A Fourier transform method for nonparametric estimation of multivariate volatility

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOS633 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Declining Use of Unskilled Labour in Italian Manufacturing: Is Trade to Blame? CEPS Working Document No. 178, December 2001

As in other industrialised countries, the manufacturing sector in Italy has recently experienced a substantial increase in the use of skilled relative to unskilled workers - skill upgrading. In this paper we estimate a model, based upon the notion of outsourcing, of the relative demand for skilled labour which allows identification of the roles of technological change and trade, the two main culprits, in skill upgrading. Compared to previous studies of Italy the model is applied to highly disaggregated industrial data and in addition the impact of trade is more precisely measured through the separate identification of import flows from low-wage labour abundant countries and those from OECD partners. Furthermore we also introduce a measure of trade variability. Our results show firstly that economic variables played little or no role in determining the relative demand for unskilled workers in the 1970s in Italy, reflecting the nature of Italian labour market institutions in the period. Subsequently, in the 1980s and 1990s, following some labour market reforms, we find that international competition, in terms of import penetration and the variability of trade prices, had a significant effect on the relative demand for blue-collar workers in Italy in skilled intensive sectors. In unskilled intensive sectors, such as textiles and clothing, where the impact of imports from low-wage countries might be expected to be more pronounced, we do not find a significant effect from imports but rather that the most important role has been played by technological change. The result is consistent with previous studies that indicate that Italian textile and clothing firms have remained internationally competitive by increasingly switching to high quality segments of the industry

Detecting a long odd hole

For each integer $t\ge 5$, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least $t$ and odd

Induced subgraphs of graphs with large chromatic number. XII. Distant stars

The Gyarfas-Sumner conjecture asserts that if H is a tree then every graph with bounded clique number and very large chromatic number contains H as an induced subgraph. This is still open, although it has been proved for a few simple families of trees, including trees of radius two, some special trees of radius three, and subdivided stars. These trees all have the property that their vertices of degree more than two are clustered quite closely together. In this paper, we prove the conjecture for two families of trees which do not have this restriction. As special cases, these families contain all double-ended brooms and two-legged caterpillars

Disjoint paths in tournaments

Given $k$ pairs of vertices $(s_i,t_i)$, $1\le i\le k$, of a digraph $G$, how can we test whether there exist $k$ vertex-disjoint directed paths from $s_i$ to $t_i$ for $1\le i\le k$? This is NP-complete in general digraphs, even for $k = 2$, but for $k=2$ there is a polynomial-time algorithm when $G$ is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen. Here we prove that for all fixed $k$ there is a polynomial-time algorithm to solve the problem when $G$ is semicomplete

Detecting an induced net subdivision

A {\em net} is a graph consisting of a triangle $C$ and three more vertices, each of degree one and with its neighbour in $C$, and all adjacent to different vertices of $C$. We give a polynomial-time algorithm to test whether an input graph has an induced subgraph which is a subdivision of a net. Unlike many similar questions, this does not seem to be solvable by an application of the "three-in-a-tree" subroutine

Induced subgraphs of graphs with large chromatic number. XI. Orientations

Fix an oriented graph H, and let G be a graph with bounded clique number and very large chromatic number. If we somehow orient its edges, must there be an induced subdigraph isomorphic to H? Kierstead and Rodl raised this question for two specific kinds of digraph H: the three-edge path, with the first and last edges both directed towards the interior; and stars (with many edges directed out and many directed in). Aboulker et al subsequently conjectured that the answer is affirmative in both cases. We give affirmative answers to both questions

Detecting a long odd hole

For each integer $t\ge 5$, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least $t$ and odd