Crop Yield Forecasted Model Based on Time Series Techniques

Li Hong-ying , Hou Yan-lin, Zhou Yong-juan and Zhao Hui-ming

1 Graduate University of Chinese Academy of Science, Beijing, 100049, China

2 Ningxia Meteorological Science Institute, Yinchuan 750002, China

Introduction

Food security is a basis for national stability and continued growth, especially for China, demand for food increased constantly because of too many people with few lands and rapid economic development.Arable land has been decreasing with urbanization and environment degradation, how to improve the output of the limited arable land has become a problem needed to solve immediately. So, the research about potential yield has become a focus for the researchers,exploring grain production-potential at uttermost is a reasonable way to improve food security (Li et al.,2005; Yu et al., 2011).

The beginning of research for potential yield is generally believed from the smallest factor rule of German chemist J. Liebig, based on the single factor,effect of environmental factors on crop yield is analyzed qualitative. With further research, from photosynthetic production potential, photosynthetic thermal productivity to climatic production potential, theory becomes perfection step by step, and method continues to be improved, and there are varieties of computing models. In 1964, Zhu Kezhen researched crop production potential from the point of climate and crop physiology, and Huang Bingwei put the concept of the photosynthetic production potential for the first time in China, referred that the highest yield of a cultivar could be got when grew in environment which it was adapted,and modified the photosynthetic potential formula of Loomis and Williams, then got a more simple calculation for potential production (Yang, et al.,2008); and the model was modified and improved by more researchers later (Chen and Long, 1984).

Based on the improvement and revision of theories and methods, subsequent studies focus on improving the application and strategy, such as analysis and research on the grain potential in northern Shaanxi,northeastern regions, Sichuan Province and Fujian Province, and so on (Wang and Gao, 2006; Liu and Wu, 1998; He and Zhou, 2004; Chen and Cai, 2006).With the development of climate change research,the impact of climate change on production potential has been concerned consistently, as Wu and Zhou(2011)studied about impact of plateau climate change on grain production potential in Qinghai; Zhang(2011)referred that global warming had provided both opportunities and challenges for further grain increase in Northeast China, which had increased the productive potential.

The above results shows that traditional potential yield was defined as the yield of a cultivar when grew in environment which it was adapted, without limitations on nutrients and water, and with pests,diseases, weeds, lodging, and other stresses effectively controlled (Evans and Fischer, 1999; Evans, 1993).In this paper, a new concept of crop yield under average climate conditions was defined, which referred to the crop yield under multi-year average climate conditions and was affected by advancement of science and technology.

Time series analysis has long been used in grain yield analysis (Yu et al., 2005; Boken, 2000;Liu, 2010; Li and Xue, 2009). The strong point was that it needed a relatively small amount of data and all the data could be obtained easily. Based on the new concept of crop yield, a forecasting model was established using time series analysis together with historical yield data. The most important technique and was parameter of the model were introduced in details.It aims to make the potential yield more practical, and to establish a simpler and more precise methods of forecasting it.

Materials and Methods

Source of materials

The model was tested in Liaoning Province, data used in the paper was grain per unit yield, which was obtained by adding a variety of crop per unit yields from 1949 to 2005, and per unit yield for every corp was collected from Agricultural Statistical Yearbook of Liaoning Province.

Introduction of forecasted model

Main methods employed in model were as the followings:

i. Moving average was used first. The mean yield in different natural years was computed by the following equation.

Where, Yiwas the average yield for year i; Yiwas the reported yield for year i; i0was the initial observation year; and n was the number of terms specified in the moving averaging technique.

ii. The following regression equation was regarded as the moving average (MA)model, in which i was taken as a dependent variable;was as the independent variable; and

iii. The difference between Yiand Y(i-1)was the fluctuation of the yield due to climate difference between successive years adjusted by the yield contributed by scientific and technological advancement for n years. Climate was periodical and fluctuating, and if science and technology make no more progress, the impact on the yield caused by climate change between two years (i and i+n )could be positive, negative or zero. However, the impact of the climate difference between two years is approximately zero, which couldn't gradually drive up the yield. So the difference between two multi-year yields which were n years away from each other was close to the contribution made by scientific and technological advancement to the potential grain productivity for n years. The impact of climate on yield can then be isolated by the multiyear yield moving average model. Therefore, the moving average model was regarded as the potential yield forecasting model.

iv. The crop yield forecasted error was computed by the following equation:

v. Rectification of forecasted error. Studies showed that the distribution of prediction error was highly regular. It exhibited a wavy pattern and reflected a variety of factors including social factors (policy),economic factors (input), and nature factors (climate fluctuation). We therefore used a micro trend rectification method to improve prediction precision.This method used the following equations:

Where, mYfiwas the forecasted yield for year i after rectification; e(i-1)was the forecasted error for year(i-1); and meiwas the forecasted error for year i after rectification.

Results

Forecasting results for Liaoning Province

Five separate series were extracted according to the equations (1)-(6)by using yield data series from 1949-2005 of Liaoning Province. Five series were modeled that was 1949-2000, 1949-2001, 1949-2002,1949-2003, and 1949-2004 series, respectively to forecast yields in 2001, 2002, 2003, 2004 and 2005.The results are shown in Table 1.

From 2001 to 2005, the average prediction error was 3.38% and the maximum absolute error was 4.57%with the static n-choosing method applied. After rectification according to equations (5)and (6), the average absolute prediction error and maximum absolute error decreased to 1.24% and 2.25% respectively.

Table 1 Forecasted results by using models

Dealing with yield turn point

Yield turn point refers to a year in which grain yield jumps or falls to a different level. In our analysis of the change of grain yield with time, the concept of yield channel was brought forward (Li et al.,2008). The in-flexion model was used to determine the exact turn point year: when the prediction error exceeded normally acceptable levels (7%-10%)in 3-5 consecutive years, the forecast model should be revised. The earlier yield data was used from 1949 to 1966 (with n=13), and forecast the potential yield of the following one by one. In theory, the error should increase and exceed the allowed range when the turn point occurs.

The results are shown in Table 2.

Table 2 Forecasted errors using yield data for Liaoning Province

Table 2 showed that before 1973, the prediction errors were all lower than 5%, the maximum absolute error was 1.54%, the average error was 1.17%, while errors of three or five consecutive years after 1973 were higher than 10%. It was concluded that 1973 was a yield turn point year. Then a simple model was applied from the year 1974 to 1976 and used to forecast yields in 1977 and the following years.Table 2 showed that the prediction errors had all fallen within the allowed range (＜5%).

Conclusions

In this paper, crop potential yield was redefined in a more practical way, which was different with traditional ones, and a relevant forecasted model was established. Basic method in the model was time series technology, in previous researches, other time series techniques such as linear regression, quadratic regression, simple exponential smoothing, double exponential smoothing, simple moving average, had been proved unsuitable to analyze crop yield (Li et al.,2008; Zhang and Zhang, 2007), so an improved moving average technique was used in the model which could be the basis of potential yield forecasting country-wide and internationally.

The crop yield forecasted model was tested in Liaoning Province, and which was validated practicable. Micro tendency rectification and static n-choosing were main methods in the model, after rectification, the average absolute prediction error to forecast yield with dynamic n using was only 1.24%. Grain yield would occasionally jump in quantity or quality in response to advance science and technology, the inflexion model was employed to the determination and qualitative analysis of these yield turn points, but the precision of yield prediction in years following such turn points was improved by establishing a readjusted simple model applied to data after each yield turning point.

In this paper, the forecasted model was only tested by one sample, in the next steps, before extended applications on a larger scale, more testings are needed to improve logic, preciseness, accuracy and application of the method and the associated model.

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