Generalized spectral tests for the martingale difference hypothesis

^aThis article proposes a test for the Martingale Difference Hypothesis (MDH) using dependence measures related to the characteristic function. The MDH typically has been tested using the sample autocorrelations or in the spectral domain using the periodogram. Tests based on these statistics are inconsistent against uncorrelated non-martingales processes. Here, we generalize the spectral test of Durlauf (1991) for testing the MDH taking into account linear and nonlinear dependence. Our test considers dependence at all lags and is consistent against general pairwise nonparametric Pitman's local alternatives converging at the parametric rate n^(-1/2), with n the sample size. Furthermore, with our methodology there is no need to choose a lag order, to smooth the data or to formulate a parametric alternative. Our approach can be easily extended to specification testing of the conditional mean of possibly nonlinear models. The asymptotic null distribution of our test depends on the data generating process, so a bootstrap procedure is proposed and theoretically justified. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. A Monte Carlo study examines the finite sample performance of our test and shows that it is more powerful than some competing tests. Finally, an application to the S and P 500 stock index and exchange rates highlights the merits of our approach

Generalized spectral tests for the martingale difference hypothesis

This article proposes a test for the martingale difference hypothesis (MDH) using dependence measures related to the characteristic function. The MDH typically has been tested using the sample autocorrelations or in the spectral domain using the periodogram. Tests based on these statistics are inconsistent against uncorrelated non-martingales processes. Here, we generalize the spectral test of Durlauf (1991) for testing the MDH taking into account linear and nonlinear dependence. Our test considers dependence at all lags and is consistent against general pairwise nonparametric Pitman's local alternatives converging at the parametric rate n-1/2, with n the sample size. Furthermore, with our methodology there is no need to choose a lag order, to smooth the data or to formulate a parametric alternative. Our approach could be extended to specification testing of the conditional mean of possibly nonlinear models. The asymptotic null distribution of our test depends on the data generating process, so a bootstrap procedure is proposed and theoretically justified. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. A Monte Carlo study examines the finite sample performance of our test and shows that it is more powerful than some competing tests. Finally, an application to the S&P 500 stock index and exchange rates highlights the merits of our approach.Publicad

Testing the martingale difference hypothesis using integrated regression functions

An omnibus test for testing a generalized version of the martingale difference hypothesis (MDH) is proposed. This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects) or testing for directional predictability. A unified approach for dealing with all of these testing problems is proposed. These hypotheses are long standing problems in econometric time series analysis, and typically have been tested using the sample autocorrelations or in the spectral domain using the periodogram. Since these hypotheses cover also nonlinear predictability, tests based on those second order statistics are inconsistent against uncorrelated processes in the alternative hypothesis. In order to circumvent this problem pairwise integrated regression functions are introduced as measures of linear and nonlinear dependence. The proposed test does not require to chose a lag order depending on sample size, to smooth the data or to formulate a parametric alternative model. Moreover, the test is robust to higher order dependence, in particular to conditional heteroskedasticity. Under general dependence the asymptotic null distribution depends on the data generating process, so a bootstrap procedure is considered and a Monte Carlo study examines its finite sample performance. Then, the martingale and conditional heteroskedasticity properties of the Pound/Dollar exchange rate are investigated.Publicad

Thermal radiation from subwavelength objects and the violation of Planck’s law

Thermal radiation is a ubiquitous physical phenomenon that has been usually described with the help of Planck’s law, but recent developments have proven its limitations. Now, experimental advances have demonstrated that the far-field thermal radiation properties of subwavelength objects drastically violate Planck’s lawJ.C.C. acknowledges financial support from the Spanish MINECO (Contract No. FIS2017–84057-P

Costs and benefits of the cap reform

This working paper presents a cost-benefit analysis of the reform of the Common Aqricultural policy (CAP) considering both its effects on farmers in the European Community (EC) and on farmers in third countries. The new questions raised by the Uruguay round of the GATT (General Aqreement on Tariffs and Tax) and the start up of the sinqle Market in Europe are considered in order to examine the possible effects on agricultural income with special reference to family farms in the south of Europe. In the case of Spain, data are presented for possible effects of restructuring work occasioned by the reform

Right-handed lepton mixings at the LHC

We study how the elements of the leptonic right-handed mixing matrix can be determined at the LHC in the minimal Left-Right symmetric extension of the standard model. We do it by explicitly relating them with physical quantities of the Keung-Senjanovi\'c process and the lepton number violating decays of the right doubly charged scalar. We also point out that the left and right doubly charged scalars can be distinguished at the LHC, without measuring the polarization of the final state leptons coming from their decays.Comment: 12 pages, 6 figures, discussion in section III expanded and sharpened, one appendix added, updated reference

El Salvador: A Central American Tiger?

El Salvador is becoming an economic success story in Central America. Since the end of the civil conflict in 1992, which left the country in ruins, El Salvador has transformed its economy by implementing a far-reaching liberalization process undertaken by democratic governments, which has included the privatization of state enterprises, deregulation, trade and financial liberalization, privatization of the pension system, and the adoption of the U.S. dollar as its official currency. According to the Fraser Institute's Economic Freedom of the World Report, El Salvador ranks among the top 25 freest economies in the world. The results of the market reforms are notable: between 1991 and 2007, the percentage of households below the poverty line fell from 60 percent to 34.6 percent. However, official figures point to mediocre average annual per capita growth during the period 1992 -- 2007 -- only 1.9 percent -- which is very similar to Latin America's average of 1.6 percent in the same period. But official figures grossly underestimate the performance of the economy because of flawed measurement. In fact, the economy is probably more than 30 percent larger than indicated by the official data. Accordingly, the average per capita growth rate since 1992 has been approximately 5.2 percent per year. El Salvador still has much to do on its policy agenda. In particular, high crime rates constitute a major hindrance to further growth. This lack of security represents the greatest threat to sustained growth and liberal policies. Nonetheless, the country is showing the rest of the region how economic freedom can pave the way for development and how globalization offers great opportunities for developing countries that are willing to implement a coherent set of mutually supportive market reforms