Publications:
Horseshoe Prior Bayesian Quantile Regression with Tibor Szendrei (First Draft: March 2020; This Version: June 2020)
In: Journal of the Royal Statstical Society Series C (forthcoming)
Abstract: This paper extends the horseshoe prior of Carvalho et al. (2010) to the Bayesian quantileregression (HS-BQR) and provides a fast sampling algorithm that speeds up computation significantly in high dimensions. The performance of the HS-BQR is tested on large scale Monte Carlo simulations and an empirical application relevant to macroeoncomics.The Monte Carlo design considers several sparsity structures (sparse, dense, block) and error structures (i.i.d. errors and heteroskedastic errors). A number of LASSO based estimators (frequentist and Bayesian) are pitted against the HS-BQR to better gauge theperformance of the method on the different designs. The HS-BQR yields as just as good,or better performance than the other estimators considered when evaluated using coefficient bias and forecast error. We find that the HS-BQR is particularly potent in sparse designs and when estimating extreme quantiles. The simulations also highlight how the high dimensional quantile estimators fail to correctly identify the quantile function of the variables when both location and scale effects are present. In the empirical application, in which we evaluate forecast densities of US inflation, the HS-BQR provides well calibrated forecast densities whose individual quantiles, have the highest pseudo R-squared, highlighting its potential for Value-at-Risk estimation
[ Working Paper] [Slides] [Code]
Flexible Bayesian MIDAS: time‑variation, group‑shrinkage and sparsity with Galina Potjagailo (This version: May 2023)
In: Bank of England Staff Working Paper No. 1025.
We propose a mixed‑frequency regression prediction approach that models a time‑varying trend, stochastic volatility and fat tails in the variable of interest. The coefficients of high‑frequency indicators are regularised via a shrinkage prior that accounts for the grouping structure and within‑group correlation among lags. A new sparsification algorithm on the posterior motivated by Bayesian decision theory derives inclusion probabilities over lag groups, thus making the results easy to communicate without imposing sparsity a priori. An empirical application on nowcasting UK GDP growth suggests that group‑shrinkage in combination with the time‑varying components substantially increases nowcasting performance by reading signals from an economically meaningful subset of indicators, whereas the time‑varying components help by allowing the model to switch between indicators. Over the data release cycle, signals initially stem from survey data and then shift towards few ‘hard’ real activity indicators. During the Covid pandemic, the model performs relatively well since it shifts towards indicators for the service and housing sectors that capture the disruptions from economic lockdowns.
[Working Paper] [Code]
Nowcasting Growth using Google Trends Data: A Bayesian Structural Time Series Model with Arnab Bhattacharjee (First Draft: October 2020, This version: May 2022)
In: International Journal of Forecasting.
This paper investigates the benefits of internet search data in the form of Google Trends for nowcasting real U.S. GDP growth in real time through the lens of mixed frequency Bayesian Structural Time Series (BSTS) models. We augment and enhance both model and methodology to make these better amenable to nowcasting with large number of potential covariates. Specifically, we allow shrinking state variances towards zero to avoid overfitting, extend the SSVS (spike and slab variable selection) prior to the more flexible normal-inverse-gamma prior which stays agnostic about the underlying model size, as well as adapt the horseshoe prior to the BSTS. The application to nowcasting GDP growth as well as a simulation study demonstrate that the horseshoe prior BSTS improves markedly upon the SSVS and the original BSTS model with the largest gains in dense data-generating-processes. Our application also shows that a large dimensional set of search terms is able to improve nowcasts early in a specific quarter before other macroeconomic data become available. Search terms with high inclusion probability have good economic interpretation, reflecting leading signals of economic anxiety and wealth effects.
[Working Paper] [Journal Version] [Code]
A Theory-based Lasso for Time-Series Data with Achim Ahrens, Christopher Aitken, Jan Ditzen, Erkal Ersoy and Mark Edwin Schaffer
In : Data Science for Financial Econometrics, Springer.
Abstract: We present two new lasso estimators, the HAC-lasso and AC-lasso, that are suitable for time-series applications. The estimators are variations of the theory-based or ‘rigorous’ lasso of Bickel et al. (2009), Belloni et al. (2011), Belloni and Chernozhukov (2013), Belloni et al. (2016) and recently extended to the case of dependent data by Chernozhukov et al. (2019), where the lasso penalty level is derived on theoretical grounds. The rigorous lasso has appealing theoretical properties and is computationally very attractive compared to conventional cross-validation. The AC-lasso version of the rigorous lasso accommodates dependence in the disturbance term of arbitrary form, so long as the dependence is known to die out after q periods; the HAC-lasso also allows for heteroskedasticity of arbitrary form. The HAC- and AC-lasso are particularly well-suited to applications such as nowcasting, where the time series may be short and the dimensionality of the predictors is high. We present some Monte Carlo comparisons of the performance of the HAC-lasso vs. penalty selection by cross-validation approach. Finally, we use the HAC-lasso to estimate a nowcasting model of US GDP growth based on Google Trends data and compare its performance to the Bayesian methods employed by Kohns and Bhattacharjee (2019).
Working Papers:
Decoupling Shrinkage and Selection for the Bayesian Quantile Regression with Tibor Szendrei (First Draft: July 2021; This Version: June 2021) [submitted ]
Abstract: This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of the art continuous priors and in the second step, we sparsify the posterior through an efficient variant of the adaptive lasso, the signal adaptive variable selection (SAVS) algorithm. We propose a new variant of the SAVS which automates the choice of penalisation through quantile specific lossfunctions that are valid in high dimensions. We show in large scale simulations that our selection procedure decreases bias irrespective of the true underlying degree of sparsity in the data, compared to the un-sparsified regression posterior. We apply our two-step approach to a high dimensional growth-at-risk (GaR) exercise. The prediction accuracy of the un-sparsified posterior is retained while yielding interpretable quantile specific variable selection results. Our procedure can be used to communicate to policymakers which variables drive downside risk to the macro economy.
Presented at: International Symposium on Forecasting (2021), 15th Computational and Financial Econometrics Conference (forthcoming)
Interpreting Big Data in the Macro Economy: A Bayesian Mixed Frequency Estimator with Arnab Bhattacharjee (First Draft: August 2018; This Version: October 2019)
Abstract: More and more are Big Data sources, such as Google Trends, being used to augment nowcast models. An often neglected issue within the previous literature, which is especially pertinent to policy environments, is the interpretability of the Big Data source included in the model. We provide a Bayesian modeling framework which is able to handle all econometric issues involved in combining Big Data with traditional macroeconomic time series, while remaining computationally simple and allowing for a high degree of interpretability. In our model, we explicitly account for the possibility that the Big Data and macroeconomic data set included have different degrees of sparsity. We test our methodology by investigating whether Google Trends in real time increase nowcast fit of US real GDP growth compared to traditional macroeconomic time series. We find that search terms improve performance of both point forecast accuracy as well as forecast density calibration not only before official information is released but also later into GDP reference quarters. Our transparent methodology shows that the increased fit stems from search terms acting as early warning signals to large turning points in GDP.
[Working Paper] [Slides: soon] [Simulation Code: soon]
Presented at: International Symposium on Forecasting (Thessaloniki, 2019), 3rd Annual Workshop on Financial Econometrics (Orebro, 2019), Modelling with Big Data and Machine Learning: Interpretability and Model Uncertainty (Bank of England, 2019), Scottish Economic Conference (Perth, 2019).
Work in Progress
House Prices at Risk: Big Data Bayesian Quantile Regression Approach with Tibor Szendrei