Macroeconomic and aggregate financial series share an unconventional type of nonlinear dynamics. Existing techniques (like co-integration) model these dynamics incompletely, hence generating seemingly paradoxical results. To avoid this, we provide a methodology to disentangle the long-run...

We detect a new stylized fact that is common to the dynamics of all macroeconomic series, including financial aggregates. Their Auto-Correlation Functions (ACFs) share a common four-parameter functional form that arises from the dynamics of a general equilibrium model with heterogeneous firms....

We provide a methodology to calculate the expectation of a variate x in terms of the moments of a transformation of x. Apart from the intrinsic interest in such a fundamental relation that relates the moments of a variate and its nonlinear transformations, our results can be used in practice to...

We derive the relation between the biases of correlograms and of estimates of auto-regressive AR(k) representations of stationary series, and we illustrate it with a simple AR example. The new relation allows for k to vary with the sample size, which is a representation that can be used for most...

This note derives an explicit formula for the numerical calculation of the square root of a matrix, when this function exists. An example is given as an illustration of the formula. The condition for the existence of the square root is also given.

Demographic change is expected to affect labour markets in very different ways on a regional scale. The objective of this paper is to explore the spatio-temporal patterns of recent distributional changes in the workers age structure, innovation output and skill composition for German regions by...

This study examines the long-run hedging ability of gold and silver prices against alternative measures of consumer price index for the UK and the US. We employ a dataset that spans from 1791 to 2010, and both a time-invariant and a time-varying cointegration framework. We find that gold can at...