Interpoint Distance Test of Homogeneity for Multivariate Mixture Models

Finite mixtures offer a rich class of distributions for modelling of a variety of random phenomena in numerous fields of study. Using the sample interpoint distances (IPDs), we propose the IPD‐test statistic for testing the hypothesis of homogeneity of mixture of multivariate power series distribution or multivariate normal distribution. We derive the distribution of the IPDs that are drawn from a finite mixture of the multivariate power series distribution and multivariate normal distribution. Based on the empirical distribution of the IPDs, we construct a bootstrap test of homogeneity for other multivariate finite mixture models. The IPD test is applied to mixture models for matrix‐valued distributions and a test of homogeneity for Wishart mixture is presented. Numerical comparisons show that IPD test has accurate type I errors and is more powerful in most multivariate cases than the expectation–maximization (EM) test and modified likelihood ratio test.     

基于MSP430单片机的流量显示表硬件CPU设计

随着计算机的发展,工业自动化水平的提高,在工程中流量显示表已得到了广泛的使用。显示仪表精确度的高低,直接影响着企业的经济效益。在我国现有经济水平下,使用单片机开发的流量显示表,在工程中是非常适用的。该表是用MSP430F135为主芯片,并辅以其他的外围模块构成的具有串行通讯功能,满足流量检测显示的嵌入式最小系统。     

Do capital flows drive credit growth and consumption in Central and Eastern Europe?

Domestic credit expansion in CEE economies, fuelled in part by foreign capital inflows, helped increase household welfare before the 2008 financial crisis caused a contraction across the region. How strong are the linkages between the current account, domestic credit and consumer spending? This study compiles a quarterly dataset of domestic credit as a share of GDP for 11 CEE European Union members and isolates structural breaks in the series’ growth rates that often align with the 2008 crisis. Vector autoregressive methods, particularly impulse response functions, show that increased current-account deficits lead to increased consumption in six of the 11 countries and increased credit growth in three, and that shocks to credit growth increase consumption in six countries. Capital inflows significantly increase consumption through domestic credit in Slovenia, while the Baltics show a large share of significant effects.     

Markov-switching dynamic factor models in real time

We extend the Markov-switching dynamic factor model to account for some of the specificities of the day-to-day monitoring of economic developments from macroeconomic indicators, such as mixed sampling frequencies and ragged-edge data. First, we evaluate the theoretical gains of using data that are available promptly for computing probabilities of recession in real time. Second, we show how to estimate the model that deals with unbalanced panels of data and mixed frequencies, and examine the benefits of this extension through several Monte Carlo simulations. Finally, we assess its empirical reliability for the computation of real-time inferences of the US business cycle, and compare it with the alternative method of forecasting the probabilities of recession from balanced panels.     

The M4 Competition: Results,findings, conclusion and way forward

The M4 competition is the continuation of three previous competitions started more than 45 years ago whose purpose was to learn how to improve forecasting accuracy, and how such learning can be applied to advance the theory and practice of forecasting. The purpose of M4 was to replicate the results of the previous ones and extend them into three directions: First significantly increase the number of series, second include Machine Learning (ML) forecasting methods, and third evaluate both point forecasts and prediction intervals. The five major findings of the M4 Competitions are: 1. Out Of the 17 most accurate methods, 12 were “combinations” of mostly statistical approaches. 2. The biggest surprise was a “hybrid” approach that utilized both statistical and ML features. This method’s average sMAPE was close to 10% more accurate than the combination benchmark used to compare the submitted methods. 3. The second most accurate method was a combination of seven statistical methods and one ML one, with the weights for the averaging being calculated by a ML algorithm that was trained to minimize the forecasting. 4. The two most accurate methods also achieved an amazing success in specifying the 95% prediction intervals correctly. 5. The six pure ML methods performed poorly, with none of them being more accurate than the combination benchmark and only one being more accurate than Naïve2. This paper presents some initial results of M4, its major findings and a logical conclusion. Finally, it outlines what the authors consider to be the way forward for the field of forecasting.     

Steady state adjusting trends using a data-driven local polynomial regression

Economic variables usually follow a dynamic trend pattern. However, it is difficult to estimate this trend precisely as numerous economically- and statistically-based estimation methods exist. This contribution proposes a data-driven nonparametric trend that is local polynomial, to improve arbitrary trend estimations of commonly used methods concerning the selection of the smoothing parameter and the dependence structure. An iterative plug-in (IPI) algorithm determines the bandwidth endogenously and allows a theory-based interpretation of the length of growth processes. This length of the bandwidth reflects the lengths of the steady state periods. Consequently, the bandwidth identifies the time period of stable economic conditions and can detect economic changes. To demonstrate the power of this estimation approach, an extensive simulation study is performed. Furthermore, examples using US and UK GDP data along with a guide for the optimal choice of algorithms for empirical applications are provided. This proposed method yields new insights for growth dynamics, cyclical movements and their dependence.     

大学数学素质拓展课程的教学实践

本文结合昆明理工大学实际,探讨了在新的时代要求下为高校非数学专业学生开设数学拓展课程的必要性,并提出了相关的理论依据。同时,本文在已开设拓展课程的基础上总结了取得的成绩和存在的不足,为今后课程设置及教学的进一步完善提出了相关建议。     

Updating Input–Output Tables with Benchmark Table Series

Numerous methods have been proposed to update input–output (I–O) tables. They rely on the assumption that the economic structure will not change significantly during the interpolation period. However, this assumption may not always hold, particularly for countries experiencing rapid development. This study attempts to combine forecasting with a matrix transformation technique (MTT) to provide a new perspective on updating I–O tables. Under the assumption that changes in the trend of an economic structure are statistically significant, the method extrapolates I–O tables by combining time series models with an MTT and proceeds with only the total value added during the target years. A simulation study and empirical analysis are conducted to compare the forecasting performance of the MTT to the Generalized RAS (GRAS) and Kuroda methods. The results show that the comprehensive performance of the MTT is better than the performance of the GRAS and Kuroda methods, as measured by the Standardized Total Percentage Error, Theil's U and Mean Absolute Percentage Error indices.     

A critical overview of privacy-preserving approaches for collaborative forecasting

Cooperation between different data owners may lead to an improvement in forecast quality—for instance, by benefiting from spatiotemporal dependencies in geographically distributed time series. Due to business competitive factors and personal data protection concerns, however, said data owners might be unwilling to share their data. Interest in collaborative privacy-preserving forecasting is thus increasing. This paper analyzes the state-of-the-art and unveils several shortcomings of existing methods in guaranteeing data privacy when employing vector autoregressive models. The methods are divided into three groups: data transformation, secure multi-party computations, and decomposition methods. The analysis shows that state-of-the-art techniques have limitations in preserving data privacy, such as (i) the necessary trade-off between privacy and forecasting accuracy, empirically evaluated through simulations and real-world experiments based on solar data; and (ii) iterative model fitting processes, which reveal data after a number of iterations.     

基于泰勒公式的交错级数审敛准则的改进

本文利用泰勒公式,对文献[2]中交错级数的一种收敛准则给出了新的证明,并将此准则进行了改进,使其可以应用于由复合函数构成的更复杂的级数形式。