**1. Introduction**

Heightened macroeconomic uncertainty, as observed over the last decade and half due to the global financial crisis (GFC), the European sovereign debt crisis, and, of course, the ongoing COVID-19 pandemic, has tended to make the path of the future aggregate demand of commodities, and, as a result, also aggregate production, less predictable. Given this, risk averse commodity producers prefer to hold physical inventory, which causes a rise in the convenience yield, which, in turn, results in increased volatility of commodity prices, as outlined in the 'Theory of Storage' [1,2]. With crude oil being undoubtedly the most actively traded commodity, quite a few recent studies have analyzed the role of uncertainty in forecasting the volatility of the oil market (see, for example, [3–7]). For earlier studies, the reader is referred to the references cited in these papers.

As far as the existing literature is concerned, Bonaccolto et al. [3], analyzed the relevance of newspaper-based measures of economic policy and equity market uncertainty of the United States (US) in predicting the conditional quantiles of crude oil returns and volatility, using a nonparametric *k*-th order causality-in-quantiles model. A dynamic analysis showed that these US-based uncertainty indexes are primarily relevant during periods of market distress, when the role of oil risk is the predominant interest, with heterogeneous effects over different quantile levels.

Along similar lines, Bouri et al. [4] analyzed the predictive power of a daily newspaperbased index of US uncertainty associated with infectious diseases (EMVID) for oil-market volatility. These authors documented that incorporating EMVID into a forecasting setting significantly improved the forecast accuracy of oil volatility at short-, medium-, and long-run horizons, based on a heterogenous autoregressive model of (realized) volatility. Li et al. [5], using a mixed data sampling generalized autoregressive conditional heteroscedastic (MIDAS-GARCH) model, highlighted the role of monetary policy uncertainty in addition to overall economic policy uncertainty of the US in forecasting oil market volatility.

**Citation:** Gupta, R.; Pierdzioch, C. Forecasting the Volatility of Crude Oil: The Role of Uncertainty and Spillovers. *Energies* **2021**, *14*, 4173. https://doi.org/10.3390/en14144173

Academic Editor: Sang Hoon Kang

Received: 21 May 2021 Accepted: 8 July 2021 Published: 10 July 2021

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However, Dutta et al. [7], relying on a quantiles-based approach, showed that, unlike the overall uncertainty of the US related to policy decisions, equity market volatility of the US in general, and the same due to commodity market movements and crises, carried higher forecasting power for oil market volatility. Interestingly, while Li et al. [5] did not find a metric of global uncertainty to be important in forecasting oil market volatility, Liang et al. [6] did highlight its relevance along with the importance of the overall equity market volatility indices of the US, as the existing studies above discussed , using a standard predictive regression framework, model combination, and shrinkage approaches.

As can be observed from the concise review presented in the preceding paragraph, a general tendency of the above studies is to primarily incorporate the role of the uncertainty of the US in predicting movements of the oil market volatility, barring to some extent the work of Liang et al. [6], who considered a role of a measure of global uncertainty. While this is understandable to some extent given the dominance of the US as a major player in the global oil market (and also because the GFC originated in the US), Bahloul and Gupta [8] and Dinçer et al. [9], indicated that uncertainties of other economies within the G7 (comprising of Canada, France, Germany, Italy, Japan, the United Kingdom and the US) and China, also tend to drive oil market volatility due to the importance of their position as exporters and importers in the oil market.

In light of this, and the fact that oil is a global market, we forecast the quarterly realized variance (*RV*) of oil (West Texas Intermediate, WTI, and Brent crude) price volatility and consider not only the role of uncertainties of all the G7 countries and China but also their respective spillover of uncertainty to the rest of the world, over the period from 1996Q1 to 2020Q4. Accounting for the total amount of uncertainty spillovers of these major economies onto other countries renders it possible to better model worldwide uncertainty and its influence on global oil demand in a parsimonious manner, i.e., without incorporating the information from uncertainties of multiple other (135 to be exact, based on our data source, which we shall discuss later in detail) countries in the world.

In this regard, we were motivated by the work of Liang et al. [6], who suggested the need to look at a global measure of uncertainty (based on 22 countries, unlike 143 in our case) over and above the same of the US in predicting oil-price volatility. Following Andersen and Bollerslev [10], we captured *RV* as the sum of squared returns over a quarter, which yielded an observable, unconditional, measure of volatility, which is otherwise a latent process. Conventionally, the time-varying volatility was modeled and the fit assessed using various GARCH models, under which the conditional variance is a deterministic function of the model parameters and past data. Alternatively, some recent papers considered stochastic volatility (SV) models, where the volatility is a latent variable that follows a stochastic process. Irrespective of whether one uses GARCH or SV models, the underlying estimate of volatility is not model-free (or unconditional) as in the case of *RV*.

One must realize that identifying factors that, in our case, happen to be the uncertainties of the G7 and their spillovers, that help to accurately forecast oil market volatility also has economic implications that are of key importance for both policymakers and investors. This is because, as shown by van Eyden et al. [11], movements in the second-moment of crude oil can predict slowdowns in worldwide economic growth.

Moreover, the recent financialization that has characterized developments in the oil market has led to the increased participation of hedge funds, pension funds, and insurance companies in the market, as per Bampinas and Panagiotidis [12], Degiannakis and Filis [13], and Bonato [14], which resulted in oil being viewed as an alternative investment in the portfolio decisions of financial institutions (especially post the GFC). Precise forecasts of oil-price volatility are of vital importance to oil traders, since volatility is a key input to investment decisions and portfolio choices [15].

To the best of our knowledge, this is the first paper to evaluate the out-of-sample forecasting power of uncertainties of the G7 and China and its spillovers for oil returns volatility. In order to account for the fact that market agents care about the level and nature of volatility, the latter making it important to distinguish between upside ("good") and

downside ("bad") volatilities [16], we also forecast good *RV* (the sum of daily squared positive returns only over a quarter) and bad *RV* (the sum of daily squared negative returns only over a quarter), in addition to the overall *RV*.

Given that our data sample spans a 25 year period (1996–2020) of 100 quarterly observations, and we have 16 predictors, besides one lag of *RV* that captures the well-known persistence of *RV* associated with the oil market [17,18], we use, as our econometric approach, a machine-learning technique known as least absolute shrinkage and selection operator (Lasso), proposed by Tibshirani [19], which, in turn, is a regression-analysis method that performs both variable selection and regularization (i.e., the process of adding information to prevent overfitting) in order to enhance the prediction accuracy and interpretability of the resulting statistical model.

In this regard, it should be noted that the better performance of the Lasso model over forecast-combination methods in forecasting oil-market volatility has been demonstrated by Liang et al. [6] and, hence, motivates us to rely on this framework as well. Our paper, thus, adds to the already existing large literature on the forecastability of oil-returns volatility by considering the role of the uncertainties of major economies in the world and the associated spillover, where the literature can be grouped into the following broad categories, using a wide variety of models and macroeconomic, financial, behavioral, and climate pattern-related predictors (see, for example, Lux et al. [20]), Bonato et al. [21], Demirer et al. [22,23], Gkillas et al. [24], Bouri et al. [25]; Salisu et al. [26], and the references cited within these papers).

We organize the remainder of this paper as follows: In Section 2, we describe our data. In Section 3, we briefly discuss the forecasting models, along with the Lasso approach used to estimate these models. In Section 4, we present the results from our forecasting experiment. In Section 5, we conclude.
