Dynamic Factor Model Research Articles

Energy forecast for a cogeneration system using dynamic factor models

Cogeneration is used in different sectors of industry and it allows that two types of energy to be efficiently obtained from a single source. Accurate predictions are fundamental to optimize energy production, considering the variability that occurs in the daily market. This study adjusts and predicts cogeneration using real data from a Spanish energy technology center, using dynamic factor analysis methodology and incorporating covariates such as temperature and relative humidity. A comparative analysis is performed to evaluate the improvements achieved by implementing cluster-structured dynamic models versus other methods. Furthermore, a robust interpolation method has been implemented to handle missing data in both the main variable and the covariates.

Health outcome convergence and the roles of public health financing and governance in Africa.

Progress in health outcomes across Africa has been uneven, marked by significant disparities among countries, which not only challenges the global health security but impede progress towards achieving the United Nations' Sustainable Development Goals 3 and 10 (SDG 3 and SDG 10) and Universal Health Coverage (UHC). This paper examines the progress of African countries in reducing intra-country health outcome disparities between 2000 and 2019. In other words, the paper investigates the convergence hypothesis in health outcome using a panel data from 40 African countries. Data were sourced from the World Development Indicators, the World Governance Indicators, and the World Health Organization database. Employing a non-linear dynamic factor model, the study focused on three health outcomes: infant mortality rate, under-5 mortality rate, and life expectancy at birth. The findings indicate that while the hypothesis of convergence is not supported for the selected countries, evidence of convergence clubs is observed for the three health outcome variables. The paper further examine the factors contributing to club formation by using the marginal effects of the ordered logit regression model. The findings indicate that the overall impact of the control variables aligns with existing research. Moreover, governance quality and domestic government health expenditure emerge as significant determinants influencing the probability of membership in specific clubs for the child mortality rate models. In the life expectancy model, governance quality significantly drives club formation. The results suggest that there is a need for common health policies for the different convergence clubs, while country-specific policies should be implemented for the divergent countries. For instance, policies and strategies promoting health prioritization in national budget allocation and reallocation should be encouraged within each final club. Efforts to promote good governance policies by emphasizing anti-corruption measures and government effectiveness should also be encouraged. Moreover, there is a need to implement regional monitoring mechanisms to ensure progress in meeting health commitments, while prioritizing urbanization plans in countries with poorer health outcomes to enhance sanitation access.

Comparative analysis of the predictive power of statistical models of macroeconomic indicators in conditions of permanent crises

Subject. The article discusses prediction of the state of the economy, the accuracy of forecasts of traditional models during crises, the need to find more effective model specifications to predict macro indicators. Objectives. The purpose is to carry out a comparative analysis of the predictive ability of ensemble methods in comparison with a set of models, including traditional statistical algorithms and machine learning algorithms. Methods. The comparative analysis of predictive ability of the models and interpretation of results obtained were performed using a dynamic factor model (DFM), a neural network with long-term short-term memory (LSTM), and integrated gradient methods (IG). Results. We performed the analysis of predictive ability of the ensemble model to forecast GDP, which combines DFM and LSTM to account for both linear and nonlinear dependencies in the data; the analysis of predictive power of various indicators, which showed that an increase in forecast error is observed for all models except DFM, the ensemble model with an error correction structure, and ARMAX. The obtained results can be used to build models of macroeconomic indicators in order to make strategic decisions by enterprises of various industries operating in a highly uncertain environment. Conclusions. The combination of DFM and LSTM in the ensemble provides higher accuracy forecasts than LSTM and competitor models, however, with less predictive power than DFM.

What drives labor force participation rate variability? The case of West Virginia

This study examines the dynamics of labor force participation rates across counties in West Virginia to better understand local labor market integration and the factors influencing fluctuations in participation. Drawing on county-level data from January 1990 to July 2020, the research employs a dynamic factor model to decompose labor force participation rates into latent factors at the state, metropolitan/non-metropolitan, and county levels. The findings reveal a general lack of labor market integration across West Virginia, highlighting potential opportunities for growth through enhanced integration. Further analysis using panel data models identifies key determinants of labor force participation, including personal income, education, infrastructure, and the prominence of industries such as agriculture and natural gas. The results underscore the necessity for targeted county-level policies to bolster employment and promote economic expansion within the state.

Large-Dimensional Portfolio Selection with a High-Frequency-Based Dynamic Factor Model

Large-Dimensional Portfolio Selection with a High-Frequency-Based Dynamic Factor Model

Low- and middle-income countries’ external debt cycle and global economic prospect

The rapid growth of peripheral countries has brought significant changes to the global economic and financial system, making it crucial to examine the relationship between their cyclical debt fluctuations and the world economy. Using the Bayesian dynamic factor model, this paper documents the presence of a set of common factors, known as global debt cycles, in the external debt accumulation of the low- and middle-income countries (LMICs). The interesting finding is that this debt cycles differ from well-known factors for global financial cycles in capital flows, such as U.S. monetary policy and global risk aversion. Even after controlling the factors for global financial cycles, our results reveal a significantly negative predictive effect of estimated debt cycles on global economic growth. Moreover, we demonstrate that this negative effect is primarily dominated by LMICs occupying prominent positions in international debt market networks, especially during the post-2008 financial crisis period. These findings emphasize the increasing importance of peripheral countries in the world system, which has been largely ignored in existing literature.

A two-step dynamic factor modelling approach for forecasting inflation in small open economies

We build a dynamic factor model to forecast inflation in a small open economy. The model is estimated with both market and survey data, and a unique two-step methodology to incorporate exogenous factors. Estimations with market data provide a better fit for in-sample and out-of-sample values of inflation. More importantly, our model outperforms univariate and estimated DSGE models, the more common approaches to inflation forecasting that perform well for advanced economies. Our findings, therefore, suggest that a dynamic factor modelling approach for a small open economy such as Jamaica can be a good alternative to the preferred methods for forecasting inflation in advanced economies.

The comovement of bubbles’ responses to monetary policy shocks

In this paper, we present a two-step methodology designed to elucidate the extent of co-movement in the behavior of asset bubbles across a selected group of developed and emerging economies, with observations extending from the year 2000 onwards. We characterize the behavior of these bubbles, conceptualized as the disparity between fundamental and market values, by examining their responses to monetary policy shocks. Our investigation into their co-movement dynamics post-2000 involves the estimation of a Bayesian Dynamic Factor Model that incorporates the reactions of asset bubbles to monetary policy shocks, both in the short term and the long term. Notably, our findings reveal a convergence in short-term responses among these bubbles prior to the onset of the financial crisis. However, as the crisis unfolded, our results indicate a shift towards divergence. Concerning the long-term response of bubbles to monetary policy, divergence was observed before the crisis, but once the crisis had taken hold, there was a noticeable trend towards convergence. An influential idiosyncratic factor was identified for countries like the United States, South Korea, and Japan, impacting both short-term and long-term behavior. Conversely, the long-term behavior of bubbles in most emerging economies appears to be influenced by idiosyncratic factors. Furthermore, our results largely maintain their robustness even when utilizing an alternative measure of monetary policy stance during the period of the zero lower bound. Nevertheless, this secondary analysis suggests heightened volatility in the factors affecting both emerging and advanced markets.

Dynamic increase factor of concrete compressive strength in confined split hopkinson pressure bar tests

This study presented a methodology to evaluate the pure strain-rate effect on concrete compressive strength and developed a pure rate dynamic increase factor (DIF) model through numerical and experimental investigations into confined split Hopkinson pressure bar (SHPB) tests. The numerical investigation proposed the methodology to determine the pure rate DIF through confined SHPB tests. Subsequently, the confined SHPB tests were conducted on concrete specimens, and a pure rate DIF model was developed based on this methodology. Additionally, conventional SHPB tests were performed to obtain an apparent DIF, which was then compared to the developed pure rate DIF. The results indicated that the apparent DIF exceeded the pure rate DIF, thus confirming its tendency to overestimate the strain-rate effect on concrete. Therefore, the proposed methodology using confined SHPB tests provides an alternative approach to overcome the limitations of the apparent DIF determined from conventional SHPB tests. Lastly, the developed pure rate DIF model was validated through numerical analyses on conventional SHPB tests and drop-weight impact tests of reinforced concrete beams. This validation demonstrated that the proposed pure rate DIF model effectively considers the strain-rate effect on concrete structures, thereby enabling assessment of the performance of concrete structures under extreme loading conditions.

A new method for measuring financial resilience

This paper proposes a new model to measure financial resilience from the perspective of external risk shocks, which composes of three submodels, namely, the dynamic factor model, the time-varying parameter vector autoregression (TVP-VAR) model, and the resilience characteristic measurement model with two dimensions: absorption intensity and absorption duration. At the theoretical level, we simulate and analyze the changing paths of financial resilience under different scenarios. At the empirical level, we apply the model to study the resilience of the UK financial market. The results indicate that the UK financial resilience fluctuations exhibit phased characteristics and there is a clear inverse relationship between absorption intensity and absorption duration. Notably, periods of low resilience often coincide with specific risk events.

International interest rate comovements and monetary policy in Bazil

This article shows that international spillovers or coordination in central bank interest rate setting are significant components of the Brazilian Taylor rule. For this, the short-term interest rate comovements of 28 countries and Euribor were estimated through a dynamic factor model. A nonlinear reaction function for the Central Bank of Brazil that includes global and regional factors evidenced that monetary policy in Brazil is influenced by the policy of other broad groups of countries and not just the United States and the Eurozone.

Dynamic factor models for claim reserving

This study presents a new approach to claim reserving in the insurance industry using dynamic factor models (DFMs). Traditional methods often struggle to adapt to temporal variations in loss development, a gap that DFMs can effectively address. By employing DFMs on a multivariate time series of loss development factors (LDFs), we offer a more sensitive adaptation and understanding of loss development over time. Our methodology not only facilitates adjustment to trends in loss development but also provides clear explanations for the underlying reasons behind these trends. This aspect is crucial for actuaries, whose responsibilities include offering transparent and understandable reserve estimates. We apply the proposed DFMs to datasets from two different lines of business, demonstrating their ability to capture the temporal evolution of factors influencing loss development. The results indicate that our approach enhances fitting ability and provides deep insights into the dynamics of claim reserving. Furthermore, we assess the uncertainty in the ultimate loss amounts required for risk management to ensure financial stability and compliance with insurance regulatory requirements. This study contributes to the field of actuarial science by highlighting the potential of DFMs in enhancing the accuracy and reliability of claim reserving processes.

Structured prior distributions for the covariance matrix in latent factor models

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p×p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \ imes p$$\\end{document} covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p×k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \ imes k$$\\end{document} factor loadings matrix and its transpose. If k≪p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\ll p$$\\end{document}, this defines a parsimonious factorisation of the covariance matrix. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings is order invariant. In this work, a class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures while also facilitating inference over the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Two substantive applications showcase the scope of the methodology and its inferential benefits.

Common and idiosyncratic conditional volatility: Theory and empirical evidence from electricity prices

. We propose and develop a robust score-driven multiplicative dynamic factor model for the conditional volatility of electricity prices. This model allows us to identify both common and idiosyncratic conditional volatility factors in the spot price of electricity across key Nord Pool European markets. Both factors are extracted using a single observation-driven filter that is simple and parsimonious. The common factor is robust by construction as it averages information over the cross-section of the high-dimensional vector of electricity price changes. The idiosyncratic factors are designed to capture the erratic shocks in prices and therefore rely on a robust updating equation which allows for outliers and fat-tailed innovations. Our model is suitable for high-dimensional applications and does not necessarily suffer from the curse of dimensionality. The parsimonious nature of the observation-driven filter leads to simple computations for the estimation of parameters and the signal extraction of factors. We derive the stochastic properties of the filter and its underlying factor model, including bounded moments, stationarity, ergodicity, and filter invertibility. We further establish the consistency and asymptotic normality of the maximum likelihood estimator. The finite sample properties of the estimator and the filter are explored in a Monte Carlo study. Finally, we apply our model and filter to the Nord Pool spot price data and find evidence that net-import and net-export electricity markets exhibit substantially different common and idiosyncratic volatilities. In particular, we confirm that net-import markets are considerably more exposed to cross-market volatility spillovers, and we quantify the relevant degree of exposition.

Estimating the Output Gap with High-Dimensional Time Series

The output gap measures the deviation of observed output from its potential, thereby defining imbalances in the real economy that affect utilization of resources and price inflation. A novel estimator of the output gap is proposed. It is based on a dynamic factor model that extracts from a high-dimensional set of time series the common component of a stationary transformation of the individual series. The latter results from the application of a nonlinear gap filter, such that for each of the individual time series the gap filter removes from the current value the historical local maximum, which in turn defines the potential. The smooth generalized principal components are extracted and the resulting common components are aggregated into a global output gap measure. An application is presented dealing with the U.S. industrial sector, where the proposed measure is constructed using the disaggregated market and industry groups time series. An evaluation of its external validity is conducted in comparison to alternative measures.

Measuring persistent global economic factors with output, commodity price, and commodity currency data

AbstractIn this study, we use monthly G7 industrial production data, commodity price index data, and commodity currency exchange rate data in a dynamic factor model to examine the global economic factors useful for commodity price prediction. We differentiate between the dynamic factors by specifying a persistent factor and a non‐persistent factor, both as a single global factor using all data and as factors for each category of data. The in‐sample predictive performances of the three persistent factors together are better than the non‐persistent factors and the single global factors. Out‐of‐sample outcomes based on forecast combinations also support the presence of predictive information in the persistent factors for overall commodity prices and for most sub‐categories of commodity price indexes relative to their means. The gains in forecast accuracy are heterogeneous, ranging from 5% to 7% in the 1‐ to 6‐month horizon for overall commodity prices to a high of around 20% for fertilizers in the 12‐month horizon in the recent sample. We further show that the information in the persistent factors, especially in the commodity currency exchange rate‐based persistent factor, can be integrated with other global measures to further improve the predictive performances of the global measures.

Dynamic factor models for binary data in circular spaces: an application to the US Supreme Court

Abstract Latent factor models are widely used in the social and behavioural sciences as scaling tools to map discrete multivariate outcomes into low-dimensional, continuous scales. In political science, dynamic versions of classical factor models have been widely used to study the evolution of justices’ preferences in multi-judge courts. In this paper, we discuss a new dynamic factor model that relies on a latent circular space that can accommodate voting behaviours in which justices commonly understood to be on opposite ends of the ideological spectrum vote together on a substantial number of otherwise closely divided opinions. We apply this model to data on nonunanimous decisions made by the US Supreme Court between 1937 and 2021, and show that for most of this period, voting patterns can be better described by a circular latent space.

Expecting the unexpected: Stressed scenarios for economic growth

SummaryWe propose the construction of conditional growth densities under stressed factor scenarios to assess the level of exposure of an economy to small probability but potentially catastrophic economic and/or financial scenarios, which can be either domestic or international. The choice of severe yet plausible stress scenarios is based on the joint probability distribution of the underlying factors driving growth, which are extracted with a multilevel dynamic factor model (DFM) from a wide set of domestic/worldwide and/or macroeconomic/financial variables. All together, we provide a risk management tool that allows for a complete visualization of the dynamics of the growth densities under average scenarios and extreme scenarios. We calculate growth‐in‐stress (GiS) measures, defined as the 5% quantile of the stressed growth densities, and show that GiS is a useful and complementary tool to growth‐at‐risk (GaR) when policymakers wish to carry out a multidimensional scenario analysis. The unprecedented economic shock brought by the COVID‐19 pandemic provides a natural environment to assess the vulnerability of US growth with the proposed methodology.

Path and Direction Discovery in Individual Dynamic Factor Models: A Regularized Hybrid Unified Structural Equation Modeling with Latent Variable

There has been an increasing call to model multivariate time series data with measurement error. The combination of latent factors with a vector autoregressive (VAR) model leads to the dynamic factor model (DFM), in which dynamic relations are derived within factor series, among factors and observed time series, or both. However, a few limitations exist in the current DFM representatives and estimation: (1) the dynamic component contains either directed or undirected contemporaneous relations, but not both, (2) selecting the optimal model in exploratory DFM is a challenge, (3) the consequences of structural misspecifications from model selection is barely studied. Our paper serves to advance DFM with a hybrid VAR representations and the utilization of LASSO regularization to select dynamic implied instrumental variable, two-stage least squares (MIIV-2SLS) estimation. Our proposed method highlights the flexibility in modeling the directions of dynamic relations with a robust estimation. We aim to offer researchers guidance on model selection and estimation in person-centered dynamic assessments.

Synthetic wind speed time series generation by dynamic factor model

The global transition to renewable energy is driven by the fight against climate change. Wind power plays a crucial role in reducing dependence on fossil fuels and greenhouse gas emissions. Therefore, addressing uncertainties in wind speed variations requires innovative solutions. This study proposes a Bayesian-based approach using a Dynamic Factor Model to generate synthetic monthly average wind speed series. The Dynamic Factor Model framework captures temporal and spatial correlations, improving wind resource representation in operational planning models. The model's autoregressive configuration with common factors, prior distributions, and Bayesian inference techniques enhances predictive capabilities. Validation exercises confirm the model's reliability, accurately capturing seasonal oscillations and spatial correlations across eight wind farms. The study highlights the usefulness of the Dynamic Factor Model in evaluating wind projects and optimizing energy generation strategies, effectively mitigating wind uncertainty, and facilitating renewable energy integration in Brazil's power mix.