Expectation of Rice Pod Production in Iraq by Using Time Series

The research aims to shed light on the reality of the production of Rice pods  in Iraq during the period of time (1943-2019) and its development with time, then predict the production of Rice pods based on three Models of prediction Models, which are the time regression Model on production, in addition to studying the effect of harvested area on production quantities. Then forecasting the production of the Rice pods  according to the Model of the regression of the harvested area on the production, the Autoregression Model, and the integrative moving averages (Box Jenkins Models), and in the end the comparison between the expected values ​​of production through the three Models to know the best Model to represent the time series of production of the Rice pods , through the use of the statistical program (SPSS (, Based on annual secondary data represented by the quantities of Rice pods, and the size of the harvested areas of this material in Iraq for the period from 1945 until 2019 obtained from (Central Statistical Organization, Iraq, 2020)


Research Hypotheses :
The research deals with the following hypotheses 1-There is a statistically significant relationship between production and time that can be used to estimate future forecast of production quantities.
2-There is a statistically significant relationship between harvested area and time that can be used to predict the future harvested area.
3-There is a statistically significant relationship between production and harvested area that can be used to estimate future forecast of production quantities.

4-The proposed Model for Autoregression and complementary moving averages (Box Jenkins Models) is
considered the best Model for predicting the production of Rice pods in Iraq.

5-The Autoregression
Model and the integrative moving averages are the best Model for predicting the future quantities of production compared to the regression Models.
We will study the regression of the time series for the production of Rice pods in Iraq during the time period (1945 -2019) as a dependent variable and time as an independent variable. The following table includes the production of Rice pods in Iraq between (1945-2019): Production  We draw the time series for the production of the Rice pods during the studied period of time as: The graph shows that there is a clear fluctuation in the development of Rice pods production over time, especially in the period from 2000 until 2003, but production has increased again in the last three years.
In the study of the evolution of the production of Rice pods material over time, that is, the study of the relationship between the production of Rice pods As a dependent variable and time as an independent variable, by using program SPSS, we obtain the following results: a value of the time correlation coefficient was 0.324, which is a positive and weak correlation. And Upon testing the significance of this coefficient, we found that sig = 0.005, which is less than the significance level of 0.0 5, indicating that the coefficient of correlation between production and time is statistically significant at a significance level of 0.0 5.

Model
As for the value of the coefficient of determination 2 , it reached 0.105, meaning that approximately 10% of the changes in the production of Rice pods go back to time, while the remainder of the percentage is due to other factors that were not taken into account.
We also note from the coefficients table that the significant values of the constants of the regression equation, the constant, and the slope are less than 0.05, that is, they are statistically significant at the level of significance 0.05, which proves the validity of the first hypothesis. Through the table of analysis of variance, it becomes clear to us that there is a linear relationship between the production of Rice pods and time, through which we can predict the future production of Rice pods , and thus the regression equation between time and production of Rice pods is as follows:

3-Evolution of areas harvested with Rice pods in Iraq with time
We will study the development of harvested area production in relation to time in order to predict areas during the next five years to be used in the future prediction of Rice pods when we apply the simple regression equation between the production of Rice pods and the harvested areas.  The Figure   Harvested areas The study of the evolution of the harvested area over time, that is, the study of the relationship between the harvested area As a dependent variable and time as an independent variable, we obtain the following results:

Model Summary
Model the correlation coefficient value with time was 0.368, It is an inverse and weak correlation, And when the significance of this coefficient was tested, we found that the value of the sig=0.001, It is less than the significance level 0.05, which indicates the correlation coefficient, Between area harvested and time is statistically significant at a significance level of 0.05. As for the value of the coefficient of determination, it reached 0.135, meaning that approximately 13% of the changes in the harvested area date back to the time, while the remainder of the percentage is due to other factors that were not taken into account. We also note from the coefficients table that the significant values of the constants in the regression equation the constant and the slope were less than 0.05, meaning that they are statistically significant at the level of significance 0.05, which proves the validity of the second hypothesis.
We notice through the analysis of variance

Studying the relationship between the production of Rice pods and the harvested areas in Iraq
The following  The coefficient of correlation with time was 0.555, which is a positive and median relationship. When testing the significance of this coefficient, we found that the value of sig = 0.000 is less than the significance level of 0.05, which indicates that the correlation coefficient between the production of the Rice pods and the harvested area is statistically significant at a significance level of 0.05. As for the value of the coefficient of determination, it amounted to 0.308, meaning that more than 30% of the changes in Rice pods production are due to the harvested areas, while the rest of the percentage is due to other factors that were not taken into account.
We also note from the coefficients table that the significant values of the constants of the constant regression equation and slope were less than 0.05, meaning that they are statistically significant at a significance level of 0.05, which proves the validity of the third hypothesis.
Through the analysis table of variance, it becomes clear to us that there is a linear relationship between the Rice production and the harvested area, and this relationship is significant at the level of statistical significance 0.05, and accordingly, through which we can predict the future production of the Rice, and thus the regression equation between the Rice production and the harvested area is as follows: = 117434,471 + 0,263 Through this Model, we can predict the harvested area in Iraq during the next five years, so we get the following  We notice from the table that the production of Rice is decreasing with the decrease in the harvested area, and this matter is due to the decrease in the harvested area from year to year. In order to compare the two regression Models, which is better, to represent the time series of production of Rice, draw the following Figure: We note that the harvest area regression Model is better than the time regression Model on production as its data are closer to the real values of production.

Use Autoregression Integrated Moving Average Models (ARIMA) to Predict the production of Rice[13],[15],[14],[11]
By showing, the Figure (4) of the time series, the Box shape to detect the existence of extreme values in the quantities of production of the Rice for the period studied, and we get the following:

Stability analysis[11],[9][6]
It can be seen from Figure (1) of the time series for the production of the Rice that the series is somewhat stable, and to ensure the stability of the chain or not, we find the autocorrelation coefficients and the partial selfcorrelation coefficients at 16-time slots:

Figure(5) :shows the autocorrelation coefficients for the production of Rice at 16 -time slots
It is clear from the autoregressive form that the time series is stable as the autocorrelation coefficients slope towards zero exponentially with the change of the signal, but there is one significant value, which is the value of the first autocorrelation coefficient.
As for the form of partial self-association, it is as follows:

Figure (6): the partial autocorrelation coefficients for production of Rice at 16 time slots
We notice from the form of partial autocorrelation that the autocorrelation coefficients slope exponentially towards zero and that there is one significant value, which is the value of the first partial autocorrelation coefficient.
It is clear to us through the two forms of self-correlation and partial self-correlation that the time series is stable and there is no need to take differences, and it is clear that there is one significant value in the form of selfcorrelation, which is the value of the first self-correlation coefficient, and there is also one significant value in the form of partial self-correlation, which is the value of the coefficient The first partial self-correlation, which suggests to us that the proposed Model for producing Rice pods in Iraq is the following Model: (1 ,1) and it's the same Model : (1,0,1)

Study the proposed Model
(1 ,1) Depending on the two forms of autocorrelation and partial autocorrelation, the Model was determined (1 ,1) As a proposed Model for a time series. By studying this Model, we obtain the following results:

Statistics
Ljung-Box The results show that the parameters of the proposed Model are statistically substantial only for the constant and Autoregression ones, as for the moving averages coefficient AM It is not significant, as its significant value reached 0.379, which is greater than 0.05, so we say that the proposed Model is not the best Model, and we study the Model after excluding the moving averages coefficient, which is the Model ARMA(1 ,0)

Study the Model ( , ).
By studying this model, we obtain the following results: We note that the coefficients of the Model are statistically significant, which are the onstant and the Autoregression coefficient, the value of BIC = 22,843 which is less than the value of BIC = 22.90, for the production of the Rice of the proposed Model, meaning that (1, 1) is the best Model for representing and predicting the time series.

Model-Statistics
We will now study the two adjacent Models, the higher Model and the lower Model, and since there is no inferior Model, therefore we will only study the higher Model, which is (2 ,1) As the supreme Model (1 ,0)

Study the Model ( , ):
We study the indicators and parameters of the top Model, so we get the following tables: We note that all the parameters of the Model are not statistically significant, and the value of The results showed that we could not predict the proposed Model (the proposed Model is the Model that we proposed depending on the two forms of the self-correlation coefficients and the partial self-correlation), but the ideal Model through which we can predict the Model to production is ARIMA (1, 0), That is, the hypothesis was not fulfilled.

Comparison between regression Models and the Box Jenkins Model for production of Rice
In this research, we used three Models to predict the production of Rice in Iraq, namely: 1-Time regression Model on production.
2-A Model of regression of harvested area on production.

3-Autoregression Models and integrative moving averages (Box Jenkins Models).
In order to know the best regression Model for the production of Rice, we compare the results of the three Models to see how their results match the actual data of production, by drawing a graph of the expected values according to the three Models.
The following Figure shows the expected values of Rice production: Which proves the validity of the fourth hypothesis saying The Autoregression Model and integrative moving averages are the best Model for predicting future quantities of production compared to regression Models.

Results and Discussion
The study and analysis of the time series for the production of Rice pods during the time period (1945-2019) showed the following: 1-There is a statistically significant relationship between Rice production and time, which is a direct relationship, but it is weak, meaning that there are other reasons that are more influential on the production of Rice than the time factor.
2-The existence of a statistically significant correlation between the harvested area and time, but this relationship is inverse and weak, meaning that the harvested area decreases with time, in addition to the weakness of this relationship indicates the presence of other factors that affect the harvested area more than the time factor.
3-The presence of a significant correlation between the production of material Rice and the harvested area, and this relationship is positive and average.

4-
The factor of harvested area affects more than the effect of the time factor on the production of Rice, and this is evident by comparing the value of the two determination factors. That is, the harvested area explains 30% of the changes in Rice production.

5-
The study showed that the Autoregression Model and the proposed integrative moving averages depending on the two forms of self-correlation and partial self-correlation was not the ideal Model because the parameters of the Model were not significant as required, so we cannot predict the proposed Model.
6-The study showed that the ideal Model for studying the time series for the production of Rice and its future prediction is the Model ARMA(0,1) Rifle production was predicted with this Model until 2025.
7-A comparison was made between the two regression Models, which is the best to study the series. The Model of rampage of the harvested area on the production of Rice was the best Model compared to the Model of time regression of the production of reeds, and this is evident by comparing the real values of production of reeds and both of the estimated values of production of reeds through the Models of time regression and ramp of harvested area.
8-A comparison was fully made between the three Models that were predicted for the time series of production, so the Autoregression Model and the integrative moving averages were the best Model compared to the two Models of regression, harvested area and time, where the data of the Autoregression Model and the integrative moving averages were the closest to representing the series data through The period studied is almost applicable to the graph line of the real values of production, compared to the graph of the time regression and the graph of the harvested area regression.

8-Conclusions
1-The bodies working in the field of producing Rice pods must identify the factors that greatly affect the production of this material, as the apparent fluctuation of the production of Rice pods in Iraq is due to multiple factors that cannot be limited to the factors of time and harvested area, which makes it necessary to determine the factors affecting significantly And finding ways to treat it is of utmost importance.