Operational risk quantified with spectral risk measures: a refined closed-form approximation

The quantification of operational risk has become an important issue as a result of the new capital charges required by the Basel Capital Accord (Basel II) to cover the potential losses of this type of risk. In this paper, we investigate second-order approximation of operational risk quantified with spectral risk measures (OpSRMs) within the theory of second-order regular variation (2RV) and second-order subexponentiality. The result shows that asymptotically two cases (the fast convergence case and the slow convergence) arise depending on the range of the second-order parameter. We also show that the second-order approximation under 2RV is asymptotically equivalent to the slow convergence case. A number of Monte Carlo simulations for a range of empirically relevant frequency and severity distributions are employed to illustrate the performance of our second-order results. The simulation results indicate that our second-order approximations tend to reduce the estimation errors to a great degree, especially for the fast convergence case, and are able to capture the sub-extremal behavior of OpSRMs better than the first-order approximation. Our asymptotic results have implications for the regulation of financial institutions, and may provide further insights into the measurement and management of operational risk.     

基于谱分析的连续加工过程检验批量的确定

在连续加工过程中 ,合理地确定检验批量 ,不仅可以反映加工过程的稳定性 ,而且也是确定抽样检验方案及检验频次的基础。本文主要利用时间序列的谱分析方法对连续加工过程的质量检测数据进行周期划分 ,从而确定抽样检验的批量 ,并根据周期分析结果 ,指出了导致加工质量产生波动的一些原因。     

Business Cycles Synchronisation and Symmetries in the Transition to East African Monetary Union

Our paper explores the prospects for the proposed East African Monetary Union (EAMU) by employing rigorous empirical tools to analyse business cycles synchronisation, structural cross-correlations, spectral decomposition and regional clusters to identify different cyclical episodes, periodicities and characterise the economic cycles of East African countries. We find that cyclical movements reflect various idiosyncratic, common, historical and external shocks in the region. Secondly, all countries appear to be structurally correlated with each other except for South Sudan and Burundi. Our results also observe that the contemporaneous co-movements of East African Community (EAC) cycles with those of Kenya and Tanzaniaare procyclical with coincidental path shift, while the same EAC cycles appear to be acyclical with those of Burundi. Additionally, from the spectral decomposition, Kenyan cycles take 10 years to complete, while those of Tanzania and Rwanda take 8 years. Ugandan and Burundian cycles take approximately 5 years, while the cyclical frequency for South Sudan corresponds to 3.3 years. Finally, the cluster characterisation of countries reveals that South Sudan, Burundi and Rwanda form a group, while Kenya and Tanzania from a group distinct from the rest. We urge the member countries to prioritise policies on regional risk-sharing and adjustment mechanisms, in addition to establishing credible institutional infrastructure that ensures surveillance and enforcement of convergence conditions adopted in EAMU protocol.     

移动通信信号自动调制识别的谱相关方法

一些不同的数字调制信号有着相同或相近的功率谱密度,但它们的谱相关函数却有明显区别。平稳的噪声和干扰的谱相关为零。利用谱相关函数的这些性质可以识别出噪声中的调制信号。本文提出了一种用于移动通信信号自动调制识别的谱相关算法,该方法可以识别各种主要无线系统和标准所采用的调制类型。     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

Measuring and testing Granger causality over the spectrum: An application to European production expectation surveys

Decomposing Granger causality over the spectrum allows us to disentangle potentially different Granger causality relationships over different frequencies. This may yield new and complementary insights compared to traditional versions of Granger causality. In this paper, we compare two existing approaches in the frequency domain, proposed originally by Pierce [Pierce, D. A. (1979). R-squared measures for time series. Journal of the American Statistical Association, 74, 901–910] and Geweke [Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77, 304–324], and introduce a new testing procedure for the Pierce spectral Granger causality measure. To provide insights into the relative performance of this test, we study its power properties by means of Monte Carlo simulations. In addition, we apply the methodology in the context of the predictive value of the European production expectation surveys. This predictive content is found to vary widely with the frequency considered, illustrating the usefulness of not restricting oneself to a single overall test statistic.     

Detecting self-organisational change in economic processes exhibiting logistic growth

This paper offers an econometric methodology for the detection of self-organisational change (defined in terms of the presence of time irreversibility, structural change and fundamental uncertainty) in economic processes that follow logistic diffusion growth paths in historical time. The approach we adopted is built upon recent developments in `moving window' spectral methods which are applied to the scaled residuals generated by estimated logistic diffusion models. We illustrate the use of such methods by examining the case of a financial instrument, namely, the Australian Building Society Deposit, which experienced logistic growth in its market share until bank deregulation was enacted in the 1980s. We show that there is clear evidence that self-organisational change is present over the historical period considered.     

Dynamic principal component CAW models for high-dimensional realized covariance matrices

We propose a new dynamic principal component CAW model (DPC-CAW) for time-series of high-dimensional realized covariance matrices of asset returns (up to 100 assets). The model performs a spectral decomposition of the scale matrix of a central Wishart distribution and assumes independent dynamics for the principal components' variances and the eigenvector processes. A three-step estimation procedure makes the model applicable to high-dimensional covariance matrices. We analyze the finite sample properties of the estimation approach and provide an empirical application to realized covariance matrices for 100 assets. The DPC-CAW model has particularly good forecasting properties and outperforms its competitors for realized covariance matrices.     

非平稳条件下的市场可预测性问题研究

本文研究了非平稳对线性、非线性可预测性检验的影响,从非平稳角度解释了"非线性可预测性难题"。在此基础上对传统的Box-Pierce-Ljung线性检验法和广义谱密度非线性检验法进行了修正,并运用严格的理论证明和蒙特卡罗模拟证实了它们在大样本和有限样本情况下的非平稳稳健性。最后,运用修正的检验方法对我国第一只股指期货标的沪深300统一指数的可预测性进行了分析。本文结论对于我国金融市场实证研究具有重要的指导意义,也反映了我国新兴金融市场的独有特性以及成熟统计方法在我国的实用性。     

Spectral Risk Measures: Properties and Limitations

Spectral risk measures (SRMs) are risk measures that take account of user risk-aversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems are identified with both types of spectral risk measure. The general lesson is that users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs.