Showing 1 - 10 of 11
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...
Persistent link: https://www.econbiz.de/10010551736
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...
Persistent link: https://www.econbiz.de/10010551741
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.
Persistent link: https://www.econbiz.de/10010551747
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...
Persistent link: https://www.econbiz.de/10010551749
Persistent link: https://www.econbiz.de/10008738771
This paper deals with models allowing for trending processes and cyclical component with error processes that are possibly nonstationary, nonlinear, and non-Gaussian. Asymptotic confidence intervals for the trend, cyclical component, and memory parameters are obtained. The confidence intervals...
Persistent link: https://www.econbiz.de/10008504405
Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution that we derive. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We...
Persistent link: https://www.econbiz.de/10008504406
This paper introduces a new method for estimating large variance matrices. Starting from the orthogonal decomposition of the sample variance matrix, we exploit the fact that orthogonal matrices are never ill-conditioned and therefore focus on improving the estimation of the eigenvalues. We...
Persistent link: https://www.econbiz.de/10008504407
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...
Persistent link: https://www.econbiz.de/10005001511
We detect a new stylized fact about the common dynamics of macroeconomic and financial aggregates. The rate of decay of the memory of these series is depicted by their Auto-Correlation Functions (ACFs). They all share a common four-parameter functional form that we derive from the dynamics of an...
Persistent link: https://www.econbiz.de/10005091097