A Minimal Control Family of Dynamical Syetem for Universal Approximation

The universal approximation property (UAP) of neural networks is a fundamental characteristic of deep learning. It is widely recognized that a composition of linear functions and non-linear functions, such as the rectified linear unit (ReLU) activation function, can approximate continuous functions on compact domains. In this paper, we extend this efficacy to the scenario of dynamical systems with controls. We prove that the control family $\mathcal{F}_1 = \mathcal{F}_0 \cup \{ \text{ReLU}(\cdot)\}$ is enough to generate flow maps that can uniformly approximate diffeomorphisms of $\mathbb{R}^d$ on any compact domain, where $\mathcal{F}_0 = \{x \mapsto Ax+b: A\in \mathbb{R}^{d\times d}, b \in \mathbb{R}^d\}$ is the set of linear maps and the dimension $d\ge2$. Since $\mathcal{F}_1$ contains only one nonlinear function and $\mathcal{F}_0$ does not hold the UAP, we call $\mathcal{F}_1$ a minimal control family for UAP. Based on this, some sufficient conditions, such as the affine invariance, on the control family are established and discussed. Our result reveals an underlying connection between the approximation power of neural networks and control systems.Comment: 19 page

货币供给数量、结构与经济增长—来自ADL门限协整检验与时变格兰杰因果关系检验的证据

本文在粘性价格理论的基础上建立了具有前瞻性的货币数量理论模型，应用ADL门限协整检验与时变因果关系检验实证分析了货币供给数量M1与M2、货币供给结构M1、M2增速差对经济增长的影响，对我国的“货币中性”进行再检验。结果证实了货币供给数量与结构是经济增长的时变格兰杰原因，但持续的时间较短；在绝大多数的时间段内，表现出“货币中性”。此外，自2015年10月以来，M1、M2增速差持续扩大，但实证结果表明尽管货币增速差与经济增长呈现负相关关系，但时变因果关系表明M1、M2增速差并不是驱动GDP的格兰杰原因

短期资本流动、经济政策不确定性与恐慌指数—基于时变分析框架下的研究

本文在时变分析框架内对我国的短期资本流动、经济政策不确定性以及恐慌指数之间的动态关系进行研究。基于滚动窗口拔靴方法的格兰杰因果检验的结果表明：短期资本流动与经济政策不确定性之间存在时变的格兰杰因果关系，而2015年“股灾”期间，投资者由于“羊群效应”，使得经济政策不确定性不是短期资本流动的格兰杰原因；短期资本流动是恐慌指数的单向格兰杰因果关系；而经济政策不确定性与恐慌指数之间存在双向的格兰杰因果关系。随后，我们建立TVP-VAR模型，并利用等时间间隔的脉冲响应函数以及时点脉冲响应函数分析了三个变量的动态调整路径。研究结果表明：近年来，我国经济政策对短期资本流动的影响由“被动调节”转为“主动引导”。此外，由于我国资本账户尚未完全开放，国际资本市场的金融恐慌对我国短期资本流动的影响较小。相反，由于我国经济不断发展，短期资本流动已经成为影响国际金融恐慌的重要原因

货币增速剪刀差与股票市场收益率的时变格兰杰因果关系研究

本文从理论上分析了货币增速剪刀差对股票市场的作用机制，同时借助于基于滚动窗口拔靴法的格兰杰因果检验实证检验了两者之间的时变因果关系。实证结果表明两者具有显著的时变格兰杰因果关系。通常情况下，货币增速剪刀差的增加能够刺激股票市场的繁荣，存在正向的格兰杰因果关系。但在2015年的“牛市”期间，货币增速剪刀差是股市收益率的负向格兰杰因果关系。自2015年10月以来，尽管货币剪刀差持续攀升，但实证结果表明剪刀差的增加仅能提供较弱的相关关系的证据，而不存在因果关系

货币增速剪刀差与股票市场收益率的时变格兰杰因果关系研究

本文从理论上分析了货币增速剪刀差对股票市场的作用机制，同时借助于基于滚动窗口拔靴法的格兰杰因果检验实证检验了两者之间的时变因果关系。实证结果表明两者具有显著的时变格兰杰因果关系。通常情况下，货币增速剪刀差的增加能够刺激股票市场的繁荣，存在正向的格兰杰因果关系。但在2015年的“牛市”期间，货币增速剪刀差是股市收益率的负向格兰杰因果关系。自2015年10月以来，尽管货币剪刀差持续攀升，但实证结果表明剪刀差的增加仅能提供较弱的相关关系的证据，而不存在因果关系

经济增长与政府债务的非线性研究及其政策治理

This paper empirically analyze the nonlinear relation between real output per capital and public debt by employing threshold cointegration method based on ARDL model. Empirical results show that there exists a threshold cointegration relationship between government debt and real output per capital. In case of the empirical results, cutting government debt could boost economic growth in the long term. However, the short term variation of government debt makes little impact on real output per capital. Comparatively speaking, human capital and investment rate and trade openness make larger influence on real output per capital. From the perspective of economic policy, the government should take full advantage of the fiscal policy to cut the government debt with the operation space of monetary policy being compressed

经济增长与政府债务的非线性研究及其政策治理

This paper empirically analyze the nonlinear relation between real output per capital and public debt by employing threshold cointegration method based on ARDL model. Empirical results show that there exists a threshold cointegration relationship between government debt and real output per capital. In case of the empirical results, cutting government debt could boost economic growth in the long term. However, the short term variation of government debt makes little impact on real output per capital. Comparatively speaking, human capital and investment rate and trade openness make larger influence on real output per capital. From the perspective of economic policy, the government should take full advantage of the fiscal policy to cut the government debt with the operation space of monetary policy being compressed

How do weather risks in Canada and the United States affect global commodity prices? Implications for the decarbonisation process

Given that the probability of extreme weather has been dramatically increasing, this study contributes to the existing literature by bridging the relation between weather risks and global commodity prices with a secondary dataset (e.g., weather risks of Canada and the United States, agricultural raw materials price, gold price, and crude oil price). The results from the vector autoregression model and impulse response functions show that rising weather risks increase the price of agricultural raw materials and gold. However, the negative impact of weather risks on the crude oil price is found. Finally, the paper discusses the findings' potential implications (e.g., developing decarbonised supply chains) for decreasing weather risks' effects on commodity market uncertainties