Discussant:
Leopoldo Catania (University of Aarhus).
Abstract
Circular observations pose special problems for time series modelling, such as the frequent display of rapid movements all around the circle due to data circularity. The aim of the present work is to develop a new comprehensive class of time series models that addresses these issues and yields a coherent model specification methodology staightforward to implement. The novel approach is based on a circular conditional distribution, such as the von Mises, while the dynamics are driven by the score of the conditional distribution following the approach of Harvey (2013) and Creal et al. (2013). The flexibility of this approach allows its application on various directional distributions also with heavy tails, such as the Cardioid or the Skewed Cauchy distributions. The asymptotic distribution of the maximum likelihood estimator is derived for a first-order model. The paper shows also how the new score-driven model can be applied on non-stationary circular time series introducing a general class of non-stationary specifications. Furthermore, extending the univariate model with the adaptive dynamic mixture DAMM framework of Catania (2019), an extension of the previous work presents new model that can capture the presence of multiple regimes in wind direction, often caused by rapid movements across prevailing wind directions. The new model is then further extended with the use of the Weibul-Von Mises Distribution of Abe and Ley (2017) allowing for the joint modeling of wind direction and velocity. In doing so, through the conditional score update, the new model manages to handle directly the presence of missing observation in wind direction due to absence of wind. Moreover it is also capable of modeling the time varying heteroscedasticity in wind direction and velocity caused by extreme wind behaviour allowing for an additional dynamic "volatility parameter". Moreover the paper shows how a testing methodology based on the LM test and analysis of the residual correlation in the correlograms of the fitted scores can be use to detect the presence of dynamic parameters in between regimes and in the switching probabilities. The model is tested empirically on data from wind farms in Galicia, North West Spain, showing an improved fit in comparison with existing Mixture and Hidden Markov Chains models.
Organizzatore
Alessandra Luati