Stochastic Differential Equations and Temperature — NASA Climate Data pt. 2

The Ornstein-Uhlenbeck process, a type of stochastic differential equation, offers a powerful way to model the random fluctuations of temperature over time. This model is particularly effective because it is "mean-reverting," reflecting how temperatures naturally gravitate back toward a seasonal average after an unusual spike or dip. A crucial parameter known as kappa (κ) governs the speed of this reversion, quantifying how quickly temperatures correct themselves. This method has significant practical applications beyond forecasting, such as in finance for pricing weather derivatives that help companies manage climate-related financial risks.