
on Econometric Time Series 
By:  Alessandro Giovannelli; Marco Lippi; Tommaso Proietti 
Abstract:  The paper deals with the construction of a synthetic indicator of economic growth, obtained by projecting a quarterly measure of aggregate economic activity, namely gross domestic product (GDP), into the space spanned by a finite number of smooth principal components, representative of the mediumtolongrun component of economic growth of a highdimensional time series, available at the monthly frequency. The smooth principal components result from applying a crosssectional filter distilling the lowpass component of growth in real time. The outcome of the projection is a monthly nowcast of the mediumtolongrun component of GDP growth. After discussing the theoretical properties of the indicator, we deal with the assessment of its reliability and predictive validity with reference to a panel of macroeconomic U.S. time series. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.06618&r=ets 
By:  XIN JING (Yonsei University); JIN SEO CHO (Yonsei University) 
Abstract:  This study utilizes modal regression to forecast the cumulative confirmed COVID19 cases in Canada, Japan, South Korea, and the United States. The objective is to improve the accuracy of the forecasts compared to standard mean and median regressions. To evaluate the performance of the forecasts, we conduct simulations and introduce a metric called the coverage quantile function (CQF), which is optimized using modal regression. By applying modal regression to popular timeseries models for COVID19 data, we provide empirical evidence that the forecasts generated by the modal regression outperform those produced by the mean and median regressions in terms of the CQF. This finding addresses the limitations of the mean and median regression forecasts. 
Keywords:  Forecasting COVID19 cases; Modal regression; Conditional mode; MEM algorithm; Density estimation. 
JEL:  C22 C53 I18 
Date:  2023–06 
URL:  http://d.repec.org/n?u=RePEc:yon:wpaper:2023rwp217&r=ets 
By:  FrançoisÉric Racicota; David Tessierc 
Abstract:  The main objective of this research note is to establish a link between the local projection (LP) approaches of Jorda (2005), Kilian and Kim (2011), and more recently PlagborgMøller and Wolf (2021), Li et al. (2022) and the multihorizon causality analysis of Dufour and Renault (1998) and Dufour et al. (2006). Our detailed review of these papers with particular attention to Jorda?s local projection methodology make an enlightened comparison with Dufour et al.?s generalized causality methodology which is based on the (p, h)autoregression concept. In particular, we highlight the fact that Jorda?s approach relies on standard Cholesky decomposition to compute the IRF while we use the GIRF?i.e., the Koop et al. (1996) and Pesaran and Shin (1998) generalized impulse response function (see also Warne, 2008)?to make this comparison more reliable and in line with Dufour et al.?s robust methodology, which also refers to GIRF coefficients. Dufour et al.?s methodology does not require orthogonalization of the disturbances. We therefore call their method ?the Dufour et al.?s GIRF??a new type of GIRF?that, unlike the usual IRF which is for horizon h = 1, is for any horizon h ? 1. We also highlight the fact that our multihorizon causality test based on the (p, h)autoregression relies on Monte Carlo simulation, which can greatly improve test level in small samples, alleviating substantially the variance problem observed in the literature. As shown in Li et al. (2022), while LP is less biased than VAR OLS methods, there is a serious variance problem that makes the LP method quite erratic. Our Monte Carlo simulation method seems therefore quite well adapted for tackling this issue, improving LP or our (p, h)autoregression method sufficiently to make it reliable in small samples. This multihorizon causality test that we develop and apply in this paper, and the empirical evidence we present shows that it is reliable when applied to classical monetary causations. 
Keywords:  Multihorizon causality; (p, h)autoregression; Local projection IRF and GIRF; Conservative Monte Carlo test; VAR estimatio 
JEL:  C01 C12 C32 
Date:  2023–06–01 
URL:  http://d.repec.org/n?u=RePEc:ipg:wpaper:2023001&r=ets 
By:  Hafner, Christian M. (Université catholique de Louvain, LIDAM/ISBA, Belgium); Herwartz, Helmut; Wang, Shu 
Abstract:  Independent component analysis has recently become a promising databased approach to detect structural relations in multivariate dynamic systems in cases when apriori knowledge about causal patterns are scant. This paper suggests a kernelbased ML estimation that is largely agnostic with regard to the distributional features of the structural origins of data variation and enables causal analysis under the assumption of having only a subset of independent shocks. In an empirical application to the global oil market model of Kilian (2009) we illustrate the benefits of allowing for an unmodelled higherorder dependence among the oil supply and speculative oil demand shocks. 
Keywords:  Structural VAR ; structural MGARCH ; Independent component analysis 
JEL:  C14 C32 Q43 
Date:  2023–01–25 
URL:  http://d.repec.org/n?u=RePEc:aiz:louvad:2023004&r=ets 
By:  Samuel N. Cohen; Silvia Lui; Will Malpass; Giulia Mantoan; Lars Nesheim; \'Aureo de Paula; Andrew Reeves; Craig Scott; Emma Small; Lingyi Yang 
Abstract:  Key economic variables are often published with a significant delay of over a month. The nowcasting literature has arisen to provide fast, reliable estimates of delayed economic indicators and is closely related to filtering methods in signal processing. The path signature is a mathematical object which captures geometric properties of sequential data; it naturally handles missing data from mixed frequency and/or irregular sampling  issues often encountered when merging multiple data sources  by embedding the observed data in continuous time. Calculating path signatures and using them as features in models has achieved stateoftheart results in fields such as finance, medicine, and cyber security. We look at the nowcasting problem by applying regression on signatures, a simple linear model on these nonlinear objects that we show subsumes the popular Kalman filter. We quantify the performance via a simulation exercise, and through application to nowcasting US GDP growth, where we see a lower error than a dynamic factor model based on the New York Fed staff nowcasting model. Finally we demonstrate the flexibility of this method by applying regression on signatures to nowcast weekly fuel prices using daily data. Regression on signatures is an easytoapply approach that allows great flexibility for data with complex sampling patterns. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.10256&r=ets 
By:  Jie Wei; Yonghui Zhang 
Abstract:  This paper studies the principal component (PC) methodbased estimation of weak factor models with sparse loadings. We uncover an intrinsic nearsparsity preservation property for the PC estimators of loadings, which comes from the approximately upper triangular (block) structure of the rotation matrix. It implies an asymmetric relationship among factors: the rotated loadings for a stronger factor can be contaminated by those from a weaker one, but the loadings for a weaker factor is almost free of the impact of those from a stronger one. More importantly, the finding implies that there is no need to use complicated penalties to sparsify the loading estimators. Instead, we adopt a simple screening method to recover the sparsity and construct estimators for various factor strengths. In addition, for sparse weak factor models, we provide a singular value thresholdingbased approach to determine the number of factors and establish uniform convergence rates for PC estimators, which complement Bai and Ng (2023). The accuracy and efficiency of the proposed estimators are investigated via Monte Carlo simulations. The application to the FREDQD dataset reveals the underlying factor strengths and loading sparsity as well as their dynamic features. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.05934&r=ets 
By:  Sauvenier, Mathieu (Université catholique de Louvain, LIDAM/CORE, Belgium); Van Bellegem, Sébastien (Université catholique de Louvain, LIDAM/CORE, Belgium) 
Abstract:  A goodnessoffit test for the outcome of variable selection in a high dimensional linear model is studied. The test minimizes a moment condition that reflects the sparsity constraint. Testing this constraint is possible thanks to a high dimensional central limit Theorem that is proved under heteroskedasticity. To implement the test a multiplesplitting projection test procedure that has been recently proposed in the literature is employed. Monte Carlo experiments demonstrate the power of the test. A real data application considers the problem of selecting predictors to nowcast quarterly GDP. The empirical results show that it is possible to select a minimal number of variables such that every larger set of variables would pass the goodnessoffit test. 
Keywords:  High dimensional model ; Sparsity ; GoodnessofFit ; Projection test ; Nowcasting 
Date:  2023–03–17 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2023008&r=ets 
By:  Pesaran, M. H.; Yang, L. 
Abstract:  This paper considers a firstorder autoregressive panel data model with individual specific effects and a heterogeneous autoregressive coefficient. It proposes estimators for the moments of the crosssectional distribution of the autoregressive coefficients, with a focus on the first two moments, assuming a random coefficient model for the autoregressive coefficients without imposing any restrictions on the fixed effects. It is shown that the standard generalized method of moments estimators obtained under homogeneous slopes are biased. The paper also investigates conditions under which the probability distribution of the autoregressive coefficients is identified assuming a categorical distribution with a finite number of categories. Small sample properties of the proposed estimators are investigated by Monte Carlo experiments and compared with alternatives both under homogenous and heterogeneous slopes. The utility of the heterogeneous approach is illustrated in the case of earning dynamics, where a clear upward pattern is obtained in the mean persistence of earnings by the level of educational attainments. 
Keywords:  Dynamic panels, categorical distribution, random and group heterogeneity, short T panels, earnings dynamics 
JEL:  C22 C23 C46 
Date:  2023–06–06 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2342&r=ets 