Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.

Gold nanoparticles functionalised with fast water exchanging Gd3+ chelates: Linker effects on the relaxivity

The relaxivity displayed by Gd3+ chelates immobilized onto gold nanoparticles is the result of complex interplay between nanoparticle size, water exchange rate and chelate structure. In this work we study the effect of the length of -thioalkyl linkers, anchoring fast water exchanging Gd3+ chelates onto gold nanoparticles, on the relaxivity of the immobilized chelates. Gold nanoparticles functionalized with Gd3+ chelates of mercaptoundecanoyl and lipoyl amide conjugates of the DO3A-N-(-amino)propionate chelator were prepared and studied as potential CA for MRI. High relaxivities per chelate, of the order of magnitude 28-38 mM-1s-1 (30 MHz, 25 ºC) were attained thanks to simultaneous optimization of the rotational correlation time and of the water exchange rate. Fast local rotational motions of the immobilized chelates around connecting linkers (internal flexibility) still limit the attainable relaxivity. The degree of internal flexibility of the immobilized chelates seems not to be correlated with the length of the connecting linkers. Biodistribution and MRI studies in mice suggest that the in vivo behavior of the gold nanoparticles is determined mainly by size. Small nanoparticles (HD= 3.9 nm) undergo fast renal clearance and avoidance of the RES organs while larger nanoparticles (HD= 4.8 nm) undergo predominantly hepatobiliary excretion. High relaxivities, allied to chelate and nanoparticle stability and fast renal clearance in vivo suggests that functionalized gold nanoparticles hold great potential for further investigation as MRI Contrast Agents. This study contributes to understand the effect of linker length on the relaxivity of gold nanoparticles functionalized with Gd3+ complexes. It is a relevant contribution towards “design rules” for nanostructures functionalized with Gd3+ chelates as Contrast Agents for MRI and multimodal imaging.