Statistical Analysis and Evaluation of Macroeconomic Policies: A Selective Review

In this paper,we highlight some recent developments of a new route to evaluate macroeconomic policy effects,which are investigated under the framework with potential outcomes.First,this paper begins with a brief introduction of the basic model setup in modern econometric analysis of program evaluation.Secondly,primary attention goes to the focus on causal effect estimation of macroeconomic policy with single time series data together with some extensions to multiple time series data.Furthermore,we examine the connection of this new approach to traditional macroeconomic models for policy analysis and evaluation.Finally,we conclude by addressing some possible future research directions in statistics and econometrics.     

A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for Asset Prices

Methodology and Computing in Applied Probability - We propose a new approach for bivariate financial time series modelling which allows for mutual excitation between shocks. Jumps are triggered by...     

Deep learning models for inflation forecasting

We propose a hybrid deep learning model that merges Variational Autoencoders and Convolutional LSTM Networks (VAE-ConvLSTM) to forecast inflation. Using a public macroeconomic database that comprises 134 monthly US time series from January 1978 to December 2019, the proposed model is compared against several popular econometric and machine learning benchmarks, including Ridge regression, LASSO regression, Random Forests, Bayesian methods, VECM, and multilayer perceptron. We find that VAE-ConvLSTM outperforms the competing models in terms of consistency and out-of-sample performance. The robustness of such conclusion is ensured via cross-validation and Monte-Carlo simulations using different training, validation, and test samples. Our results suggest that macroeconomic forecasting could take advantage of deep learning models when tackling nonlinearities and nonstationarity, potentially delivering superior performance in comparison to traditional econometric approaches based on linear, stationary models.     

我国股市网络稳定性及其宏观影响因素——基于三种网络拓扑结构、鲁棒性的实证研究

基于金融时间序列的多重分形特征及衡量市场风险的VaR模型,建立我国沪深股市的股票关联网络,实证研究三种网络拓扑结构特征,并使用协整检验方法分析网络稳定性和宏观经济变量间的长期均衡关系。结果表明:股票价格网络不具有无标度性,多标度网络和风险网络都具有无标度性;在三种网络中,风险网络具有更强的鲁棒性。此外,股市波动率和网络稳定系数间互为格兰杰因果关系,股市波动的前期变化能有效解释网络稳定性系数的变化;网络稳定性与宏观经济变量间具有长期的均衡关系,GDP增长率、消费者物价水平CPI对网络稳定性具有正向效应,利率对网络稳定性具有负向效应。风险网络的提出有助于分析我国股市的短期风险及稳定性,并为制定系统风险防御策略提供参考。     

Eigenanalysis on a bivariate covariance kernel

Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative distribution function is used. Some bounds for the trace of the kernel and some inequalities for a continuous random variable concerning a function and its derivative are obtained. We also obtain relations to diagonal expansions and canonical correlation analysis and, as a by-product, series of constants for some particular distributions.     

Local times of stochastic processes with positive definite bivariate densities

A new class of stochastic processes, called processes of positive bivariate type, is defined. Such a process is typically one whose bivariate density functions are positive definite, at least for pairs of time points which are sufficiently mutually close. The class includes stationary Gaussian processes and stationary reversible Markov processes, and is closed under the operations of composition and convolution. The purpose of this work is to show that the local times of such processes can be investigated in a natural way. One of the main contributions is an orthogonal expansion of the local time which is new even in the well-studied stationary Gaussian case. The basic tool in its construction is the Lancaster-Sarmanov expansion of a bivariate density in a series of canonical correlations and canonical variables.     

Bivariate occupation measure dimension of multidimensional processes

Bivariate occupation measure dimension is a new dimension for multidimensional random processes. This dimension is given by the asymptotic behavior of its bivariate occupation measure. Firstly, we compare this dimension with the Hausdorff dimension. Secondly, we study relations between these dimensions and the existence of local time or self-intersection local time of the process. Finally, we compute the local correlation dimension of multidimensional Gaussian and stable processes with local Hölder properties and show it has the same value that the Hausdorff dimension of its image have. By the way, we give a new a.s. convergence of the bivariate occupation measure of a multidimensional fractional Brownian or particular stable motion (and thus of a spatial Brownian or Lévy stable motion).     

Chaos and nonlinear dynamics in financial and nonfinancial time series: Evidence from Finland

This paper contains a set of tests for nonlinearities in economic time series. The tests comprise both standard diagnostic tests for revealing nonlinearities and some new developments in modelling nonlinearities. The latter test procedures make use of models in chaos theory, so-called long-memory models and some asymmetric adjustment models. Empirical tests are carried out with Finnish monthly data for ten macroeconomic time series covering the period 1920–1994. Test results support unambiguously the notion that there are strong nonlinearities in the data. The evidence for chaos, however, is weak. Nonlinearities are detected not only in a univariate setting but also in some preliminary investigations dealing with a multivariate case. Certain differences seem to exist between nominal and real variables in nonlinear behaviour. Some differences are also detected in terms of short and long-term behaviour.     

A Kendall correlation coefficient between functional data

Measuring dependence is a very important tool to analyze pairs of functional data. The coefficients currently available to quantify association between two sets of curves show a non robust behavior under the presence of outliers. We propose a new robust numerical measure of association for bivariate functional data. We extend in this paper Kendall coefficient for finite dimensional observations to the functional setting. We also study its statistical properties. An extensive simulation study shows the good behavior of this new measure for different types of functional data. Moreover, we apply it to establish association for real data, including microarrays time series in genetics.

     

Behavioral Models for List Decoding

Recently it has been shown that list decoding of Reed-Solomon codes may be translated into a bivariate interpolation problem. The data consist of pairs in a finite field and the aim is to find a bivariate polynomial that interpolates the given pairs and is minimal with respect to some criterion. We present a systems theoretic approach to this interpolation problem. With the data points we associate a set of time series, also called trajectories. For this set of trajectories we construct the Most Powerful Unfalsified Model (MPUM). This is the smallest possible model that explains these trajectories. The bivariate polynomial is then derived from a specific polynomial representation of the MPUM.     

基于二元连分式的散乱数据递推插值格式

本文首先基于新的非张量积型偏逆差商递推算法,分别构造奇数与偶数个插值节点上的二元连分式散乱数据插值格式,进而得到被插函数与二元连分式间的恒等式.接着,利用连分式三项递推关系式,提出特征定理来研究插值连分式的分子分母次数.然后,数值算例表明新的递推格式可行有效,同时,通过比较二元Thiele型插值连分式的分子分母次数,发现新的二元插值连分式的分子分母次数较低,这主要归功于节省了冗余的插值节点. 最后,计算此有理函数插值所需要的四则运算次数少于计算径向基函数插值.     

关于二元样条空间下的三角剖分的分解

本文指出，在一定条件下，对于一个二元样条空间，所考虑的三种剖分中的某些胞腔和网线可以消去，而前后两个三角剖分下样条空间的结构有着紧密的联系，从而可以用简单划分下的空间结构表示复杂剖分下的空间结构。该分解剖分的步骤可以递推的进行，尤其对Ｓ＾１ｓ。据此，本文还分析了剖分对Ｓ＾１２的奇异性并给出一组奇异的剖分。     

灰色预测法的进一步推广及应用

把原始时间序列进行多次累加,产生多个新序列,研究它们之间的关系,建立多元线性(或非线性)回归模型.给定显著性水平α,对回归方程进行显著性检验,在置信度1-α下,利用微分,差分关系建立相应的高阶微分方程,从而实现对原序列的预测或控制.该方法进一步推广了灰色预测法,为时间序列建模提供了一个新手段,一些著名的微分方程模型成为这一方法的特例,最后,用该方法对中国1979年至2008年的GDP序列建立微分方程模型并进行预测.     

Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games

We study reference-dependent preference relations defined by a real-valued bivariate function and prove an existence criterion for maximal elements. Then we formulate a generalized version of the well-known Brondsted maximum principle and apply it to behavioral traps and Nash equilibrium in games with preference relations that are not necessarily partial orders.     

Stress testing network reconstruction via graphical causal model

An resilience optimal evaluation of financial portfolios implies having plausible hypotheses about the multiple interconnections between the macroeconomic variables and the risk parameters. In this article, we propose a graphical model for the reconstruction of the causal structure that links the multiple macroeconomic variables and the assessed risk parameters, it is this structure that we call stress testing network. In this model, the relationships between the macroeconomic variables and the risk parameter define a “relational graph” among their time‐series, where related time‐series are connected by an edge. Our proposal is based on the temporal causal models, but unlike, we incorporate specific conditions in the structure which correspond to intrinsic characteristics this type of networks. Using the proposed model and given the high‐dimensional nature of the problem, we used regularization methods to efficiently detect causality in the time‐series and reconstruct the underlying causal structure. In addition, we illustrate the use of model in credit risk data of a portfolio. Finally, we discuss its uses and practical benefits in stress testing.     

COPAR—multivariate time series modeling using the copula autoregressive model

The analysis of multivariate time series is a common problem in areas like finance and economics. The classical tools for this purpose are vector autoregressive models. These however are limited to the modeling of linear and symmetric dependence. We propose a novel copula‐based model that allows for the non‐linear and non‐symmetric modeling of serial as well as between‐series dependencies. The model exploits the flexibility of vine copulas, which are built up by bivariate copulas only. We describe statistical inference techniques for the new model and discuss how it can be used for testing Granger causality. Finally, we use the model to investigate inflation effects on industrial production, stock returns and interest rates. In addition, the out‐of‐sample predictive ability is compared with relevant benchmark models. Copyright © 2014 John Wiley & Sons, Ltd.     

A fractional credit model with long range dependent default rate

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today’s prices of European calls and compare our results to the classical Brownian model.     

Adaptive Bivariate Chebyshev Approximation

We propose an adaptive algorithm which extends Chebyshev series approximation to bivariate functions, on domains which are smooth transformations of a square. The method is tested on functions with different degrees of regularity and on domains with various geometries. We show also an application to the fast evaluation of linear and nonlinear bivariate integral transforms.     

Divided-difference equation and three-term recurrence relations of some systems of bivariate q-orthogonal polynomials

Partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial divided (or q)-difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials.     

An optimization technique based on a vector autoregression model with state space representation: application to Ukrainian cargo transport data

This paper proposes to forecast indicators of the Ukrainian cargo transport system, taking into account their relations with macroeconomic indicators. Increased forecast accuracy at a priori information uncertainty is attained through an optimization technique, starting with a Vector Autoregression (VAR) model of observed multiple time series, its state space representation and subsequent adaptive filtering. The adaptive filter, earlier proposed by the authors, minimizes forecasting errors. Under an optimization criterion, the information divergence of Kullback–Leibler between probability distributions of real values and their estimations is established. The main advantage of the proposed technique is connected with the opportunity to estimate future values of multiple time series even in presence of structural breaks (describing the changes of the status ‘before crisis’ / ‘after crisis’). The observations are available from 2003:1–2011:12, the analysis is performed for the period 2003:1–2011:9. In-sample forecasting of multiple time series of cargo volumes transferred by different transport modes and two macro indicators is compared with the forecast based on a VAR model. In-sample forecast is realized for the last three months 2011:10–2011:12.