Forecasting interval-valued crude oil prices using asymmetric interval models

Abstract

Practitioners and policy makers rely on accurate crude oil forecasting to avoid price risks and grasp investment opportunities, but the core of existing predictive models for such prices is based on point-valued inputs and outputs, which may suffer from informational loss of volatility. This paper addresses this issue by proposing a modified threshold autoregressive interval-valued models with interval-valued factors (MTARIX), as extended by Sun et al. [Threshold autoregressive models for interval-valued time series. J. Econom., 2018, 206, 414–446], to analyze and forecast interval-valued crude oil prices. In contrast to point-valued data methods, MTARIX models simultaneously capture nonlinear features in price trend and volatility, and this informational gain can produce more accurate forecasts. Several interval-valued factors and point-valued threshold variables are analyzed, including supply and demand, speculation, stock market, monetary market, technical factor, and search query data. Empirical results suggest that MTARIX models with appropriate threshold variables outperform other competing forecast models (ACIX, CR-SETARX, ARX, and VARX). The findings indicate that oil price range information is more valuable than oil price level information in forecasting crude oil prices.

Keywords:

• Crude oil price
• Interval time series
• Nonlinearity
• Threshold autoregressive interval model

JEL Classification codes:

• C2
• C13
• Q4

Acknowledgments

The authors thank participants at the Fourth International Symposium on Interval Data Modelling: Theory and Applications at Beijing for their insightful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 See the definition of negative intervals at equation (1(1) $\mathrm{\Delta }{Y}_t=Z_t^{\prime }{\theta }_{1}I(q_t⩽\gamma )+Z_t^{\prime }{\theta }_{2}I(q_t>\gamma )+u_t,t=1,\dots ,T,$(1) ).

2 As a special case of random sets, the $D_K$ metric for the observed interval $\mathrm{\Delta }{Y}_t$ and the fitted interval $\mathrm{\Delta }{\hat{Y}}_t$ is $\begin{array}{rl}{\text{D}}_k^2(\mathrm{\Delta }{Y}_t,\mathrm{\Delta }{\hat{Y}}_t)& ={\int }_{(u,\upsilon )\in s^0}\left[s_{\mathrm{\Delta }{Y}_t}\right(u)-s_{\mathrm{\Delta }{\hat{Y}}_t}(u\left)\right]\\ & \times \left[s_{\mathrm{\Delta }{Y}_t}\right(\upsilon )-s_{\mathrm{\Delta }{\hat{Y}}_t}(\upsilon \left)\right]\mathrm{d}K(u,\upsilon )\\ & =〈s_{Y_t-\mathrm{\Delta }{\hat{Y}}_t},s_{Y_t-\mathrm{\Delta }{\hat{Y}}_t}{〉}_K=\Vert Y_t-\mathrm{\Delta }{\hat{Y}}_t{\Vert }_K^2=\Vert u_t{\Vert }_K^2,\end{array}$ where the unit space $s^0=\{u\in R^1,|u|=1\}=\{1,-1\}$, $K(u,\upsilon )$ is a symmetric positive definite weighing function on $s^0$ to ensure that $D_K(Y_t,Z_t^{\prime }(\gamma \left)\varrho \right)$ is a metric for extended intervals, and $〈\cdot ,\cdot 〉$ indicates the inner product in $s^0$ with respect to kernel $K(u,\upsilon )$.

Additional information

Funding

This work was partially supported by China NSF Grant [grant numbers 72073126, 72103185, 72091212, 71973116], NSF Grant for Basic Scientific Center Project [grant number 71988101] entitled as Econometric Modeling and Economic Policy Studies, and Young Elite Scientists Sponsorship Program by CAST (YESS) [grant number 2020QNRC001].