Forecasting urea prices

ABSTRACT

Managing urea price risk is a concern of firms in the urea supply chain due to high price volatility and relatively slow transportation. This study develops urea price forecasting models as a way to reduce price risk. The forecasting models are evaluated based on multiple accuracy measures and compared to Fertilizer Week, a commercial forecast. An autoregressive model with exogenous variables (ARX) using a window size of 48 months outperforms the other models. No statistical difference exists between our best model and Fertilizer Week. Encompassing tests show that a combination model using the two models outperforms using Fertilizer Week forecasts alone. A combined model using 66.8% of $FertilzerWeek$and 33.2% of the ARX brings about the minimum forecast error.

KEYWORDS:

• Encompassing
• forecasting
• optimal forecasting conditions
• rolling window regression
• time series
• urea

JEL CLASSIFICATION:

• C53
• D80
• Q10

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Urea occupies the highest proportion of nitrogen fertilizer and nitrogen shows the highest consumption of plant nutrients in the U.S. (USDA 2013).

² The annualized price volatilities are calculated as the standard deviation of monthly returns multiplied by the square root of the number of trading months in the year.

³ For comparison, the price volatility of diammonium phosphate (DAP) in U.S. Gulf and potash in Vancouver are 19.5% and 9.84% between 2003 and 2007 and 23.3% and 23.1% between 2009 and 2014 (World Bank 2016).

⁴ Even though a variety of alternative forecasting methods such as neural networks and support vector machines (Claveria, Monte, and Torra 2016) are available, relatively simple autoregressive models are applied in this article since the trendy data science methods need a larger sample in order to be estimated precisely (Fletcher and Goss 1993; Kavzoglu 2009; Tkacz and Hu 1999).

⁵ 81 months is the longest possible window size since the time span of in-sample is 81 months.

⁶ A random walk model assumes no difference between the values at t and t-1 as $y_t-{y_t}_{-1}={\epsilon }_t,$ where ${\epsilon }_{\mathrm{t}}$ indicates a white noise error term. Hyndman and Koehler (2006) also use the weighted error terms based on the random walk assumption to get a measure of forecast accuracy such as mean absolute scaled error. The same adjustment needs to be used on all series in order to not distort the comparisons.

⁷ It is inappropriate to conduct the DM test when the competing forecasting models are nested since they are asymptotically perfectly correlated, which results in very poorly sized tests. In that case, the Clark and West (2006) test can be used. In this article, the MDM test is conducted between a constructed forecast and Fertilizer Week forecast because they are not nested.

⁸ The average proportion of nitrogen fertilizer consumption for corn, wheat, and cotton are 42.1%, 12.1%, and 3.5% from 2006 to 2010 (USDA 2013).

⁹ The U.S. imported 7.65 million tons in 2012. In detail, the overseas countries export urea to the U.S.as much as 6.06 million tons and Canada and Mexico do as much as 1.58 million tons (USDA 2014).

¹⁰ Fertilizer Week issued its forecast of the urea price from April to September 2008, November 2008, from January to May 2009, from July 2009 to June 2010, and April 2013 to the present.

¹¹ Given a unit root in price level data, the cointegration test is conducted among urea price and explanatory variables, but the null hypothesis of cointegration is rejected.

Additional information

Funding

Brorsen receives financial support from the A.J. and Susan Jacques Chair as well as the Oklahoma State University Division of Agricultural Sciences and Natural Resources and USDA National Institute of Food and Agriculture through Hatch Project number OKL02939.