投资者信心和中国宏观经济波动——基于MIDAS混频模型

将投资者信心指数引入MIDAS混频模型之中,可以考察新冠疫情背景下投资者信心对于中国宏观经济波动的影响。基于投资者信心指数和“三驾马车”对我国季度GDP增长率进行预测,通过实证发现:引入投资者信心指数的MIDAS混频模型在预测精准度方面和基准模型进行比较,预测精准度高于未加入投资者信心的模型,均方根残差比值更小;在多元MIDAS混频模型之中,加入投资者信心指数的回归模型对我国GDP的实时预报和短期预测结果更加稳定,可为决策者提供更加精确的参考区间;宏观经济的波动对投资者信心指数变化反应,和投资、消费和进出口相比是最灵敏的。这为定量追踪宏观经济波动提供了一个新的视角。     

Inference of the derivative of nonparametric curve based on confidence distribution

Abstract

This paper focuses on inference based on the confidence distributions of the nonparametric regression function and its derivatives, in which dependent inferences are combined by obtaining information about their dependency structure. We first give a motivating example in production operation system to illustrate the necessity of the problems studied in this paper in practical applications. A goodness-of-fit test for polynomial regression model is proposed on the basis of the idea of combined confidence distribution inference, which is the Fisher’s combination statistic in some cases. On the basis of this testing results, a combined estimator for the p-order derivative of nonparametric regression function is provided as well as its large sample size properties. Consequently, the performances of the proposed test and estimation method are illustrated by three specific examples. Finally, the motivating example is analyzed in detail. The simulated and real data examples illustrate the good performance and practicability of the proposed methods based on confidence distribution.     

Multiparous women's confidence to have a publicly-funded homebirth: a qualitative study

Background

Hospital birth is commonly thought to be a safer option than homebirth, despite many studies showing similar rates of safety for low risk mothers and babies when cared for by qualified midwives with systems of back-up in place. Recently in Australia, demand has led to the introduction of a small number of publicly-funded homebirth programs. Women's confidence in having a homebirth through a publicly-funded homebirth program in Australia has not yet been explored.

Aim

The aim of the study was to explore the reasons why multiparous women feel confident to have a homebirth within a publicly-funded model of care in Australia.

Methods

Ten multiparous English-speaking women who chose to have a homebirth with the St George Hospital Homebirth Program were interviewed in the postnatal period using semi-structured, open-ended questions. Interviews were transcribed, then a thematic analysis was undertaken.

Results

Women, having already experienced a normal birth, demonstrated a strong confidence in their ability to give birth at home and described a confidence in their bodies, their midwives, and the health system. Women weighed up the risks of homebirth through information they gathered and integration with their previous experience of birth, their family support and self-confidence.

Discussion

Women choosing publicly-funded homebirth display strong confidence in both themselves to give birth at home, and their belief in the health system's ability to cope with any complications that may arise.

Implications for practice

Many women may benefit from access to publicly-funded homebirth models of care. This should be further investigated.     

Sample Splitting and Threshold Estimation

Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously‐distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are super‐consistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either cross‐section or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates (the threshold and the regression slopes) is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of Durlauf and Johnson (1995).     

Bias-corrected confidence bands in nonparametric regression

Bias-corrected confidence bands for general nonparametric regression models are considered. We use local polynomial fitting to construct the confidence bands and combine the cross-validation method and the plug-in method to select the bandwidths. Related asymptotic results are obtained. Our simulations show that confidence bands constructed by local polynomial fitting have much better coverage than those constructed by using the Nadaraya–Watson estimator. The results are also applicable to nonparametric autoregressive time series models.     

THE CONVERGENCE RATE OF SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS

Let X₁X₂,.be i.i.d. random variables and let U_n= (n r)^-1S?^(n,r) h (X_i1,., X_ir,) be a U-statistic with EU_n= v, v unknown. Assume that g(X₁) =E[h(X₁,.,X_r) - v |X₁]has a strictly positive variance s?². Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S²_n be the Jackknife estimator of n Var U_n. Consider the stopping times N(d)= min {n: S²_n: + n^-1≤²a^-2},d > 0, and a confidence interval for v of length 2d,of the form I_n,d= [U_n,-d, Un + d]. We assume that Var U_n is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let I_N(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. lim_{d → 0}P(v ∈ I_N(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ I_N(d),d) converges to α is investigated. We obtain that |P(v ∈ I_N(d),d) - α| = 0 (d^{1/2-(1+k)/2(1+m)}), d → 0, where K = max {0,4 - m}, under the condition that E|h(X₁, X_r)|^m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).     

Estimation of smooth regression functions in monotone response models

We consider the estimation of smooth regression functions in a class of conditionally parametric co-variate-response models. Independent and identically distributed observations are available from the distribution of (Z,X)$(Z,X)$, where Z is a real-valued co-variate with some unknown distribution, and the response X conditional on Z   is distributed according to the density p(·,ψ(Z))$p(·,\psi (Z))$, where p(·,θ)$p(·,\theta )$ is a one-parameter exponential family. The function ψ$\psi$ is a smooth monotone function. Under this formulation, the regression function E(X|Z)$E(X|Z)$ is monotone in the co-variate Z   (and can be expressed as a one–one function of ψ$\psi$); hence the term “monotone response model”. Using a penalized least squares approach that incorporates both monotonicity and smoothness, we develop a scheme for producing smooth monotone estimates of the regression function and also the function ψ$\psi$ across this entire class of models. Point-wise asymptotic normality of this estimator is established, with the rate of convergence depending on the smoothing parameter. This enables construction of Wald-type (point-wise) as well as pivotal confidence sets for ψ$\psi$ and also the regression function. The methodology is extended to the general heteroscedastic model, and its asymptotic properties are discussed.     

Conditional statistical inference and quantification of relevance

Summary. We argue that it can be fruitful to take a predictive view on notions such as the precision of a point estimator and the confidence of an interval estimator in frequentist inference. This predictive approach has implications for conditional inference, because it immediately allows a quantification of the concept of relevance for conditional inference. Conditioning on an ancillary statistic makes inference more relevant in this sense, provided that the ancillary is a precision index. Not all ancillary statistics satisfy this demand. We discuss the problem of choice between alternative ancillary statistics. The approach also has implications for the best choice of variance estimator, taking account of correlations with the squared error of estimation itself. The theory is illustrated by numerous examples, many of which are classical.     

Data tilting for time series

Summary. We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as 'empirical likelihood with nuisance parameters'.     

基于机器学习LSTM&US模型的消费者信心指数预测研究

消费者信心指数等宏观经济指标具有时间上的滞后效应和动态变化的多维性,不易精确预测。本文基于机器学习长短时间记忆(Long Short-Term Memory,LSTM)神经网络模型,结合大数据技术挖掘消费者信心指数相关网络搜索数据(User Search,US),进而构建一种LSTM&US预测模型,并将其应用于对我国消费者信心指数的长期、中期与短期的预测研究,同时引入多个基准预测模型进行了对比分析。结果发现:引入网络搜索数据能够提高LSTM神经网络模型的预测性能与预测精度;LSTM&US预测模型具有较好的泛化能力,对不同期限的预测效果均较稳定,其预测性能与预测精度均优于其他六种基准预测模型(LSTM、SVR&US、RFR&US、BP&US、XGB&US和LGB&US);预测结果显示本文提出的LSTM&US预测模型具有一定的实用价值,该预测方法为消费者信心指数的预测与预判提供了一种新的研究思路,丰富了机器学习方法在宏观经济指标预测领域中的理论研究。