Monthly forecasting of GDP with mixed-frequency multivariate singular spectrum analysis

The literature on mixed-frequency models is relatively recent and has found applications across economics and finance. The standard application in economics considers the use of (usually) monthly variables (e.g. industrial production) for predicting/fitting quarterly variables (e.g. real GDP). This paper proposes a multivariate singular spectrum analysis (MSSA) based method for mixed-frequency interpolation and forecasting, which can be used for any mixed-frequency combination. The novelty of the proposed approach rests on the grounds of simplicity within the MSSA framework. We present our method using a combination of monthly and quarterly series and apply MSSA decomposition and reconstruction to obtain monthly estimates and forecasts for the quarterly series. Our empirical application shows that the suggested approach works well, as it offers forecasting improvements on a dataset of eleven developed countries over the last 50 years. The implications for mixed-frequency modelling and forecasting, and useful extensions of this method, are also discussed.     

A three-frequency dynamic factor model for nowcasting Canadian provincial GDP growth

This paper estimates a three-frequency dynamic factor model for nowcasting the Canadian provincial gross domestic product (GDP). The Canadian provincial GDP at market prices is released by Statistics Canada annually with a significant lag (11 months). This necessitates a mixed-frequency approach that can process timely monthly data, the quarterly national accounts, and the annual target variable. The model is estimated on a wide set of provincial, national and international data. In a pseudo real-time exercise, we find that the model outperforms simple benchmarks and is competitive with more sophisticated mixed-frequency approaches (MIDAS models). We also find that variables from the Labour Force Survey are important predictors of real activity. This paper expands previous work that has documented the importance of foreign variables for nowcasting Canadian GDP. This paper finds that including national and foreign predictors is useful for Ontario, while worsening the nowcast performance for smaller provinces.     

Mixed-frequency machine learning: Nowcasting and backcasting weekly initial claims with daily internet search volume data

We propose an out-of-sample prediction approach that combines unrestricted mixed-data sampling with machine learning (mixed-frequency machine learning, MFML). We use the MFML approach to generate a sequence of nowcasts and backcasts of weekly unemployment insurance initial claims based on a rich trove of daily Google Trends search volume data for terms related to unemployment. The predictions are based on linear models estimated via the LASSO and elastic net, nonlinear models based on artificial neural networks, and ensembles of linear and nonlinear models. Nowcasts and backcasts of weekly initial claims based on models that incorporate the information in the daily Google Trends search volume data substantially outperform those based on models that ignore the information. Predictive accuracy increases as the nowcasts and backcasts include more recent daily Google Trends data. The relevance of daily Google Trends data for predicting weekly initial claims is strongly linked to the COVID-19 crisis.     

The influence and predictive powers of mixed-frequency individual stock sentiment on stock returns

In this article, we construct mixed-frequency individual stock sentiment using MIDAS model. We first investigate the influence power of mixed-frequency individual stock sentiment on excess returns. The results indicate that the higher the frequency of individual stock sentiment is, the better it explains the variation of excess returns, that mixed-frequency individual stock sentiment, especially mixed high-frequency sentiment, exerts greater influence on excess returns than the same frequency one and that the mixed-frequency sentiment has a stronger explanatory power to the variation of excess returns than size factor, book-to-market factor, profitability factor and investment factor do. Then, we study the predictive content of mixed-frequency individual stock sentiment. The results show that the higher the frequency of individual stock sentiment is, the better the forecast performs. Moreover, by comparing the corresponding statistics in influence and predictive power models, we find that the influence power of mixed-frequency individual stock sentiment is more significant than its predictive power.     

Bayesian analysis of a Tobit quantile regression model

This paper develops a Bayesian framework for Tobit quantile regression. Our approach is organized around a likelihood function that is based on the asymmetric Laplace distribution, a choice that turns out to be natural in this context. We discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments. We show how the posterior distribution can be sampled and summarized by Markov chain Monte Carlo methods. A method for comparing alternative quantile regression models is also developed and illustrated. The techniques are illustrated with both simulated and real data. In particular, in an empirical comparison, our approach out-performed two other common classical estimators.     

Variable selection via composite quantile regression with dependent errors

We propose composite quantile regression for dependent data, in which the errors are from short‐range dependent and strictly stationary linear processes. Under some regularity conditions, we show that composite quantile estimator enjoys root‐n consistency and asymptotic normality. We investigate the asymptotic relative efficiency of composite quantile estimator to both single‐level quantile regression and least‐squares regression. When the errors have finite variance, the relative efficiency of composite quantile estimator with respect to the least‐squares estimator has a universal lower bound. Under some regularity conditions, the adaptive least absolute shrinkage and selection operator penalty leads to consistent variable selection, and the asymptotic distribution of the non‐zero coefficient is the same as that of the counterparts obtained when the true model is known. We conduct a simulation study and a real data analysis to evaluate the performance of the proposed approach.     

Common correlated effects estimation of heterogeneous dynamic panel quantile regression models

This paper proposes a quantile regression estimator for a heterogeneous panel model with lagged dependent variables and interactive effects. The paper adopts the Common Correlated Effects (CCE) approach proposed in the literature and demonstrates that the extension to the estimation of dynamic quantile regression models is feasible under similar conditions to the ones used in the literature. The new quantile regression estimator is shown to be consistent and its asymptotic distribution is derived. Monte Carlo studies are carried out to study the small sample behavior of the proposed approach. The evidence shows that the estimator can significantly improve on the performance of existing estimators as long as the time series dimension of the panel is large. We present an application to the evaluation of Time-of-Use pricing using a large randomized control trial.     

A comparison of mixed frequency approaches for nowcasting Euro area macroeconomic aggregates

In this paper, we focus on the different methods which have been proposed in the literature to date for dealing with mixed-frequency and ragged-edge datasets: bridge equations, mixed-data sampling (MIDAS), and mixed-frequency VAR (MF-VAR) models. We discuss their performances for nowcasting the quarterly growth rate of the Euro area GDP and its components, using a very large set of monthly indicators. We investigate the behaviors of single indicator models, forecast combinations and factor models, in a pseudo real-time framework. MIDAS with an AR component performs quite well, and outperforms MF-VAR at most horizons. Bridge equations perform well overall. Forecast pooling is superior to most of the single indicator models overall. Pooling information using factor models gives even better results. The best results are obtained for the components for which more economically related monthly indicators are available. Nowcasts of GDP components can then be combined to obtain nowcasts for the total GDP growth.     

Quantile models and estimators for data analysis

Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate than the regression quantiles.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

SCAD‐penalized quantile regression for high‐dimensional data analysis and variable selection

The present penalized quantile variable selection methods are only applicable to finite number of predictors or do not have oracle property associated with estimator. This technique is considered as an alternative to ordinary least squares regression in case of the outliers and the heavy‐tailed errors existing in linear models. The variable selection through quantile regression with diverging number of parameters is investigated in this paper. The convergence rate of estimator with smoothly clipped absolute deviation penalty function is also studied. Moreover, the oracle property with proper selection of tuning parameter for quantile regression under certain regularity conditions is also established. In addition, the rank correlation screening method is used to accommodate ultra‐high dimensional data settings. Monte Carlo simulations demonstrate finite performance of the proposed estimator. The results of real data reveal that this approach provides substantially more information as compared with ordinary least squares, conventional quantile regression, and quantile lasso.     

Nonparametric expected shortfall forecasting incorporating weighted quantiles

A new semi-parametric expected shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of value at risk (VaR) at different quantile levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantile weighting structure is parsimoniously parameterized by means of a beta weight function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler–Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using two data generating processes. Two forecasting studies with different out-of-sample sizes are then conducted, one of which focuses on the 2008 Global Financial Crisis period. The proposed models are applied to seven stock market indices, and their forecasting performances are compared to those of a range of parametric, non-parametric, and semi-parametric models, including GARCH, conditional autoregressive expectile (CARE), joint VaR and ES quantile regression models, and a simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of the proposed models.     

A quantile-based approach for relative efficiency measurement

Two popular approaches for efficiency measurement are a non-stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms. Copyright © 1999 John Wiley & Sons, Ltd.     

Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970

Output growth estimates for regions of the UK are currently published at an annual frequency only, released with a long delay, and offer limited historical coverage. To improve the regional database this paper develops a mixed-frequency multivariate model and uses it to produce consistent estimates of quarterly regional output growth dating back to 1970. We describe how these estimates are updated and evaluated on an ongoing, quarterly basis to publish online (at www.escoe.ac.uk/regionalnowcasting ) more timely regional growth estimates. We illustrate how the new quarterly data can contribute to our historical understanding of business cycle dynamics and connectedness between regions.     

Analyzing quantile spillover effects among international financial markets

This paper investigates the quantile-based spillover effects among 17 stock markets from January 1993 to January 2022, utilizing a quantile approach based on the variance decomposition of a quantile vector autoregression (QVAR) model. Compared with the traditional mean-based spillover measures, this new quantile approach allows for a nuanced investigation of spillovers at every quantile and capture spillovers under extreme events. The results show that: (1) the total spillover is high and exhibits strong time-varying characteristics, and the tail spillover is higher and more complex in scale and direction; (2) the spillover at each quantile level shows an upward trend, especially during the 2008 crisis and the COVID-19 epidemic; (3) developed countries (or regions) are the net exporters of stock market spillovers, while the developing countries are the net importers; and (4) the 17 stock markets constitute different local financial networks, which may be related to economic conditions and geographical location.     

Cross-sectional quantile regression for estimating conditional VaR of returns during periods of high volatility

Evaluating value at risk (VaR) for a firm’s returns during periods of financial turmoil is a challenging task because of the high volatility in the market. We propose estimating conditional VaR and expected shortfall (ES) for a given firm’s returns using quantile regression with cross-sectional (CSQR) data about other firms operating in the same market. An evaluation using US market data between 2000 and 2020 shows that our approach has certain advantages over a CAViaR model. Identification of low-risk firms and a reduction in computing times are additional advantages of the new method described.     

Quantile regression for the qualifying match of GEFCom2017 probabilistic load forecasting

We present a simple quantile regression-based forecasting method that was applied in the probabilistic load forecasting framework of the Global Energy Forecasting Competition 2017 (GEFCom2017). The hourly load data are log transformed and split into a long-term trend component and a remainder term. The key forecasting element is the quantile regression approach for the remainder term, which takes into account both weekly and annual seasonalities, such as their interactions. Temperature information is used only for stabilizing the forecast of the long-term trend component. Information on public holidays is ignored. However, the forecasting method still placed second in the open data track and fourth in the definite data track, which is remarkable given the simplicity of the model. The method also outperforms the Vanilla benchmark consistently.     

Predicting failure risk using financial ratios: Quantile hazard model approach

This study examines the role of financial ratios in predicting companies’ default risk using the quantile hazard model (QHM) approach and compares its results to the discrete hazard model (DHM). We adopt the LASSO method to select essential predictors among the variables mentioned in the literature. We show the preeminence of our proposed QHM through the fact that it presents a different degree of financial ratios’ effect over various quantile levels. While DHM only confirms the aftermaths of “stock return volatilities” and “total liabilities” and the positive effects of “stock price”, “stock excess return”, and “profitability” on businesses, under high quantile levels QHM is able to supplement “cash and short-term investment to total assets”, “market capitalization”, and “current liabilities ratio” into the list of factors that influence a default. More interestingly, “cash and short-term investment to total assets” and “market capitalization” switch signs in high quantile levels, showing their different influence on companies with different risk levels. We also discover evidence for the distinction of default probability among different industrial sectors. Lastly, our proposed QHM empirically demonstrates improved out-of-sample forecasting performance.     

Weak identification robust tests in an instrumental quantile model

We develop a testing procedure that is robust to identification quality in an instrumental quantile model. In order to reduce the computational burden, a multi-step approach is taken, and a two-step Anderson–Rubin (AR) statistic is considered. We then propose an orthogonal decomposition of the AR statistic, where the null distribution of each component does not depend on the assumption of a full rank of the Jacobian. Power experiments are conducted, and inferences on returns to schooling using the Angrist and Krueger data are considered as an empirical example.