LÉVY PROCESS BASED ORNSTEIN-UHLENBECK TEMPERATURE MODEL WITH TIME VARYING SPEED OF MEAN REVERSION - Dzupire, Nelson Christopher; Ngare, Philip; Odongo, Leo (Pushpa Publishing House, 2018)
In this study we develop a Lévy process driven Ornstein-Uhlenbeck daily temperature model. The model takes into account a time dependent speed of mean reversion. It is statistically demonstrated that historical data and temperature differences are not normally distributed and hence we have argued against modeling temperature residuals as a Wiener process rather we have used the normal inverse Gaussian distribution which can ably describe skewed and heavy tailed data. Neural networks have been applied to estimate parameters of the detrended and deseasonalized temperature data because there is no prior knowledge on the nature of the function that describes the speed of mean reversion in the model
Keywords: Lévy process; Ornstein-Uhlenbeck; Mean reversion; Wiener process; Normal inverse Gaussian; Neural networks; Deseasonalized; Detrended; Temperature; Residuals.