Dynamic Factor Model Research Articles

Ignoring cross-correlated idiosyncratic components when extracting factors in dynamic factor models

In economics, Principal Components, its generalized version that takes into account heteroscedasticity, and Kalman filter and smoothing procedures are among the most popular procedures for factor extraction in the context of Dynamic Factor Models. This paper analyzes the consequences on point and interval factor estimation of using these procedures when the idiosyncratic components are wrongly assumed to be cross-sectionally uncorrelated. We show that not taking into account the presence of cross-sectional dependence increases the uncertainty of point estimates of the factors. Furthermore, the Mean Square Errors computed using the usual expressions based on asymptotic approximations, are underestimated and may lead to prediction intervals with extremely low coverages.

Foreign portfolio investment and the US macroeconomic conditions

This paper examines how foreign portfolio investment (FPI) in the US and its components affect the US macroeconomic conditions. We estimate a Dynamic Factor Model to extract comovements from 31 indicators to obtain three composite measures of the US macroeconomic conditions, which correspond to real economic activity, monetary policy, and aggregate uncertainty. We find that an unexpected rise in FPI reduces long-term interest rates, raises real output production and employment, and lowers aggregate risks. Our results also show that the equity portion of FPI is significantly more sensitive to shocks to domestic market conditions than the debt portion of FPI. However, both components contribute substantially to the fluctuations of the US macroeconomic conditions. Finally, we find that shocks to FPI are one of the most significant contributors to the historical fluctuations in all output, monetary, and risk conditions. In particular, the equity component contributes substantially during economic recessions, while the debt component is the dominant force during economic booms.

Estimating Census Tract House Price Indexes: A New Spatial Dynamic Factor Approach

AbstractGeographically and temporally granular housing price indexes are difficult to construct. Data sparseness, in particular, is a limiting factor in their construction. A novel application of a spatial dynamic factor model allows for the construction of census tract level indexes on a quarterly basis while accommodating sparse data. Specifically, we augment the repeat sales model with a spatial dynamic factor model where loadings on latent trends are allowed to follow a spatial random walk thus capturing useful information from similar neighboring markets. The resulting indexes display less noise than similarly constructed non-spatial indexes and replicate indexes from the traditional repeat sales model in tracts where sufficient numbers of repeat sales pairs are available. The granularity and frequency of our indexes is highly useful for policymakers, homeowners, banks and investors.

High-frequency monitoring of China's green growth-at-risk.

With industrialization and urbanization, China faces enormous challenges from energy security and environmental issues. To address these challenges, it is imperative to establish a green accounting system for economic growth and to measure the uncertainty of China's green GDP (GGDP) growth from a risk management perspective. With this in mind, we follow the idea of growth-at-risk (GaR) to propose the concept of green GaR (GGaR) and extend it to the mixed-frequency data environment. Specifically, we first measure China's annual GGDP using the System of Environmental Economic Accounting (SEEA), then construct China's monthly green financial index by a mixed-frequency dynamic factor model (MF-DFM), and finally monitor China's GGaR from 2008M1 to 2021M12 with the mixed data sampling-quantile regression (MIDAS-QR) method. The main findings are as follows: First, the proportion of China's GGDP to traditional GDP gradually increases from 81.97% in 2008 to 89.34% in 2021, which illustrates that the negative environmental externalities caused by China's economic growth are gradually decreasing. Second, the high-frequency GGaR has favorable predictive performance and is significantly superior to the common-frequency GGaR at most quantiles. Third, the high-frequency GGaR has good nowcasting performance, and its 90% and 95% confidence intervals include true value for all prediction horizons. Furthermore, it can provide early warning of economic downturns through probability density prediction. Overall, our main contribution lies in constructing a quantitative assessment and high-frequency monitoring of China's GGDP growth risk, which provides an effective tool for investors and companies to predict risk, and a reference for the Chinese government to better formulate sustainable development strategies.

Dynamic ICAR Spatiotemporal Factor Models

We propose a novel class of dynamic factor models for spatiotemporal areal data. This novel class of models assumes that the spatiotemporal process may be represented by some few latent factors that evolve through time according to dynamic linear models. As the dimension of the vector of latent factors is typically much smaller than the number of subregions, our proposed class of models may achieve substantial dimension reduction. At each time point, the vector of observations is linearly related to the vector of latent factors through a matrix of factor loadings. Each column of this matrix may be seen as a vectorized map of factor loadings relating one latent factor to the vector of observations. Thus, to account for spatial dependence, we assume that each column of the matrix of factor loadings follows an intrinsic conditional autoregressive (ICAR) process. Hence, we call our class of models the Dynamic ICAR Spatiotemporal Factor Models (DIFM). We develop a Gibbs sampler for exploration of the posterior distribution. In addition, we develop model selection through a Laplace-Metropolis estimator of the predictive density. We present two case studies. The first case study, which is for simulated data, demonstrates that our DIFMs are identifiable and that our proposed inferential procedure works well at recovering the underlying data generating process. Finally, the second case study demonstrates the utility and flexibility of our DIFM framework with an application to the drug overdose epidemic in the United States from 2015 to 2021.

Dynamic factor, leverage and realized covariances in multivariate stochastic volatility

In the stochastic volatility models for multivariate daily stock returns, it has been found that the estimates of parameters become unstable as the dimension of returns increases. To solve this problem, we focus on the factor structure of multiple returns and consider two additional sources of information: first, the stock index associated with the market factor and, second, the realized covariance matrix calculated from high-frequency data. The proposed dynamic factor model with the leverage effect and realized measures is applied to 10 top stocks composing the exchange traded fund linked with the investment return of the S&P 500 index and the model is shown to have a stable advantage in portfolio performance.

High-dimensional conditionally Gaussian state space models with missing data

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced datasets and large Bayesian VARs with variables in multiple frequencies. A key observation underlying the proposed approach is that the joint distribution of the missing data conditional on the observed data is Gaussian. Furthermore, the inverse covariance or precision matrix of this conditional distribution is sparse, and this special structure can be exploited to substantially speed up computations. We illustrate the methodology using two empirical applications. The first application combines quarterly, monthly and weekly data using a large Bayesian VAR to produce weekly GDP estimates. In the second application, we extract latent factors from unbalanced datasets involving over a hundred monthly variables via a dynamic factor model with stochastic volatility.

Refining Sentiment Predictions: Obtaining an Unbiased Business Sentiment Index from Japanese Newspapers

Economic indices, such as the consumer price index, gross domestic product, and purchasing managers’ index, are typically computed based on economic data (e.g., prices of goods and incomes) and surveys. Recently, there has been considerable research to predict these indices using alternative data. One such approach is to utilize textual data, specifically newspaper articles, to predict a business sentiment index (BSI). However, newspapers often exhibit biases, which may impact the resulting index. This potential issue has not received adequate attention. Thus, this work first investigates whether these biases do influence the predicted indices and then proposes an approach to obtaining an unbiased business sentiment index. For this purpose, we analyze multiple Japanese newspapers, including one financial and three general papers with varied political orientations. We then predict a monthly BSI for each newspaper based on its content using a Transformer-based sentiment analysis model. To achieve an unbiased BSI, we employ the dynamic factor model. This model decomposes the time series of BSIs into a common dynamic factor shared across different newspapers and specific dynamic factors unique to individual newspapers. Our experiment indicates that the magnitudes of the predicted BSIs and the specific dynamic factors closely align with the political stances of the newspapers. Furthermore, the common dynamic factor exhibits a stronger and more positive correlation with composite indices and a survey-based BSI, namely the Tankan index.

A Dynamic Spatial Factor Model to Describe the Opioid Syndemic in Ohio.

The opioid epidemic has been ongoing for over 20 years in the United States. As opioid misuse has shifted increasingly toward injection of illicitly produced opioids, it has been associated with HIV and hepatitis C transmission. These epidemics interact to form the opioid syndemic. We obtain annual county-level counts of opioid overdose deaths, treatment admissions for opioid misuse, and newly diagnosed cases of acute and chronic hepatitis C and newly diagnosed HIV from 2014 to 2019. Aligned with the conceptual framework of syndemics, we develop a dynamic spatial factor model to describe the opioid syndemic for counties in Ohio and estimate the complex synergies between each of the epidemics. We estimate three latent factors characterizing variation of the syndemic across space and time. The first factor reflects overall burden and is greatest in southern Ohio. The second factor describes harms and is greatest in urban counties. The third factor highlights counties with higher than expected hepatitis C rates and lower than expected HIV rates, which suggests elevated localized risk for future HIV outbreaks. Through the estimation of dynamic spatial factors, we are able to estimate the complex dependencies and characterize the synergy across outcomes that underlie the syndemic. The latent factors summarize shared variation across multiple spatial time series and provide new insights into the relationships between the epidemics within the syndemic. Our framework provides a coherent approach for synthesizing complex interactions and estimating underlying sources of variation that can be applied to other syndemics.

Experimental, Theoretical and Numerical Research Progress on Dynamic Behaviors of RC Structural Members

In this paper, research on dynamic behaviors of RC structural members was reviewed using experimental, theoretical and numerical perspectives. First, in a basic overview, measurement methods, main conclusions and current limitations of available dynamic loading tests were presented. Then, theoretical studies on the dynamic constitutive models of RC materials, the dynamic increase factor (DIF) model for concrete and reinforced steel and proposed modified models of dynamic behavior parameters at the structural member level were summarized. Finally, the available modeling approach and method for incorporating dynamic effects in numerical simulations of RC structures were reviewed. Moreover, the work involved a brief introduction to a dynamic hysteretic model established using experimental data, which was designed to provide an alternative approach to the commonly-used DIF method for considering these dynamic effects. This paper, therefore, aimed to provide a valuable reference for experimental studies and numerical simulations on the dynamic behaviors of RC structures—while also putting forward issues that need to be addressed by future work.

Financial and Macroeconomic Data Through the Lens of a Nonlinear Dynamic Factor Model

Through the lens of a nonlinear dynamic factor model, we study the role of exogenous shocks and internal propagation forces in driving the fluctuations of macroeconomic and financial data. The proposed model 1) allows for nonlinear dynamics in the state and measurement equations; 2) can generate asymmetric, state-dependent, and size-dependent responses of observables to shocks; and 3) can produce time-varying volatility and asymmetric tail risks in predictive distributions. We find evidence in favor of nonlinear dynamics in two important U.S. applications. The first uses interest rate data to extract a factor allowing for an effective lower bound and nonlinear dynamics. Our estimated factor coheres well with the historical narrative of monetary policy. We find that allowing for an effective lower bound constraint is crucial. The second recovers a credit cycle. The nonlinear component of the factor boosts credit growth in boom times while hinders its recovery post-crisis. Shocks in a credit crunch period are more amplified and persist for longer compared with shocks during a credit boom.

Health expenditure convergence and the roles of trade and governance in Africa

This study investigates the convergence hypothesis in health expenditures in 40 African countries over the 2000–2019 period. The new non-linear dynamic factor model is used on panel data extracted from the World Development Indicator and the World Governance Indicator. We consider two categories of health expenditures: the domestic general government health expenditure as a percentage of government expenditure and the domestic general government health expenditure per capita. The results show the absence of full panel convergence for the two indicators used. However, there is evidence of convergence clubs. The overall marginal effect of the control variables is consistent with the existing literature. The results further show a strong influence of trade in attaining convergence among the clubs for both models. However, governance quality only affects the probability of converging in a club for the general government health expenditure as a percentage of government expenditure model. The findings suggest that policies on promoting health expenditure convergence should pursue initiatives that encourage trade. Efforts should also be targeted to improve the quality of governance.

Serial Dynamics, Spatial Spillover and Common Factors of Carbon Emission Intensity in China’s Bohai Economic Rim

The Bohai Economic Rim (BER) is an important economic Rim in north China. Since the implementation of the Beijing−Tianjin−Hebei Coordinated Strategy in 2014, the provinces have become more closely connected in economic development and environmental governance. This paper investigates the dynamics and spillover effects of carbon emission intensity in the BER before and after removing the common factors, and analyzes the reasons for the difference. In this study, the serial dynamics characteristics and spatial spillover effects of the carbon emission intensity of provinces were analyzed in the BER provinces between 2000 and 2019. Based on the Moran index and the spatial Durbin model, the provincial carbon emission intensity and influence factors were examined. CD (Correlation Dependence) tests were then applied, with the test results indicating that the carbon intensities had strong spatial correlation. Therefore, the dynamic spatial Durbin common factor model was introduced, characterizing the dynamic characteristics of the carbon emission intensity and the spatial spillover effect in the BER. The consequences obtained are as follows: (1) The carbon emission intensities in the BER were influenced by the energy intensity, urbanization level, economic growth, and population density. There was a significant spatial spillover effect between a province and its neighboring provinces. (2) The carbon emission intensities of the provinces exhibited a strong correlation. (3) The reason for the strong carbon emission intensity correlation is associated with environmental protection policies that are similar and the common external development environment. Combining the above findings and study conclusions, the authors offer the following policy suggestions: (1) optimize the energy structure; (2) improve the industrial structure; (3) construct a regional collaborative governance mechanism for carbon emissions; and (4) formulate a precise policy. This study is crucial for reducing regional carbon emissions, promoting the transition to a green economy and society, and achieving the “carbon peaking” and “carbon neutrality” targets in China.

Estimating speed-through-water by Dynamic Factor Models fusing metocean and propeller data

In vessel performance analysis, reliable information about speed-through-water (STW) is key for realistic modeling of the single ship’s fuel efficiency. It is paramount that STW measurements are reliable such that they can be adopted as input in fuel consumption forecast models. This paper presents a study where three variations of a Dynamic Factor Model are used to estimate the STW. A simulation study is presented to demonstrate the estimation and smoothing techniques for the Dynamic Factor Model. The model variations are then applied to real vessel data, including STW and propeller measurements, in combination with metocean data (sea currents). The present study suggests that the developed model can minimize the systematic STW measurement error even under highly non-stationary conditions.

Global and local components of output gaps

This paper proposes a multi-level dynamic factor model to identify common components in output gap estimates. We pool multiple estimates for 157 countries and decompose them into one global, eight regional, and 157 country-specific cycles. Our approach easily deals with mixed frequencies, ragged edges, and discontinuities in the underlying output gap estimates. To restrict the parameter space in the Bayesian state space model, we apply a stochastic search variable selection approach and base the prior inclusion probabilities on spatial information. Our results suggest that the global and the regional cycles explain a substantial proportion of the output gaps. On average, 18% of a country’s output gap is attributable to the global cycle, 24% to the regional cycle, and 58% to the local cycle.

The role of porosity in the dynamic disturbance resistance of water-saturated coal

Porosity significantly affects the dynamic response of water-saturated coal and the safety of coal mine engineering in water-rich areas. For mastering the dynamic response of water-saturated coal to the porosity, this study used the coal with four levels of the porosity for dynamic tests. In this process, the dynamic compressive tests were operated on these coal specimen in both of water saturation and dry states, and the reduction factor of dynamic mechanical parameters of the coal in water-saturated state to these in dry state were focused to eliminate the effect of self dynamic properties of the coal. The results indicate that the dynamic mechanical properties non-linear positively correlate with the porosity, and its sensitivity to porosity gradually weakens as with the increase of the porosity. This effect is intuitively expressed in the dominant fracture propagation features recorded by a high-speed camera, and microscopically attributed by the size and number of microfractures around the dominant fracture. The dynamic stress intensity factor model of the dominant fracture was further established with consideration of total cohesive force for the equivalent particle on the fracture surface. It well reveals the effect mechanism of porosity on the meso-deterioration and macroscopic mechanical properties of the coal around the roadway. On this basis, the applicable conditions and suggested methods were put forward to improve the dynamic stability of water-saturated coal with various porosity.

WHAT DRIVES CHINA’S LONG-TERM ECONOMIC GROWTH TREND? A RE-MEASUREMENT BASED ON A TIME-VARYING MIXED-FREQUENCY DYNAMIC FACTOR MODEL

The unprecedented downward pressure of China’s economic growth trend raises several questions, including what the current level of China’s long-term economic growth trend is, and what drives and how to inhibit the downward trend. Therefore, we develop a time-varying mixedfrequency dynamic factor model using data with different start dates to measure the trend, and perform a real-time decomposition of changes in the trend. We find that the trend has entered a downward stage since 2007, left a high-speed phase since 2012, and stepped in an accelerated downward stage since 2018. The current level of the trend is about 4%. However, the lower limit of the 90% confidence interval is below 2%, which is lower than natural rate level. Additionally, decelerated capital deepening, diminishing demographic dividend and technological recession all drive the downward trend. Compared to the relatively weak push-down effects of capital deepening and demographic dividend that are less than two percentage points, the downward trend is mainly driven by technological recession. Given that technological progress is unlikely to improve significantly in the short run, mitigating the mismatch between technological progress and obsolete capital, revitalizing existing capital stock, and increasing the efficiency of technology utilization become more feasible means.

Inflation Forecasting for Pakistan in a Data-rich Environment

This paper uses machine learning methods to forecast the year-on-year CPI inflation of Pakistan and compare their forecasting performance against the comprehensive traditional forecasting suite contained in Hanif and Malik (2015). It also augments the comprehensive forecasting suite with the dynamic factor model which is able to handle a large amount of information and put all of these models in competition against the latest machine learning models. A set of 117 predictors covering a period of July 1995 to June 2020 is used for this purpose. We set the naïve mean model as the benchmark and compare its forecasting performance against 14 traditional and 5 sophisticated machine learning models. We forecast the year-on-year CPI inflation over a 24 months horizon. Forecasting performance is measured using the RMSE. Our results show that the machine learning approaches perform better than the traditional econometric models at 18 forecast horizons.

The Role of Wages in Trend Inflation: Back to the 1980s?

This paper examines whether the measurement of trend inflation can be improved by using wage data in a dynamic factor model of disaggregated prices and wages for the United States. The model features time-varying coefficients and stochastic volatility. An estimate of trend inflation is a time-varying distributed lag of prices and wages, where the weight on a series depends on its time-varying volatility, persistence, and comovement with other series. The results show that wages inform estimates of trend inflation. The weight on wages was highest around 1980, drifted down through the 2000s, and returned to its 1980s value by 2022. In addition, inflation in the 2020s appears to have unmoored moderately from the 2 percent range that prevailed for decades, as the role of the persistent component of inflation increased in recent year. However, accounting for wages lowers the model's view of the increase in the volatility of trend inflation.

A dynamic factor model to predict homicides with firearm in the United States

PurposeResearch on temporal dynamics of crime in the United States is growing. Yet, mathematical tools to reliably predict homicides with firearm are still lacking, due to delays in the release of official data lagging up to almost two years. This study takes a critical step in this direction by establishing a reliable statistical tool to predict homicides with firearm at a monthly resolution, combining official data and easy-to-access explanatory variables. MethodWe propose a dynamic factor model to predict homicides with firearm from 1999 to 2020 using official monthly data released yearly by the Centers for Disease Control and Prevention, provisional quarterly data from the same agencies, media output from newspapers, and crowdsourced information from the Guns Violence Archive. ResultsStatistical findings demonstrate that the dynamic factor model outperforms state-of-the-art techniques (AI and classical autoregressive models). The dynamic factor model offers improved ability to backcast, nowcast, and forecast homicides with firearm, and can anticipate sudden changes in the time-series. ConclusionsBy decomposing the time-series of homicides with firearm on common and idiosyncratic components, the dynamic factor model successfully captures their complex time-evolution. This approach offers a vantage point to policymakers and practitioners, allowing for timely predictions, otherwise unfeasible.