世界経済・社会統計 = World development indicators

During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.

Variational Mode Decomposition

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

This chapter discusses leading problems linked to energy that the world is now confronting and to propose some ideas concerning possible solutions. Oil deserves special attention among all energy sources. Since the beginning of 1981, it has merely been continuing and enhancing the downward movement in consumption and prices caused by excessive rises, especially for light crudes such as those from Africa, and the slowing down of worldwide economic growth. Densely-populated oil-producing countries need to produce to live, to pay for their food and their equipment. If the economic growth of the industrialized countries were to be 4%, even if investment in the rational use of energy were pushed to the limit and the development of nonpetroleum energy sources were also pursued actively, it would be extremely difficult to prevent a sharp rise in prices. It is evident that it is absolutely necessary to pursue actively the development of coal, natural gas, and nuclear power if a physical shortage of energy is not to block economic growth.

World energy outlook

Volatility spillovers between oil prices and stock sector returns: Implications for portfolio management

The paper examines the extent of the current global crisis and the contagion effects it induces by conducting an empirical investigation of the extreme financial interdependences of some selected emerging markets with the US. Several copula functions that provide the necessary flexibility to capture the dynamic patterns of fat tail as well as linear and nonlinear interdependences are used to model the degree of cross-market linkages. Using daily return data from Brazil, Russia, India, China (BRIC) and the US, our empirical results show strong evidence of time-varying dependence between each of the BRIC markets and the US markets, but the dependency is stronger for commodity-price dependent markets than for finished-product export-oriented markets. We also observe high levels of dependence persistence for all market pairs during both bullish and bearish markets.

Global Financial Crisis, Extreme Interdependences, and Contagion Effects: The Role of Economic Structure?

https://hal.archives-ouvertes.fr/hal-00507823/document

Duc Khuong Nguyen

Papers

Volatility spillovers between oil prices and stock sector returns: Implications for portfolio management

Global Financial Crisis, Extreme Interdependences, and Contagion Effects: The Role of Economic Structure?

Oil prices, stock markets and portfolio investment: Evidence from sector analysis in Europe over the last decade ☆

Causal interactions between CO2 emissions, FDI, and economic growth: Evidence from dynamic simultaneous-equation models

On the impacts of oil price fluctuations on European equity markets: Volatility spillover and hedging effectiveness