DETECTION OF THE SEASONAL VARIATIONS OF POTATO SALES IN WHOLESALE MARKETS OF BAGHDAD PROVINCE DURING THE PERIOD ( 2010-2015 ) AND FORECASTING BY USING SEASONAL TIME SERIES MODELS ( SARIMA )

45 DETECTION OF THE SEASONAL VARIATIONS OF POTATO SALES IN WHOLESALE MARKETS OF BAGHDAD PROVINCE DURING THE PERIOD (2010-2015) AND FORECASTING BY USING SEASONAL TIME SERIES MODELS(SARIMA) K. S Rand A.. D. K. Alhiyali Researcher Prof. Dept. of Agricultural economics College of Agriculture University of Baghdad adk_1966@yahoo.com ABSTRACT This research was aimed to detect the seasonal phenomenon of the monthly sales of potato crop in Baghdad for the period (January 2010 December 2015), using the krusskle Wallis method. The research also aimed to determine the shape of the time series of the monthly sales of the potato crop whether to follow additive or multiplicative model. The problem of the research is presence of the seasonal phenomenon in the monthly sales of the potato crop, which will be reflected in one way or another on the short-term planning process. According to the results obtained, the monthly sales of the potato crop were predicted at 60 observations for the period January 2016 December 2020, where the results were consistent with those in the original time series. We conclude from the results obtained that the monthly sale of the potato crop contains seasonal variations and confirms the nature of the pattern that the potato crop has been affected by the season to a large extent. This research was concluded that there was an increase in sales of potato crop during specific months of the year. This is confirmed by the results of the research, which will be reflected in one way or another on the low prices in the months of high sales according to the law of supply and demand. The research included recommendations such as preventing import at peak time (peak season of production) and the need to work on the development of laws and legislation to protect local agricultural products. The research also recommended the imposition of taxes and customs duties on imported agricultural products and not to allow entry into Iraq during the peak season of production.


INTRODUCTION
Among the objectives of private and public institutions is expansion and growth to achieve satisfactory rates of welfare, stability and development for the purpose of achieving an acceptable and appropriate level of economic welfare of society, These two organizations combine to achieve this goal and because any economic activity is based on satisfying the desires of consumers in quantity and quality through the production of goods and services in quantities and specifications and providing them at the appropriate prices.However, the amount which consumers need and the prices at which they are sold are considered unknown or difficult to expect, but these must be known or at least estimated so that producers or relevant organizations can work and produce, and sales are likely to increase or decrease depending on different factors and circumstances, The ability to manage the production and sales process and then to predict both will have important implications for their future in general and will form the basis upon which plans, programs and decisions will be built (10).One of the objectives of establishing wholesale markets is to provide a marketing environment and a climate conducive to the commercial activity of fruit and vegetable crops according to international standards (18).It also contributes to improving the activity of agricultural crops on the basis of scientific studies, and build an integrated system of services for the bidding processes in the wholesale and purchase of vegetables and fruit, and identifying surplus agricultural crops and monitoring crop changes throughout the season by building an information base.As well as maintaining the safety and health of the consumer through direct supervision of the quality of agricultural crops, and to contribute to the service of the farms through the marketing of crops in one location and integrated services, and the provision of integrated civil service facilities, space that are suitable for farmers, traders , and consumers and providing maximum comfort for them (12).Potato is considered one of important agricultural crops in many countries of the world, including Iraq, which gives a profitable income to the farmer, Potato production is heavily influenced by natural conditions and factors, as well as seasonality in prices, resulting in sharp fluctuations in the level of supply of potato, or in price levels throughout the year (20).There is a great economic importance of the potato crop as statistics show a significant expansion of the cultivated areas of this crop in Iraq for several reasons, including high population and high standard of living as well as the spread of health food and awareness.
It is very important to note the economic importance and knowledge of the contribution of these crops to the net farm income as well as to the quantity of imports and exports.The total imports of potato in Iraq in 2012 reached about 11.7 million kg at a value of 6.7 million dollars , while in 2014 it increased to about 26.4 million kgs and a value of 5.6 million dollars, as for the income of the farmers from the potato crop during the year 2012 is about (2.316 million dinars) (15).The economic analysis of the monthly sales of the potato crop is particularly important because of the importance of this commodity to both citizens and farmers.Studies of forecasting are especially important when it comes to sales planning because these crops have a great importance to the segments of society, which induced many researchers to study them using seasonal time series models as these models have high accuracy and flexibility in analysis (5).The problem of research is the seasonal phenomenon of sales of potato crop, which will be reflected in one way or another on the short-term planning process, In order to avoid bias in forecasting process, which is very important in future planning processes, these seasonal variations should be studied to be neutralized and excluded from the time series, this will make sales forecasting possible, Especially that seasonal variations take a more regular form of other variations such as cyclical variations and thus facilitate the process of forecasting and in turn reflected on the process of short-term planning.In addition, the presence of factors that neutralized the effect of the seasonal phenomenon and reduce the impact on the sales of potato crop.The research assumes the fluctuation of sales of potato crop may be due to the presence of the seasonality phenomenon and characterized by low volatility from one season to another.The research also assumes that the form of the time series follows the multiplicative model.In addition the research assumes the benefit of using the seasonal time series models in the monthly sales forecast for the potato crop in Baghdad province.The research aims at analyzing of the monthly sales of potato crop in the city of Baghdad during the period (2010-2015) and studies the model of these variations if follow the multiplicative or additive model, also detect these seasonal variations to be excluded from the time series, finally, forecasting the monthly sales of the potato crop for a short period in the future using seasonal time series models (SARIMA).The research was based on secondary sources of monthly sales of potato crop in Baghdad during the period (January 2010 -December 2015), where it was obtained from the Ministry of Agriculture and the Ministry of Planning and related departments, which adopted an average price of vegetable crops.The subject of seasonal time series is an important subject.A large group of researchers have dealt with this issue, especially when it comes to forecasting and among these researchers (1, 2, 3, 4, 7, 13, 14, 17, and 18).

MATERIALS AND METHODS
This research was focused mainly on the data and information obtained from secondary data.The method used in the analysis for the purpose of detection of the seasonal variations will be using the statistical test called the Krusskal-Wallis (KW) and its formula is ( 9  The number of values and views corresponding to the season i (more often  i m number of years).
In order to determine the shape of the time series, whether to follow the multiplicative or additive model, the annual standard deviation method will be used to match the time series in the research.For the purpose of forecasting the time series, the Seasonal Autoregressive Integrated Moving averages (SARIMA) method will be used.

RESULTS AND DISCUSSION
The method of analysis consists of several steps that are inherently descriptive and analytical as there are sequential steps in detecting the seasonal variations for the monthly sales of the potato crop to be clarified as it follows: First: Detection of the seasonal variations of the monthly sales of potato crop using the test (krusskl-wallis) The first step: In this step, a table will be drawn up which includes the monthly data for the potato crop sales obtained from the Ministry of Agriculture.These data are the period from January 2010 to December 2015.The second step of setting a table in which the values of the string from the smallest value to the highest value of the ascending order of the monthly data of the potato crop, Finally, the seasonal variation is calculated by the aforementioned law, and all these details will be reviewed in practice until the final result is reached and interpreted.
. 0  There is a seasonal variation in the monthly sales of the potato crop because the value of KW is greater than the value of 2  .

Second: Determination of the shape of the time series of the monthly sales of the Potato crop
After confirming the existence of the seasonal variations in the sales of the monthly potato crop, we determine the shape of these variations (within the whole time series) whether it is multiplicative or additive.There are several ways to detect the shape of the time series, but the method used is the annual standard deviation.In this method, we determine the annual standard deviation for each year.Third: forecasting the monthly sales of potato crop using seasonal time series models (SARIMA) After several steps, an initial plot of the time series is used to identify its initial properties, then testing the stationary of the time series, In order to obtain stationary in the variance of the time series, the natural logarithm (LN) of the data is processed once and the square root is taken again.In order to test the stationary of the time series, the values of the (ACF) and (PACF) coefficients will be extracted, as shown in the figure below, which shows the non-stationary of the time series as it lies outside the confidence intervals and therefore the values of the coefficients of (ACF) extracted at the 71 gap was around 132.06, while the value of 2  at the same gap is equal to 86.635,The decision is as follows: Therefore, we reject the null hypothesis that all autocorrelation coefficients|(ACF) are equal and equal to zero: We accept the alternative hypothesis, which means that the time series is non-stationary.

Figure 1. The autocorrelation function of the original data of the sales of the Potato crop Removing the non-stationary of the time series:
In order to remove the non-stationary of the series, the first difference was taken in the modified data.Thus we obtained a stable time series as shown in the following figure (2).To confirm this, the results extracted for the values of the coefficients of autocorrelation after taking the first difference may differ significantly from what it was before taking the first difference and this is illustrated in the following table.The value of LBQ after taking the first difference at gap 70 is about 76.98 and if compared to the value of 2  at 0.05 and 70 (85.527) the decision is as follows:   the form of the attributes of (PACF), will be known as the appropriate model in which all the values of the coefficients are significant and thus is the appropriate model and therefore the best model followed the monthly sales of potato crop is a model SARIMA (0,1,2)(1,1,0) 12 .

R
Ranks of the phenomenon values or the values of the studied variable corresponding to the season i. i m results above, we conclude, the model is good, appropriate and efficient, thus time series is stable and lies within the confidence limits‫ز‬

Figure 2 .
Figure 2. The autocorrelation function of potato sales after taking the first difference Diagnosis: It is intended to identify the model through the rank of (AR, MA), depending on

Source: Ministry of Agriculture, Department of Agricultural Statistics. Second step:
Ranking the values of the string (R t ) from the smallest value to the larges t value according to the following table:

Table4. Results of SARIMA model (0,1,2)(1,1,0) 12
1,1,0) 12 based on the statistical program (MINITAB) obtained the results listed in the table below It was logical that all the values of the coefficients were significant and so observed that all parameters were statistically significant‫ز‬