Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

“It is through others that we become ourselves.” A study of Vygotskian play in Russian and Irish schools.

50 years after publishing his seminal work on play and its role in child development, Vygotskian theory is still highly influential in education, and particularly in early years. This paper presents two examples of full integration of Vygotskian principles into schools in two very different settings. Both report improvements in learning and in well-being, and exemplify the theory-practice-theory cycle, highlighting the development of new theoretical constructs arising out of putting theory firmly into practice. In both settings, the positive results have come from years of effort, in which school personnel who may have been skeptical at first, have been inspired by the impact of adopting Vygotskian play on the children they teach. The Northern Ireland study shows that at least some of the Golden Key principles (mixed-age play and enhanced home-school links) translate perfectly into very different cultural-historical contexts.