1、The economic determinants of RV 波动率的经济决定因素：大宗商品供给的季节性、到期时间以及存货水平
Anderson and Danthine (1983) hypothesize that the key determinant of volatility is the time at which the production uncertainty is resolved. The uncertainty resolution is seasonal, for instance at the end of a crop when the supply is publicly known (see also Anderson, 1985).
Anderson and Danthine (1983)假设，波动率的关键决定因素是生产不确定性得到解决的时间。这种不确定性的解决是seasonal，例如庄稼收成中，其供给是publicly known.
This seasonality should be particularly visible for agricultural products whose production are concentrated in a single annual harvest in the northern hemisphere. It should also be present for the natural gas contract since the demand rises every winter in the northern hemisphere.
这种季节性对于北半球的农产品来说尤其明显，因为它们的生产集中在一年一次的收获中。 它也应该在天然气合同中被考虑，因为北半球的天然气需求每年冬季都会上升（seasonal）。
Despite the fact that these turning points should primarily affect the cash market, Anderson and Danthine (1983) additionally show that the link between the cash and futures markets ensures the volatility diffusion from the former to the latter.
现金与期货市场(seasonal)波动率关系是扩散的。
The research also shows that intangible commodities like electricity or those whose exchange value is higher than their consumption value, such as gold or silver, behave more like traditional financial assets.
该研究也说明了：intangible commodities（电）以及金银（交易价格>消费价格）更像传统的金融资产。
Anderson (1985), Khoury and Yourougou (1993), and Galloway and Kolb (1996) find a seasonal component in volatility, combined with a time to maturity effect.
波动率存在seasonal component，并且与a time to maturity effect结合。
Samuelson (1965, 1976) conjectures that the volatility of commodity contracts is higher when the remaining time to maturity is lower.
S发现：当remaining time to maturity较短时，大宗商品合约的波动率更高。
Despite many empirical tests, the results are contradictory. On the one hand, Rutledge (1976) and Grammatikos and Saunders (1986) do not find evidence of any increase in volatility. On the other hand, Milonas (1986), and Galloway and Kolb (1996) find support for all commodities. Consistent with the Samuelson hypothesis, Bessembinder et al. (1996) develop a model in which the spot price has negative covariance with the slope of the term structure. This implies a temporary price change, which is more likely to occur in real assets than in financial assets.
B：spot price现货价格与期限结构斜率具有负向协方差。表明暂时的价格变化更可能在真实资产中。（即波动率高）
Indeed, recent empirical tests on the NIKKEI (Chen et al., 2000) and on the S&P 500 futures (Moosa & Bollen, 2001) strongly reject the Samuelson conjecture, whereas Bessembinder et al. (1996) find empirical support mainly for agricultural commodity futures.
The theory of storage states that the relation between the volatility of storable commodities and the level of inventories is convex and negative (see, e.g., Brennan, 1958; Kaldor, 1939; Working, 1933). More recent versions of the theory of storage in equilibrium (e.g., Deaton & Laroque, 1992) also predict this link, which is confirmed empirically (see Carpantier and Samkharadze, 2012; Fama & French, 1988; Geman & Nguyen, 2005; Geman & Ohana, 2009; Ng & Pirrong, 1994). Inventories are difficult to measure at the aggregate level with a daily frequency. At the monthly frequency however, Gorton et al. (2012) find empirical evidence of a negative relation between actual inventories and the spot price volatility.
月度频率上，实际存货与现货价格波动率存在负向关系。
More importantly, they confirm the tight link between the term structure and inventories. Thus, because the term structure is readily measurable at any frequency, this variable allows to test inventory‐related hypotheses at the daily frequency. Kogan et al. (2009) extend the theory of storage prediction to a nonmonotonic and convex relation between volatility and inventories. They first document empirically that the volatility increases when the inventory levels approach their physical limits (empty or filled storage).
当存货水平到达物理极限（空仓或满仓），波动率上升。
To explain this “v‐shape” pattern, they derive a model that links the volatility to investment constraints through the capacity of firms to absorb demand shocks. They introduce the slope of the term structure conditioned on its sign in GARCH models, and find that the corresponding coefficients are statistically significant at the 1% level (see also Haugom et al., 2014). To conclude, both low and high inventories lead to high volatility.
高或低的存货都会带来较高的波动率
Consequently, I state my hypotheses as follows. The volatility of commodities futures:
- is seasonal for commodities that show seasonality in the supply or the demand, 大宗商品期货具有季节性
- increases when the time to maturity decreases, and time to maturity下降时，大宗商品期货波动率上升
- is positively related to the intensity of both low and high inventory states. 与高低存货密度呈正相关
2、Endogenous determinants of RV 波动率的内生决定因素，介绍了RV预测的难点，以及目前对相应难点解决的文献
The main idea of Corsi (2009) is that the RV at time t depends on past values of the RV at time t − 1, t − 2, …, t − p, where p can be very high (20 or more), suggesting a long‐memory process.
RV由过去20期以上的滞后性决定，表现出长记忆性。
However, this process is mean reverting toward a long‐term component. Therefore, the transitory component of the daily variance relates to the RV at t − 1 and the introduction of two additional components (weekly and monthly RVs) smooths its dynamics.
然而，这样的过程时向长记忆部分的平均回溯。因此短记忆部分和两个其他频率的RV用于平滑其变化。
Altogether, these variables give a parsimonious representation of the typical volatility exponential decay (see, e.g., Andersen et al., 2003). In the empirical part of the paper, Corsi (2009) estimates the model with the S&P 500 index, the USD/CHF exchange rate, and a 30‐year US T‐Bond futures. Based on the BIC criterion, the 1‐day ahead in‐sample performance of this model is higher than that of an AR (22), which clearly shows that the HAR (3) model is parsimonious.
HAR(3)表现优于AR（22）
Out‐of‐sample, the model steadily outperforms the short‐memory models (AR (1) and AR (3)) at the 1‐day, 1‐week, and 1‐month horizons. In addition, it is on par with an (long‐memory) ARFIMA model. Lastly, the superior performance of the ARFIMA and HAR (3) increases with the forecasting horizon.
相对优越性随着预测horizon的增加而增加
Several versions of the model have been proposed using the RV, its log, and its square. Andersen et al. (2007) show that the log of RV is the closest to normality and that jumps are negligible in terms of RV forecasting. Microstructure effects could introduce measurement errors, which lead to biased coefficients. Nevertheless, the residuals of log RV are still heteroskedastic, and the parameters of the HAR are not constant over time (see Buccheri & Corsi, 2019). Using a simple linear process could be insufficient for at least three reasons: (a) jumps, (b) measurement errors, and (c) time‐varying parameters.
log RV的残差项仍然是异方差的。简单的线性回归是不足够的：（1）跳跃；（2）测度偏差；（3）时变参数
Andersen et al. (2011a) consider that RV has (i) a continuous component for the day that is well described by an HAR‐GARCH model, (ii) a jump component for the day, and (iii) a GARCH component for the night, leading to the HAR‐CJN model. However, the out‐of‐sample performance of this model is just slightly higher than that of the HAR.
Given the measurement error that plagues the estimation of RV, Bollerslev et al. (2016) introduce the “realized quarticity” (RV) in the HAR model. The authors write an extension (HARQ model) where the coefficients are a linear function of the quarticity. The idea is to put less weight on past high values of RV when they are subject to potential mismeasurement. By the same token, this variable is supposed to capture microstructure effects and jumps. However, HARQ also shows signs of misspecification.
As an alternative, Corsi and Reno (2012), and Patton and Sheppard (2015) examine whether the RV reacts symmetrically to positive and negative shocks that affect prices, that is, the so‐called “leverage effect.” Casas et al. (2018) nest both models. Cipollini et al. (2017) show that HARQ is observationally equivalent to another model where a quadratic term in RV accounts for a faster mean reversion when volatility is high. They argue that the realized quarticity and a time‐varying mean seem to play a more important role than measurement errors. In these models, the time‐varying coefficients are linear functions of the realized quarticity (parametric specification). Chen et al. (2018) generalize this approach by considering a log HAR model with time‐varying coefficients of unspecified functional forms (HAR‐TV). These coefficients are approximated with a local linear function of time.
Casas et al. (2018) extend Chen et al. (2018) in two directions. First, they consider a potential asymmetric reaction to negative shocks. Second, the coefficients are no longer a local linear function of time but a linear function of the realized quarticity (semiparametric approach). Unfortunately, the forecasting performance of the RV is not examined specifically since the main purpose of the paper is to forecast the stock market.
Bekierman and Manner (2018) take a different stance. They propose a state‐space representation of the HAR model that can be augmented by functions of the realized quarticity. They attribute the higher performance of the state‐space HAR models to the fact that the realized quarticity is a noisy proxy for the true measurement error, which is likely to be greater in periods of high volatility. Furthermore, their state‐space models are able to capture other sources of time variation in the parameters that are not explained by the measurement error. Buccheri and Corsi (2019) generalize the state‐space representation approach in several directions. Their state‐space model allows for a time‐varying error, and considers that the updated parameters depend on the level of uncertainty that is based on the score function. This model (SHARK) appears to perform very well, both in‐ and out‐of‐sample, but there is no straightforward extension for multivariate estimations.
Overall, significant progress has been made with the development of sophisticated specifications. Their main purpose is to clean the data from microstructure effects, and to account for an asymmetric reaction to negative exogenous shocks. Yet, the focus of empirical applications has been on stock indices, currencies, individual stocks, bonds, and less frequently on futures contracts. The following methodology details the implementation of the afore- mentioned benchmark models to test the contribution of EVs.