Shrinkage and Penalized Likelihood as Methods to Improve Predictive Accuracy

A review is given of shrinkage and penalization as tools to improve predictive accuracy of regression models. The James-Stein estimator is taken as starting point. Procedures covered are Pre-test Estimation, the Ridge Regression of Hoerl and Kennard, the Shrinkage Estimators of Copas and Van Houwelingen and Le Cessie, the LASSO of Tibshirani and the Garotte of Breiman. An attempt is made to place all these procedures in a unifying framework of semi-Bayesian methodology. Applications are briefly mentioned, but not amply discussed.     

基于LASSO方法的四川农村居民食物消费支出影响因素探究

[目的]农村居民是乡村振兴的主体,其食物消费和膳食结构直接影响乡村振兴战略的顺利实施。四川省是我国西部农业大省,其农村居民的食物消费和膳食结构在中国西部地区具有一定的代表性。分析四川农村居民食物消费支出及其影响因素,对于改善农村居民食物消费和推进国家乡村振兴战略具有重要意义。[方法]根据经济发展水平进行分层抽样,选取四川省3市3县(区)156个农户,开展食物消费支出及营养认知问卷调研,采用LASSO方法对调研结果进行回归,筛选出影响农村居民食物消费支出的关键因素。[结果]在影响农村居民食物消费支出的主要因素中,家庭食物营养决策人的营养态度、家庭收入和决策人年龄与家庭食物消费支出都存在显著正相关;其中,决策人的营养态度相关系数最大,达到0.886,家庭收入和决策人年龄的相关系数分别为0.043和0.011;而在家就餐人数与食物消费之间存在显著负相关,相关系数为-0.020。[结论]影响四川农村居民食物消费支出的关键性影响因素主要有决策人的营养态度、家庭收入、在家就餐人数和决策人年龄;其中,决策人的营养态度是四川省农村居民食物消费的主要因素,且存在正相关,即决策人营养认知水平高对农村居民膳食结构优化具有重要的促进作用,这也表明营养知识宣传及消费引导的重要性。     

Short-term Covid-19 forecast for latecomers

The number of new Covid-19 cases is still high in several countries, despite vaccination efforts. A number of countries are experiencing new and severe waves of infection. Therefore, the availability of reliable forecasts for the number of cases and deaths in the coming days is of fundamental importance. We propose a simple statistical method for short-term real-time forecasting of the number of Covid-19 cases and fatalities in countries that are latecomers—i.e., countries where cases of the disease started to appear some time after others. In particular, we propose a penalized LASSO regression model with an error correction mechanism to construct a model of a latecomer country in terms of other countries that were at a similar stage of the pandemic some days before. By tracking the number of cases in those countries, we use an adaptive rolling-window scheme to forecast the number of cases and deaths in the latecomer. We apply this methodology to 45 countries and we provide detailed results for four of them: Brazil, Chile, Mexico, and Portugal. We show that the methodology performs very well when compared to alternative methods. These forecasts aim to foster better short-run management of the healthcare system and can be applied not only to countries but also to different regions within a country. Finally, the modeling framework derived in the paper can be applied to other infectious diseases.     

Forecasting economic time series using targeted predictors

This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to ‘targeted predictors’ selected using hard and soft thresholding rules. Our three main findings can be summarized as follows. First, we find improvements at all forecast horizons over the current diffusion index forecasts by estimating the factors using fewer but informative predictors. Allowing for non-linearity often leads to additional gains. Second, forecasting the volatile one month ahead inflation warrants a high degree of targeting to screen out the noisy predictors. A handful of variables, notably relating to housing starts and interest rates, are found to have systematic predictive power for inflation at all horizons. Third, the targeted predictors selected by both soft and hard thresholding changes with the forecast horizon and the sample period. Holding the set of predictors fixed as is the current practice of factor forecasting is unnecessarily restrictive.     

Sparse structures with LASSO through principal components: Forecasting GDP components in the short-run

This paper examines the use of sparse methods to forecast the real (in the chain-linked volume sense) expenditure components of the US and EU GDP in the short-run sooner than national statistics institutions officially release the data. We estimate current-quarter nowcasts, along with one- and two-quarter forecasts, by bridging quarterly data with available monthly information announced with a much smaller delay. We solve the high-dimensionality problem of monthly datasets by assuming sparse structures of leading indicators capable of adequately explaining the dynamics of the analyzed data. For variable selection and estimation of the forecasts, we use LASSO together with its recent modifications. We propose an adjustment that combines LASSO cases with principal components analysis to improve the forecasting performance. We evaluated the forecasting performance by conducting pseudo-real-time experiments for gross fixed capital formation, private consumption, imports, and exports over a sample from 2005–2019, compared with benchmark ARMA and factor models. The main results suggest that sparse methods can outperform the benchmarks and identify reasonable subsets of explanatory variables. The proposed combination of LASSO and principal components further improves the forecast accuracy.     

Understanding intraday electricity markets: Variable selection and very short-term price forecasting using LASSO

We use a unique set of prices from the German EPEX market and take a closer look at the fine structure of intraday markets forelectricity, with their continuous trading for individual load periods up to 30 min before delivery. We apply the least absolute shrinkage and selection operator (LASSO) in order to gain statistically sound insights on variable selection and provide recommendations for very short-term electricity price forecasting.     

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.     

A study of cross-industry return predictability in the Chinese stock market

We investigate cross-industry return predictability for the Shanghai and Shenzhen stock exchanges, by constructing 6- and 26- industry portfolios. The dominance of retail investors in these markets, in conjunction with the gradual diffusion of information hypothesis provide the theoretical background that allows us to employ machine learning methods to test for cross-industry predictability. We find that Oil, Telecommunications and Finance industry portfolio returns are significant predictors of other industries. Our out-of-sample forecasting exercise shows that the OLS post-LASSO estimation outperforms a variety of benchmarks and a long–short trading strategy generates an average annual excess return of 13%.     

Quantile forecasting with mixed-frequency data

We analyze the quantile combination approach (QCA) of Lima and Meng (2017) in situations with mixed-frequency data. The estimation of quantile regressions with mixed-frequency data leads to a parameter proliferation problem, which can be addressed through extensions of the MIDAS and soft (hard) thresholding methods towards quantile regression. We use the proposed approach to forecast the growth rate of the industrial production index, and our results show that including high-frequency information in the QCA achieves substantial gains in terms of forecasting accuracy.     

Variable selection and corporate bankruptcy forecasts

We investigate the relative importance of various bankruptcy predictors commonly used in the existing literature by applying a variable selection technique, the least absolute shrinkage and selection operator (LASSO), to a comprehensive bankruptcy database. Over the 1980–2009 period, LASSO admits the majority of Campbell et al. (2008) predictive variables into the bankruptcy forecast model. Interestingly, by contrast with recent studies, some financial ratios constructed from only accounting data also contain significant incremental information about future default risk, and their importance relative to that of market-based variables in bankruptcy forecasts increases with prediction horizons. Moreover, LASSO-selected variables have superior out-of-sample predictive power and outperform (1) those advocated by Campbell et al. (2008) and (2) the distance to default from Merton’s (1974) structural model.