causality (physics) , granger causality , econometrics , range (aeronautics) , statistical physics , multivariate statistics , scaling , climatology , mathematics , statistics , physics , geology , el niño southern oscillation , materials science , geometry , quantum mechanics , composite material
Conventional long‐range weather prediction is an initial value problem that uses the current state of the atmosphere to produce ensemble forecasts. Purely stochastic predictions for long‐memory processes are “past value” problems that use historical data to provide conditional forecasts. Teleconnection patterns, defined from cross‐correlations, are important for identifying possible dynamical interactions, but they do not necessarily imply causation. Using the precise notion of Granger causality, we show that for long‐range stochastic temperature forecasts, the cross‐correlations are only relevant at the level of the innovations–not temperatures. This justifies the Stochastic Seasonal to Interannual Prediction System (StocSIPS) that is based on a (long memory) fractional Gaussian noise model. Extended here to the multivariate case (m‐StocSIPS) produces realistic space‐time temperature simulations. Although it has no Granger causality, emergent properties include realistic teleconnection networks and El Niño events and indices.