Long-range Forecasting as a Past Value Problem: Correlations and Causality

Abstract:

Conventional weather forecast for long-range prediction is an initial value problem that takes the current state of the atmosphere to produce ensemble forecasts. Purely stochastic predictions for long-memory processes work as “past value” problems using historical data to provide a conditional forecast. The causal relations between teleconnection patterns are of key importance for deterministic prediction. They are ultimately expressed as cross-correlations in the atmospheric fields. Here we showed that, for stochastic forecasts, the key important relies on the concept of Granger causality and for it, the cross-correlations are only relevant at the level of the innovations. The Stochastic Seasonal to Interannual Prediction System (StocSIPS) assumes a fractional Gaussian noise model for describing the temperature variability. Here we show that this model is also adequate in the multivariate case by testing the whiteness of the vector innovations. This confirms the lack of Granger causality for the temperature in the macroweather regime.