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Working Paper
Testing for Contemporaneous Exogeneity in Linear Time-Series Models
Dovonon, Prosper; Gospodinov, Nikolay (2026-09-23)
We propose a test for contemporaneous exogeneity of regressors in linear time-series models. The test takes the form of a specification test with an expanding number of moment conditions. The test does not require external instruments and is based only on information contained in the regressors. Under the null of exogeneity, the test is characterized by a standard normal limit when the moment conditions are expanding at a particular rate relative to the sample size. We establish the consistency of the test under the alternative hypothesis when testing for exogeneity of the full set as well as ...
FRB Atlanta Working Paper , Paper 2026-14

Working Paper
Hedging and Pricing in Imperfect Markets under Non-Convexity
Gospodinov, Nikolay; Assa, Hirbod (2014-08-01)
This paper proposes a robust approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions. The generality of this framework allows us to conduct an in-depth theoretical analysis of hedging strategies for a wide family of risk measures and pricing rules, which are possibly non-convex. The practical implications of our proposed theoretical approach are illustrated with an application on hedging economic risk.
FRB Atlanta Working Paper , Paper 2014-13

Working Paper
Minimum distance estimation of possibly non-invertible moving average models
Gospodinov, Nikolay; Ng, Serena (2013)
This paper considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher-order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model has classical (root-T and asymptotic normal) properties when the moving average root is inside, outside, and on the unit circle. For more general models where the dependence of the cumulants on the model parameters is analytically intractable, we consider simulation-based estimators with two ...
FRB Atlanta Working Paper , Paper 2013-11

Working Paper
Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility
Jensen, Mark J. (2015-11-01)
Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance?but still mean reverting?behavior is commonly found with nonparametric estimates of the fractional differencing parameter d, for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic volatility (SV-FIAR) model. Joint estimates of the autoregressive and fractional differencing parameters ...
FRB Atlanta Working Paper , Paper 2015-12

Working Paper
The Anatomy of Out-of-Sample Forecasting Accuracy
Goulet Coulombe, Philippe; Rapach, David E.; Schwenk-Nebbe, Sander; Montes Schütte, Erik Christian; Borup, Daniel (2022-11-07)
We develop metrics based on Shapley values for interpreting time-series forecasting models, including“black-box” models from machine learning. Our metrics are model agnostic, so that they are applicable to any model (linear or nonlinear, parametric or nonparametric). Two of the metrics, iShapley-VI and oShapley-VI, measure the importance of individual predictors in fitted models for explaining the in-sample and out-of-sample predicted target values, respectively. The third metric is the performance-based Shapley value (PBSV), our main methodological contribution. PBSV measures the ...
FRB Atlanta Working Paper , Paper 2022-16

Working Paper
Modeling Event Studies with Heterogeneous Treatment Effects
Mroz, Thomas; Argys, Laura; Pitts, M. Melinda (2023-09-07)
This paper develops a simple approach to overcome the shortcomings of using a standard, single treatment–effect event study to assess the ability of an empirical model to measure heterogeneous treatment effects. Equally as important, we discuss how the standard errors reported in a typical event-study analysis for the posttreatment event-time effects are, without additional information, of limited use for assessing posttreatment variations in the treatment effects. The simple reformulation of the standard event—study approach described and illustrated with artificially constructed data in ...
FRB Atlanta Working Paper , Paper 2023-11

Working Paper
The Anatomy of Out-of-Sample Forecasting Accuracy
Goulet Coulombe, Philippe; Rapach, David E.; Schwenk-Nebbe, Sander; Montes Schütte, Erik Christian; Borup, Daniel (2024-02-21)
We introduce the performance-based Shapley value (PBSV) to measure the contributions of individual predictors to the out-of-sample loss for time-series forecasting models. Our new metric allows a researcher to anatomize out-of-sample forecasting accuracy, thereby providing valuable information for interpreting time-series forecasting models. The PBSV is model agnostic—so it can be applied to any forecasting model, including "black box" models in machine learning, and it can be used for any loss function. We also develop the TS-Shapley-VI, a version of the conventional Shapley value that ...
FRB Atlanta Working Paper , Paper 2022-16b

Report
Forecasting the New England States’ Tax Revenues in the Time of the COVID-19 Pandemic
Zhao, Bo (2020-07-09)
State governments across the United States face the prospect of sharply declining tax revenues due to the COVID-19 pandemic. They need reliable and up-to-date revenue forecasts to make financially sound policy decisions during this public health and economic crisis. This paper proposes an objective, transparent, simple, and efficient method to forecast state tax revenues in this time of the COVID-19 pandemic. The model is based on only two input factors: the state unemployment rate and an empirically determined time trend. The predictions from the model closely track the actual values of tax ...
Current Policy Perspectives

Working Paper
Testing for Differences in Path Forecast Accuracy: Forecast-Error Dynamics Matter
Martinez, Andrew (2017-11-02)
Although the trajectory and path of future outcomes plays an important role in policy decisions, analyses of forecast accuracy typically focus on individual point forecasts. However, it is important to examine the path forecasts errors since they include the forecast dynamics. We use the link between path forecast evaluation methods and the joint predictive density to propose a test for differences in system path forecast accuracy. We also demonstrate how our test relates to and extends existing joint testing approaches. Simulations highlight both the advantages and disadvantages of path ...
Working Papers (Old Series) , Paper 1717

Working Paper
Frequency Dependence in a Real-Time Monetary Policy Rule
Tsang, Kwok Ping; Verbrugge, Randal J.; Ashley, Richard (2014-11-19)
We estimate a monetary policy rule for the US allowing for possible frequency dependence?i.e., allowing the central bank to respond differently to more persistent innovations than to more transitory innovations, in both the unemployment rate and the inflation rate. Our estimation method uses real-time data in these rates?as did the FOMC?and requires no a priori assumptions on the pattern of frequency dependence or on the nature of the processes generating either the data or the natural rate of unemployment. Unlike other approaches, our estimation method allows for possible feedback in the ...
Working Papers (Old Series) , Paper 1430

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