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Building Macroeconomically Relevant Climate Indices via the Assemblage VAR

通过Assemblage VAR构建宏观经济相关的气候指数

What should a macroeconomically relevant climate index contain? The composition is inherently ambiguous, and aggregation choices affect structural inference. We introduce the Assemblage VAR, which jointly estimates nonnegative aggregation weights and VAR parameters by maximizing the system likelihood-gain criterion, effectively outsourcing aggregation to observed macroeconomic dynamics. Two variants operate in component-space and rank-space, reweighting named subcomponents…

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LGB+: A Macroeconomic Forecasting Road Test

LGB+:宏观经济预测的实测评估

Needless to say, linear dynamics are pervasive in economic time series, particularly autoregressive ones. While gradient boosting with trees excels at capturing nonlinearities, it is inefficient in small samples when much of the predictive content is linear, expending splits to approximate relationships better captured by simple linear terms. This paper proposes LGB+, a boosting procedure operating on a more inclusive set of basis functions. The idea comes in two flavors.…

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Quantifying the Risk-Return Tradeoff in Forecasting

量化预测中的风险—收益权衡

Average forecast accuracy is not the same as forecast reliability. I treat forecast loss differentials relative to a benchmark as a return series. I then evaluate these returns using risk-adjusted performance measures from finance, including the Sharpe ratio, Sortino ratio, Omega ratio, and drawdown-based metrics. I also introduce the Edge Ratio capturing a model's propensity to deliver uniquely informative predictions relative to the forecasting frontier. I apply this…

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Opening the Black Box of Local Projections

打开局部投影的黑箱

Local projections (LPs) are widely used in empirical macroeconomics to estimate impulse responses to policy interventions. Yet, in many ways, they are black boxes. It is often unclear what mechanism or historical episodes drive a particular estimate. We introduce a new decomposition of LP estimates into the sum of contributions of historical events, which is the product, for each time stamp, of a weight and the realization of the response variable. In the least squares case,…

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An Adaptive Moving Average for Macroeconomic Monitoring

用于宏观经济监测的自适应移动平均

The use of moving averages is pervasive in macroeconomic monitoring, particularly for tracking noisy series such as inflation. The choice of the look-back window is crucial. Too long of a moving average is not timely enough when faced with rapidly evolving economic conditions. Too narrow averages are noisy, limiting signal extraction capabilities. As is well known, this is a bias-variance trade-off. However, it is a time-varying one: the optimal size of the look-back window…

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Dual Interpretation of Machine Learning Forecasts

机器学习预测的对偶解释

Machine learning predictions are typically interpreted as the sum of contributions of predictors. Yet, each out-of-sample prediction can also be expressed as a linear combination of in-sample values of the predicted variable, with weights corresponding to pairwise proximity scores between current and past economic events. While this dual route leads nowhere in some contexts (e.g., large cross-sectional datasets), it provides sparser interpretations in settings with many…

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A Neural Phillips Curve and a Deep Output Gap

神经网络菲利普斯曲线与深度产出缺口

Many problems plague empirical Phillips curves (PCs). Among them is the hurdle that the two key components, inflation expectations and the output gap, are both unobserved. Traditional remedies include proxying for the absentees or extracting them via assumptions-heavy filtering procedures. I propose an alternative route: a Hemisphere Neural Network (HNN) whose architecture yields a final layer where components can be interpreted as latent states within a Neural PC. There are…

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From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks

利用半球神经网络实现主动与反应式波动建模

We reinvigorate maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE work in this context. First, the hemispheres share a common core at the entrance of the network which accommodates for various forms of time variation in the error variance. Second, we introduce a volatility emphasis constraint that…

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Maximally Forward-Looking Core Inflation

最大化前瞻性的核心通胀指标

Timely monetary policy decision-making requires timely core inflation measures. We create a new core inflation series that is explicitly designed to succeed at that goal. Precisely, we introduce the Assemblage Regression, a generalized nonnegative ridge regression problem that optimizes the price index's subcomponent weights such that the aggregate is maximally predictive of future headline inflation. Ordering subcomponents according to their rank in each period switches the…

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Assessing and Comparing Fixed-Target Forecasts of Arctic Sea Ice: Glide Charts for Feature-Engineered Linear Regression and Machine Learning Models

北极海冰固定目标预测的评估与比较:滑行图、特征工程回归及机器学习

We use "glide charts" (plots of sequences of root mean squared forecast errors as the target date is approached) to evaluate and compare fixed-target forecasts of Arctic sea ice. We first use them to evaluate the simple feature-engineered linear regression (FELR) forecasts of Diebold and Goebel (2021), and to compare FELR forecasts to naive pure-trend benchmark forecasts. Then we introduce a much more sophisticated feature-engineered machine learning (FEML) model, and we use…

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When Will Arctic Sea Ice Disappear? Projections of Area, Extent, Thickness, and Volume

北极海冰何时消失?面积、范围、厚度与体积的联合预测

Rapidly diminishing Arctic summer sea ice is a strong signal of the pace of global climate change. We provide point, interval, and density forecasts for four measures of Arctic sea ice: area, extent, thickness, and volume. Importantly, we enforce the joint constraint that these measures must simultaneously arrive at an ice-free Arctic. We apply this constrained joint forecast procedure to models relating sea ice to atmospheric carbon dioxide concentration and models relating…

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On Spurious Causality, CO2, and Global Temperature

伪因果关系、二氧化碳与全球温度

Stips, Macias, Coughlan, Garcia-Gorriz, and Liang (2016, Nature Scientific Reports) use information flows (Liang, 2008, 2014) to establish causality from various forcings to global temperature. We show that the formulas being used hinges on a simplifying assumption that is nearly always rejected by the data. We propose an adequate measure of information flow based on Vector Autoregressions, and find that most results in Stips et al. (2016) cannot be corroborated. Then, it is…

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Can Machine Learning Catch the COVID-19 Recession?

机器学习能否捕捉新冠疫情衰退?

Based on evidence gathered from a newly built large macroeconomic data set for the UK, labeled UK-MD and comparable to similar datasets for the US and Canada, it seems the most promising avenue for forecasting during the pandemic is to allow for general forms of nonlinearity by using machine learning (ML) methods. But not all nonlinear ML methods are alike. For instance, some do not allow to extrapolate (like regular trees and forests) and some do (when complemented with…

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