We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors. A two-stage estimator, that combines principal components and the Kalman filter, is proposed. The forecast performance is studied for a high-dimensional US macroeconomic data set, where we find that benefits from the fractional factor models can be substantial, as they outperform univariate autoregressions, principal components, and the factor-augmented error-correction model.
We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a fractional lag operator into the autoregressive polynomial of the cyclical component. The model allows for an endogenous estimation of the integration order jointly with the other model parameters and, therefore, no prior specification tests with respect to persistence are required. We relate the model to the Beveridge-Nelson decomposition and derive a modified …
We move beyond "Is Machine Learning Useful for Macroeconomic Forecasting?" by adding the "how". The current forecasting literature has focused on matching specific variables and horizons with a particularly successful algorithm. In contrast, we study the usefulness of the underlying features driving ML gains over standard macroeconometric methods. We distinguish four so-called features (nonlinearities, regularization, cross-validation and alternative loss function) and study their behavior in both the data-rich and data-poor environments. To do so, we design experiments that allow to identify …
Macroeconomic Forecasting with Large Language Models
School of Economics and Finance, Queen Mary University of London（伦敦大学女王学院经济与金融学院）；School of Business and Economics, Brandeis University（布兰迪大学商学院与经济学学院）
Olin Business School, Washington University in St. Louis（华盛顿大学圣路易斯分校奥林商学院）；Chaifetz School of Business, Saint Louis University（圣路易斯大学蔡菲兹商学院）；Center for Economic Behavior and Decision-Making, Zhejiang University of Finance and Economics（浙江财经大学经济行为与决策研究中心）；Department of Economics, University of Chicago（芝加哥大学经济学系）
In the data-rich environment, using many economic predictors to forecast a few key variables has become a new trend in econometrics. The commonly used approach is factor augment (FA) approach. In this paper, we pursue another direction, variable selection (VS) approach, to handle high-dimensional predictors. VS is an active topic in statistics and computer science. However, it does not receive as much attention as FA in economics. This paper introduces several cutting-edge VS methods to economic forecasting, which includes: (1) classical greedy procedures; (2) l1 regularization; (3) gradient d…
In many fields where the main goal is to produce sequential forecasts for decision making problems, the good understanding of the contemporaneous relations among different series is crucial for the estimation of the covariance matrix. In recent years, the modified Cholesky decomposition appeared as a popular approach to covariance matrix estimation. However, its main drawback relies on the imposition of the series ordering structure. In this work, we propose a highly flexible and fast method to deal with the problem of ordering uncertainty in a dynamic fashion with the use of Dynamic Order Pro…
Faculty of Economics, Khon Kaen University（孔敬大学经济学院）；Khon Kaen University（孔敬大学）
This paper demonstrates the potentials of the long short-term memory (LSTM) when applyingwith macroeconomic time series data sampled at different frequencies. We first present how theconventional LSTM model can be adapted to the time series observed at mixed frequencies when thesame mismatch ratio is applied for all pairs of low-frequency output and higher-frequency variable. Togeneralize the LSTM to the case of multiple mismatch ratios, we adopt the unrestricted Mixed DAtaSampling (U-MIDAS) scheme (Foroni et al., 2015) into the LSTM architecture. We assess via bothMonte Carlo simulations and …
The aim of this paper is to investigate the use of the Factor Analysis in order to identify the role of the relevant macroeconomic variables in driving the inflation. The Macroeconomic predictors that usually affect the inflation are summarized using a small number of factors constructed by the principal components. This allows us to identify the crucial role of money growth, inflation expectation and exchange rate in driving the inflation. Then we use this factors to build econometric models to forecast inflation. Specifically, we use univariate and multivariate models such as classical autor…
In a low-dimensional linear regression setup, considering linear transformations/combinations of predictors does not alter predictions. However, when the forecasting technology either uses shrinkage or is nonlinear, it does. This is precisely the fabric of the machine learning (ML) macroeconomic forecasting environment. Pre-processing of the data translates to an alteration of the regularization -- explicit or implicit -- embedded in ML algorithms. We review old transformations and propose new ones, then empirically evaluate their merits in a substantial pseudo-out-sample exercise. It is found…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either towards zero or time-invariance. Second, it introduces the frameworks of factor graphs and message passing as a means of designi…
Macroeconomic Forecasting for the G7 countries under Uncertainty Shocks
SAFIR, Sorbonne University Abu Dhabi（索邦大学阿布扎比分校 SAFIR）；BITS Pilani, Hyderabad Campus（印度皮拉尼博拉理工学院海得拉巴校区）；Fidelity Investments（富达投资）；Sorbonne Center for Artificial Intelligence, Sorbonne University（索邦大学人工智能中心）
Forecasting the Price of Carbon with Macroeconomic and Financial variables
University of Milan（米兰大学）；Fondazione Eni Enrico Mattei (FEEM)（埃尼·恩里科·马泰伊基金会）；Study Center Gerzensee, Foundation of the Swiss National Bank（瑞士国家银行格尔岑塞研究中心）；ClearBlue Markets
Recent research finds that forecasting electricity prices is very relevant. In many applications, it might be interesting to predict daily electricity prices by using their own lags or renewable energy sources. However, the recent turmoil of energy prices and the Russian-Ukrainian war increased attention in evaluating the relevance of industrial production and the Purchasing Managers' Index output survey in forecasting the daily electricity prices. We develop a Bayesian reverse unrestricted MIDAS model which accounts for the mismatch in frequency between the daily prices and the monthly macro …
The coronavirus is a global event of historical proportions and just a few months changed the time series properties of the data in ways that make many pre-covid forecasting models inadequate. It also creates a new problem for estimation of economic factors and dynamic causal effects because the variations around the outbreak can be interpreted as outliers, as shifts to the distribution of existing shocks, or as addition of new shocks. I take the latter view and use covid indicators as controls to 'de-covid' the data prior to estimation. I find that economic uncertainty remains high at the end…
MACROCAST: A Vintage-Consistent Time Series Foundation Model for Real-Time Macroeconomic Forecasting
School of Economics and Finance, Queen Mary University of London（伦敦大学玛丽女王学院经济与金融学院）；School of Business and Economics, Brandeis University（布兰迪大学商学院与经济学院）
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and widespread use for various applications ranging from genomics to finance, this methodology has predominantly remained linear. This study estimates factors nonlinearly through the kernel method, which allows flexible nonlinearities while still avoiding the curse of dimensionality. We focus on factor-augmented forecasting of a single time series in a high-dimension…
We investigate how the possible presence of unit roots and cointegration affects forecasting with Big Data. As most macroeoconomic time series are very persistent and may contain unit roots, a proper handling of unit roots and cointegration is of paramount importance for macroeconomic forecasting. The high-dimensional nature of Big Data complicates the analysis of unit roots and cointegration in two ways. First, transformations to stationarity require performing many unit root tests, increasing room for errors in the classification. Second, modelling unit roots and cointegration directly is mo…
This paper considers the problem of forecasting a collection of short time series using cross sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross-sectional information to transform the unit-specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that equals the population distribution of the random coefficients. We show that the risk of a predictor based on a non-param…
Vector autoregression (VAR) models are widely used for forecasting and macroeconomic analysis, yet they remain limited by their reliance on a linear parameterization. Recent research has introduced nonparametric alternatives, such as Bayesian additive regression trees (BART), which provide flexibility without strong parametric assumptions. However, existing BART-based frameworks do not account for time dependency or allow for sparse estimation in the construction of regression tree priors, leading to noisy and inefficient high-dimensional representations. This paper introduces a sparsity-induc…
University of Oxford（牛津大学）；Saïd Business School（赛德商学院）
This research paper explores the performance of Machine Learning (ML) algorithms and techniques that can be used for financial asset price forecasting. The prediction and forecasting of asset prices and returns remains one of the most challenging and exciting problems for quantitative finance and practitioners alike. The massive increase in data generated and captured in recent years presents an opportunity to leverage Machine Learning algorithms. This study directly compares and contrasts state-of-the-art implementations of modern Machine Learning algorithms on high performance computing (HPC…
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 linear dynamic components). This and other crucial aspects of ML-based forecasting in unprecedented times are studied in an …
We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the Fama-French factors. In diffusion index forecasts, identified factors are strongly related to several directly measurable economic variables such as consumption-wealth variable, financial ratios, and term spread. With those covariates, both the factors and loadings are identifiable up to a rotation matrix even only with a finite dimension. To incorporate the explanat…
