Zaman Serisi Analiz Yöntemlerini Kullanarak 2016-2025 Dönemi Türkiye Avokado Üretiminin Belirlenmesi

The main aim of this study was to model avocado production in Turkey for 2016-2025 period using 1988-2015 years FAOSTAT data. Avocado production time series data for the 1988-2015 period was found non-stationary. Stationarity was obtained after taking the first difference of the time series. Three Exponential Smoothing (Holt, Brown and Damped) methods were compared to model avocado production. Brown exponential smoothing model was the most appropriate forecasting model for avocado production. We forecasted that the avocado production in Turkey will show increase from 2004 tons to 3156 tons for the 2016-2025 period. The results of this study could help policy makers to develop macro-level policies for food safety and more powerful strategies for better planning avocado production in Turkey for the future.


Introduction
Avocado (Persea americana) is a very nutritious fruit. Therefore, it shows increasing popularity worldwide. Avocado is very rich in fatty acids, dietary fiber, protein, vitamins, antioxidants and minerals. The fruit contains essential nutrients and phytochemicals with potential health benefits. However, the peel and seed are also very good source of phenolics showing high antioxidant capacity important for health (Zhang et al. 2013;Calderon et al. 2016). Therefore, it is essential to establish good policies for food security and sustainability for healthy diet of the next generations. Turkey avocado production was 300 tons in 2000 year, and reached 1824 tons in 2014 (FAOSTAT 2017). Increasing avocado production would provide better nutritious diet for the people in Turkey and enhance the income of native farmers. Avocado is a valuable fruit with many health benefits and by increasing local production it will be more accessible for the consumers. It is important to establish policies for increasing avocado production for future sustainability, export incomes and food safety, as well as structuring good price for the country. Therefore, projection studies are very useful tool for predicting future prospects of avocado productions by using past trends, as well as to determine appropriate macro-level policies.
There is still lack of information on forecasting production amounts of important horticultural crops (Masuda and Goldsmith 2009;Semerci and Ozer 2011;Suresh et al., 2012;Celik et al. 2013;Hamjah 2014;Borkar 2016;Celik et al. 2017;Karadas et al. 2017a, b). To our knowledge, there is no study on forecasting avocado production in Turkey. Therefore, the objective of this study was to model avocado production in Turkey using 1988-2015 period data trend in order to predict avocado production for the next 2016-2025 period.

Materials and Methods
FAOSTAT avocado annual production for the 1988-2015 period was used to forecast production for the next 2016-2025 years. Holt, Brown and Damped Exponential Smoothing methods were compared.
Exponential smoothing methods include updating the estimates by taking account the last change and spikes within the time series. These spikes can occur by random changes, unexplained effects, or unpredictable developments ignored (Kadilar 2009). These methods are combined methods giving different weights to the time series data at the previous period (Orhunbilge 1999;Sharpe et al. 2010). Exponential smoothing methods show efficient results for short terms (Yaffe and McGee 2000). Time series showing trend use Holt exponential smoothing (Makridakis et al. 1998;Hanke and Wichern 2008). The following two coefficients (α and β) are smoothing coefficients for estimating the trend in the Holt model. Formulas of the Holt method: Where: : New smoothed value, : Actual (observed) value at period t, : Smoothing coefficient for trend estimation (0< ), : Trend predicted value, p: Number of forecasting periods, : Forecasting value after p period.
Another exponential smoothing method is Brown's linear exponential smoothing method with one parameter. The Brown model is reported to be more convenient for increasing or decreasing trends in time series data. Start equation of the model is expressed as follow (Armutlu 2008): Where: yt 1 is the value obtained for single exponential smoothing and yt 2 is the binary exponential flatted value.
Here, at and bt statistics are estimated as follows The model for the estimation after m periods is expressed as (Orhunbilge 1999). The damped trend exponential smoothing models are taken into account to perform an excellent forecasting. The forecast error variance is calculated based on ARIMA model (Sbrana 2012). The damped method is expressed in the following equations (Gardner and McKenzie 1985). Grander and McKenzie (1985) clarify that if 0< <1, then the trend is damped and the forecasts approach an asymptote given by the horizontal straight line . If = 1, the mentioned method is the same to the standard Holt method.
To select the best model, model fit statistics were calculated: Time series analysis was performed with IBM SPSS program (version 23).

Results and Discussion
In the current projection study, 1988-2015 period annual avocado production data was analyzed using exponential smoothing methods. A trend in avocado production time series was noticed ( Figure 1). Time series graphs of autocorrelation function (ACF) and partial autocorrelation function (PACF) were generated to reveal time trend (Figure 2).  Many terms in ACF graph exceeded confidence limits, which is an indicator of time series trend ( Figure 2). The first degree difference was taken to remove the trend from the times series.

Figure 3. First difference series ACF and PACF graphs
As seen from ACF and PACF graphs, the first difference time series was stationary ( Figure 3). Performances of Holt, Brown and Damped trend exponential smoothing methods were compared by using model fit statistics such as Stationary R 2 , R 2 , RMSE, MaxAE and BIC. Results of model fit statistics for the methods are shown in Table 1. Brown exponential smoothing method was the most appropriate one (Table  1).  Residuals lags relationship degrees in the ACF and PACF graphs were found within the confidence limits. The fitted and observed time series on annual avocado production were in agreement ( Figure 5). Avocado production forecasting results for the 2016-2025 period are provided in Table 3. Avocado production for 2016 year was predicted as 2004 tons and reached to 3156 tons in 2025 year. Avocado production in Turkey is expected to reach to 3156 tons in 2025 year (Table 3). The information is important for policy makers and food industry in developing new agricultural policies.
To our knowledge, there is no study on predicting avocado production in Turkey for the next years to provide security and sustainabiliy of this crop. The studies available on production forecasting of important horticultural crops such as avocado is very limited (Hamjah 2014). In the current study, Brown exponential smoothing model in general predicted increasing avocado production trend in Turkey. Mango, banana and guava production in Bangladesh were forecasted ten years forward using Box-Jenkins ARIMA model. Mango showed initially a downward, after a time stable production and at the end increasing production tendency. Banana was forecasted to have constant production tendency, whereas guava showed upward production tendency in Bangladesh (Hamjah 2014). Increasing maize production trend in Nigeria was predicted using ARIMA model (Badmus and Ariyo 2011). It was reported that the sugarcane production will increase in 2013, then will show downward production tendency in 2014, and afterwards will show upward production tendency in India using Box-Jenkins ARIMA model (Kumar and Anand 2014). Upward soybean production tendency in the world was reported for the 2020-2030 period using Damped exponential smoothing method (Masuda and Goldsmith 2009). Pistachios, walnuts, hazelnuts, almond and chestnuts productions in Turkey were projected for the 2012-2020 period and increasing production tendency was shown using different ARIMA models (Celik 2013). Upward production tendency was projected for groundnut using time series analyses (Celik et al. 2017), Holt exponential smoothing method projected sunflower and sesame upward production tendency in Turkey (Karadas et al. 2017a in press). Cotton lint production was predicted to increase using Holt exponential smoothing method (Karadas et al. 2017b in press).

Conclusion
The time series data of avocado production for the 1988-2015 period were non-stationary, and the original time series data was converted into stationary time series after the first differences of the original data were taken. Three Exponential Smoothing (Holt, Brown and Damped) models were compared and Brown exponential smoothing model was detected to be the most proper forecasting model for avocado production in Turkey. According to the Brown method, avocado production in Turkey will show increase from 2004 tons to 3156 tons for the 2016-2025 period. The projection results obtained from this study can help policy makers to establish better price structure and production strategies for avocado production in Turkey for the next ten years.