Recent results in the literature indicate that artificial neural networks
(ANNs) can outperform the dynamic factor model (DFM) in terms of the accuracy
of GDP nowcasts. Compared to the DFM, the performance advantage of these highly
flexible, nonlinear estimators is particularly evident in periods of recessions
and structural breaks. From the perspective of policy-makers, however, nowcasts
are the most useful when they are conveyed with uncertainty attached to them.
While the DFM and other classical time series approaches analytically derive
the predictive (conditional) distribution for GDP growth, ANNs can only produce
point nowcasts based on their default training procedure (backpropagation). To
fill this gap, first in the literature, we adapt two different deep learning
algorithms that enable ANNs to generate density nowcasts for U.S. GDP growth:
Bayes by Backprop and Monte Carlo dropout. The accuracy of point nowcasts,
defined as the mean of the empirical predictive distribution, is evaluated
relative to a naive constant growth model for GDP and a benchmark DFM
specification. Using a 1D CNN as the underlying ANN architecture, both
algorithms outperform those benchmarks during the evaluation period (2012:Q1 --
2022:Q4). Furthermore, both algorithms are able to dynamically adjust the
location (mean), scale (variance), and shape (skew) of the empirical predictive
distribution. The results indicate that both Bayes by Backprop and Monte Carlo
dropout can effectively augment the scope and functionality of ANNs, rendering
them a fully compatible and competitive alternative for classical time series
approaches.

人工神经网络 (ANNs) 可以比动态因素模型 (DFM) 更准确地预测国内生产总值 (GDP)，尤其在经济衰退和结构性断裂期间展现出灵活性和非线性估计模型的性能优势。为了填补 ANNs 无法生成带有不确定性的预测分布的空白，我们使用贝叶斯反向传播和 Monte Carlo dropout 两种不同的深度学习算法，使得 ANNs 能够生成美国 GDP 增长的概率预测。通过使用一维卷积神经网络作为底层 ANN 架构，这两种算法在评估期 (2012 年第一季度 ——2022 年第四季度) 中超越了基准模型和经典时间序列方法，而且能够动态调整预测分布的位置 (均值)、尺度 (方差) 和形状 (偏度)。研究结果表明，贝叶斯反向传播和 Monte Carlo dropout 可以有效扩展和加强 ANNs 的范围和功能，使其成为经典时间序列方法的全兼容和竞争性替代方案。

使用深度学习生成美国国内生产总值 (GDP) 增长的密度预测：基于贝叶斯后向传播和蒙特卡洛辍学

Generating density nowcasts for U.S. GDP growth with deep learning:  Bayes by Backprop and Monte Carlo dropout

In recent years, the dynamic factor model has emerged as a dominant tool in
economics and finance, particularly for investment strategies. This model
offers improved handling of complex, nonlinear, and noisy market conditions
compared to traditional static factor models. The advancement of machine
learning, especially in dealing with nonlinear data, has further enhanced asset
pricing methodologies. This paper introduces a groundbreaking dynamic factor
model named RVRAE. This model is a probabilistic approach that addresses the
temporal dependencies and noise in market data. RVRAE ingeniously combines the
principles of dynamic factor modeling with the variational recurrent
autoencoder (VRAE) from deep learning. A key feature of RVRAE is its use of a
prior-posterior learning method. This method fine-tunes the model's learning
process by seeking an optimal posterior factor model informed by future data.
Notably, RVRAE is adept at risk modeling in volatile stock markets, estimating
variances from latent space distributions while also predicting returns. Our
empirical tests with real stock market data underscore RVRAE's superior
performance compared to various established baseline methods.

本研究介绍了一种名为 RVRAE 的开创性动态因子模型，它是一种概率性方法，专门处理市场数据中的时间依赖性和噪声，并通过深度学习中的变分循环自编码器 (VRAE) 将动态因子建模原理巧妙地结合起来。RVRAE 的一个关键特征是其使用先验 - 后验学习方法，通过寻找未来数据驱动的最优后验因子模型来优化模型的学习过程。值得注意的是，在波动性股票市场中，RVRAE 擅长风险建模，从潜在空间分布估计方差，并预测回报。我们对真实股票市场数据进行的实证测试证实了 RVRAE 相较于不同已有基准方法的优越性能。

基于变分循环自编码器的动态因子模型用于股票收益预测

RVRAE: A Dynamic Factor Model Based on Variational Recurrent Autoencoder  for Stock Returns Prediction

In our study, we apply different statistical models to nowcast quarterly GDP
growth for the US economy. Using the monthly FRED-MD database, we compare the
nowcasting performance of the dynamic factor model (DFM) and four artificial
neural networks (ANNs): the multilayer perceptron (MLP), the one-dimensional
convolutional neural network (1D CNN), the long short-term memory network
(LSTM), and the gated recurrent unit (GRU). The empirical analysis presents the
results from two distinctively different evaluation periods. The first (2010:Q1
-- 2019:Q4) is characterized by balanced economic growth, while the second
(2010:Q1 -- 2022:Q3) also includes periods of the COVID-19 recession. According
to our results, longer input sequences result in more accurate nowcasts in
periods of balanced economic growth. However, this effect ceases above a
relatively low threshold value of around six quarters (eighteen months). During
periods of economic turbulence (e.g., during the COVID-19 recession), longer
training sequences do not help the models' predictive performance; instead,
they seem to weaken their generalization capability. Our results show that 1D
CNN, with the same parameters, generates accurate nowcasts in both of our
evaluation periods. Consequently, first in the literature, we propose the use
of this specific neural network architecture for economic nowcasting.

通过比较动态因子模型（DFM）和四种人工神经网络（ANNs）的预测表现，本文应用不同的统计模型来实时预测美国经济的季度 GDP 增长，并使用 FRED-MD 数据库进行实证研究。结果表明，虽然在经济增长平衡期间，较长的输入序列会产生更准确的预测，但是在经济动荡期间（如 COVID-19 衰退期间），较长的训练序列并不能提高模型的预测性能；在这种情况下，1D CNN 则具有较高的准确率，并被提出作为一种经济实时预测的有效方法。