"Theoretical and empirical comparison among Unobserved Components Models and some extesions of Young's methodology"
A great amount of methodologies have been proposed for the analysis and prediction of time series analysis within the univariate universe. This is also true in more restricted areas, like the Unobserved Components Models (UCM, also known as Structural Models). Therefore, a difficult problem for the user is to select which method is going to give the best performance in terms of his/her own objectives. The present thesis analyses and compares different theoretical and empirical aspects of a set of UC well-known methods (some ad-hoc; structural models; reduced form methods; and methods developed in the frequency domain). Especial emphasis is done on the hypotheses on which all these methods are based; on the properties of the estimated components; and on predictive performance. For these purposes, all methods have been applied to a number of economic indicators from both the Spanish and US economies.
There have been found a number of advantages of Young's method, from different points of view: initial hypotheses are less restrictive (e.g. certain stationarity conditions are not necessary); it gives smoother estimated components compared with other methods; the predictive performance is often superior; and the optimisation in the frequency domain avoids some problems that arises in Maximum Likelihood (ML) estimation. In particular, the likelihood surface for this kind of models is often quite flat around the optimum, and computation times are prohibitively high. On the contrary, the frequency approach allows for the optimisation of more complex models when required (with higher amount of hyper-parameters), and computation complexity is much smaller (especially useful for long series and mixture of periodic components). The way this methodology is posed allows for easy and powerful generalisations of the current formulations of the components, making possible the use of more complex and flexible models that provides richer behaviour of the forecasts, capable to adapt to a wide range of different forecast situations arising in practice.
