This paper presents an evaluation of the accuracy of machine learning (ML) techniques in forecasting the realized volatility of West Texas Intermediate (WTI) crude oil prices. We compare several ML algorithms, including regularization, regression trees, random forests, and neural networks, to several heterogeneous autoregressive (HAR) models. The results show that the ML and regularization methods are efficient, even when there are only three predictors: daily, weekly, and monthly realized volatility (RV) lags. In addition, when the ML and regularization methods are applied, the results become more pronounced over longer forecasting horizons, as well as for weekly and monthly horizons. These ML methods are effective in approximating long-term realized volatility. Furthermore, we found that additional explanatory variables for real-time currency exchange contain valuable information to forecast the RV of crude oil prices.

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth SLS1) for estimating mixed-frequency models. This SLS1 approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in SLS1 solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (SLS2). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of SLS2, compared to that of SLS1 . Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed SLS2 estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R2, which in turn leads to better forecasts.

A Stein-type control function maximum likelihood (CFML) estimator is suggested for the probit model in the presence of endogeneity. This novel estimator combines the probit maximum likelihood and CFML estimators. The asymptotic distribution and risk function for the new estimator is derived. It is demonstrated that, subject to certain conditions of the shrinkage parameter, the asymptotic risk of the new estimator is strictly smaller than the risk of the CFML. Monte Carlo simulations illustrate the method's superiority in finite samples. The method is also applied to analyze the impact of managerial incentives on the use of foreign-exchange derivatives.

In stochastic frontier analysis, the conventional estimation of unit inefficiency is based on the mean/mode of the inefficiency, conditioned on the composite error. It is known that the conditional mean of inefficiency shrinks towards the mean rather than towards the unit inefficiency. In this paper, we analytically prove that the conditional mode cannot accurately estimate unit inefficiency, either. We propose regularized estimators of unit inefficiency that restrict the unit inefficiency estimators to satisfy some a priori assumptions, and derive the closed form regularized conditional mode estimators for the three most commonly used inefficiency densities. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimators outperform the conventional (unregularized) estimators when the inefficiency is greater than its mean/mode. Based on real data from the electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators provide substantially different results for highly inefficient companies.

Agencies that regulate electricity providers often apply nonparametric data envelopment analysis (DEA) to assess the relative efficiency of each firm. The reliability and validity of DEA are contingent upon selecting relevant input variables. In the era of big (wide) data, the assumptions of traditional variable selection techniques are often violated due to challenges related to high-dimensional data and their standard empirical properties. Currently, regulators have access to a large number of potential input variables. Therefore, our aim is to introduce new machine learning methods for regulators of the energy market. We also propose a new two-step analytical approach where, in the first step, the machine learning-based adaptive least absolute shrinkage and selection operator (ALASSO) is used to select variables and, in the second step, selected variables are used in a DEA model. In contrast to previous research, we find, by using a more realistic data-generating process common for production functions (i.e., Cobb–Douglas and Translog), that the performance of different machine learning techniques differs substantially in different empirically relevant situations. Simulations also reveal that the ALASSO is superior to other machine learning and regression-based methods when the collinearity is low or moderate. However, in situations of multicollinearity, the LASSO approach exhibits the best performance. We also use real data from the Swedish electricity distribution market to illustrate the empirical relevance of selecting the most appropriate variable selection method.

This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators’ mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators’ performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners.

We suggest a wavelet filtering technique as a remedy to the problem of measurement errors when testing for cointegration using Johansen’s (1988) likelihood ratio test. Measurement errors, which more or less are always present in empirical economic data, essentially indicates that the variable of interest (the true signal) is contaminated with noise, which may induce biased and inconsistent estimates and erroneous inference. Our Monte Carlo experiments demonstrate that measurement errors distort the statistical size of Johansen’s cointegration test in finite samples; the test is significantly oversized. A contribution and major finding of this article is that the proposed wavelet-based technique significantly improves the statistical size of the traditional Johansen test in small and medium sized samples. Since Johansen’s test is a standard cointegration test, and we demonstrate that the constantly present measurement errors in empirical data over sizes the test, this simple alteration can be used in most situations with more reliable finite sample inference. We empirically examine the long-run relation between CO2 emissions and the real GDP in the G7 countries. The traditional Johansen tests provide evidence of an equilibrium relation for Canada and weak evidence for the US. However, the suggested size-unbiased wavelet-filtering approach consistently indicates no evidence of cointegration for all six countries.

In this article, we propose Liu-type shrinkage estimators for the zero-inflated Poisson regression (ZIPR) model in the presence of multicollinearity. Our new approach is a remedy to the problem of inflated variances for the ML estimation technique—which is a standard approach to estimate these types of count data models. When the data are in the form of non-negative integers with a surplus of zeros it induces overdispersion in the dependent variable. Considerable multicollinearity is frequently observed, but usually disregarded, for these types of data sets. Based on a Monte Carlo study we illustrate that our proposed estimators exhibit better MSE and MAE than the usual ML estimator and some other Liu estimators in the presence of multicollinearity. To demonstrate the advantages and the empirical relevance of our improved estimators, maternal death data are analyzed and the results illustrate similar benefits as is demonstrated in our simulation study.

This paper introduces some new methods to test for panel cointegration in the error correction framework. These methods are proposed since the previous approaches do not perform well when the number of cross-sectional units (N) is approximately equal to the number of time periods (T). By means of Monte Carlo simulations we investigate the size and power properties when N and T increase simultaneously, i.e., N/T -> c where 0 < c <= 1. Based on the simulated results we may recommend a test for panel cointegration in high dimensional setting with cross-sectional dependency.

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques - at least when multicollinearity exist among the regressors.