Working papers

Opschoor, D. and D. van Dijk, 2023, Slow Expectation-Maximization convergence in low-noise dynamic factor models, Tinbergen Institute Discussion Paper 2023-018/III.

Abstract:  This paper addresses the poor performance of the Expectation-Maximization (EM) algorithm in the estimation of low-noise dynamic factor models, commonly used in macroeconomic forecasting and nowcasting. We show analytically and in Monte Carlo simulations how the EM algorithm stagnates in a low-noise environment, leading to inaccurate estimates of factor loadings and latent factors. An adaptive version of EM considerably speeds up  convergence, producing substantial improvements in estimation accuracy. Modestly increasing the noise level also accelerates convergence. A nowcasting exercise of euro area GDP growth shows gains up to 34\% by using adaptive EM relative to the usual EM.

Keijsers, B. and D. van Dijk, 2022, Does economic uncertainty predict real activity in real-time?, Tinbergen Institute Discussion Paper 2022-069/III.

Abstract: We assess the predictive ability of 15 economic uncertainty measures in a real-time out-of-sample forecasting exercise for the quantiles of The Conference Board's coincident economic index and its components (industrial production, employment, personal income, and manufacturing and trade sales). The results show that the measures hold (real-time) predictive power for quantiles in the left tail. Because uncertainty measures are all proxies of an unobserved entity, we combine their information using principal component analysis. A large fraction of the variance of the uncertainty measures can be explained by two factors. First, a general economic uncertainty factor with a slight tilt toward financial conditions. Second, a consumer/media confidence index which remains elevated after recessions. Using a predictive regression model with the factors from the set of uncertainty measures yields more consistent gains compared to a model with an individual uncertainty measure. Further, although often better forecasts are obtained using the National Financial Conditions Index (NFCI), the uncertainty factor models are superior when forecasting employment and in general the uncertainty factors have predictive content that is complementary to the NFCI.

Lange, R.-J., B. van Os and D. van Dijk, 2022, Robust observation-driven models using proximal-parameter updates, Tinbergen Institute Discussion Paper 2022-066/III.

Abstract: We propose a novel observation-driven modeling framework that allows for time variation in the model’s parameters using a proximal-parameter (ProPar) update. The ProPar update is the solution to an optimization problem that maximizes the logarithmic observation density with respect to the parameter, while penalizing the squared distance of the parameter from its one-step-ahead prediction. The associated first-order condition has the form of an implicit stochastic-gradient update; replacing this implicit update with its explicit counterpart yields the popular class of score-driven models. Key advantages of the ProPar setup are stronger invertibility properties (especially under model misspecification) as well as extended (global rather than local) optimality properties. For the class of postulated observation densities whose logarithm is concave, ProPar’s robustness is evident from its (i) muted response to large shocks in endogenous and exogenous variables, (ii) stability under poorly specified learning rates, and (iii) global contractivity towards a pseudo-truth—in all cases, even under model misspecification. We illustrate the general applicability and the practical usefulness of the ProPar framework for time-varying regressions, volatility, and quantiles.

Van Os, B. and D. van Dijk, 2021, Pooling dynamic conditional correlation models, Tinbergen Institute Discussion Paper 2021-083/IV.

Abstract: The Dynamic Conditional Correlation (DCC) model by Engle (2002) has become an extremely popular tool for modeling the time-varying dependence of asset returns. However, applications to large cross-sections have been found to be problematic, due to the curse of dimensionality. We propose a novel DCC model with Conditional LInear Pooling (CLIP-DCC) which endogenously determines an optimal degree of commonality in the correlation innovations, allowing a part of the update to be of reduced dimension. In contrast to existing approaches such as the Dynamic EquiCOrrelation (DECO) model, the CLIP-DCC model does not restrict long-run behavior, thereby naturally complementing target correlation matrix shrinkage approaches. Empirical findings suggest substantial benefits for a minimum-variance investor in real-time. Combining the CLIP-DCC model with target shrinkage yields the largest improvements, confirming that they address distinct parts of uncertainty of the conditional correlation matrix.

Opschoor, D., D. van Dijk and P.H. Franses, 2021, Heterogeneity in manufacturing growth risk, Tinbergen Institute Discussion Paper 2021-036/III.

Abstract: We analyze output growth risk with respect to financial conditions across U.S. manufacturing industries. Using a multi-level quantile regression approach, we find strong heterogeneity in growth risk, particularly between the more vulnerable durable goods sector and the more resilient nondurable goods sector. Moreover, we show that industry characteristics significantly explain these differences. Large, or material intensive durable goods producing, or energy intensive nondurable goods producing industries are more vulnerable to adverse financial conditions, while industries engaging in labor hoarding, or with a high capital or overhead labor intensity are less susceptible.

Gong, X., M. van der Wel and D. van Dijk, 2019, Improved forecasting of the implied volatility surface.

Abstract: The (implied) volatility surface is the collection of option-implied volatilities for different strike prices and maturities. Existing literature documents that the volatility surface can be modelled by a limited number of factors using simple regression techniques, and that these factors are persistent. However, regression techniques leave substantial serial correlation in the residuals. We propose an autoregressive model and an `equilibrium correction' style model which uses the information of the deviation from put call parity to directly exploit the serial correlation. We apply the models to S&P500 index options and options of 95 stocks, and show that the new models improve the existing models with a 40% decrease of both in-sample RMSE and out-of-sample RMSFE. The economic significance evaluation shows that the new models can generate higher Sharpe ratios than existing models. 

Gong, X., M. van der Wel and D. van Dijk, 2019, Using index options to enhance the description of the implied volatility surface of equity options.

Abstract: We put forward a novel factor-based approach for modeling and forecasting the implied volatility surface (IVS) for a cross-section of equity options. Inspired by the findings of Christoffersen et al. (2017) that equity volatility levels, smiles and term structures show strong co-movement, we postulate the presence of common factors in these characteristics. We argue that liquid index options can be used to obtain estimates of these common factors, which renders a feasible modeling approach even in high-dimensional settings. We implement the model for a cross-section of 97 equity options combined with options on the S&P 500 index. We document strong explanatory power of index options factors for the equity IVSs, and find that incorporating the index option information can improve the forecasting performance, particularly for illiquid stocks.