The Forming with Seasonal Time Series Analysis of the Ayran Production Model in Türkiye

Abstract

This study was conducted to model the monthly series of ayran production amount in Türkiye. ARIMA (p, d, q) (P, D, Q)_s model was used in modeling the monthly production series for the period January 2010 April 2024. In selecting the appropriate model, whether the residuals calculated from ARIMA (p, d, q) (P, D, Q)_s models were independent or not was taken into consideration. For this reason, Ljung-Box Q(r) statistics and p (probability) values were determined for the suitability of the model. The model of the monthly production series was created and the model was considered appropriate since the p value was greater than 5 % (p= 0.145). When the stationarity of the series was examined, it was seen that the series was not stationary at level and became stationary by taking its first difference and first seasonal difference. As a result of the analysis, it was revealed that the ARIMA (0, 1, 2) (0, 1, 0)₁₂ model is suitable for prediction. In other words, a second-order integrated seasonal moving average model was obtained. The coefficients of the model were calculated as 0.277 and 0.255. The equation of the model is . Using the proposed model, monthly ayran production forecast for the period May 2024-December 2025 was calculated. As a result of the forecast, the production amount for the 2024 May-2025 December period is expected to be between 77529-99349 tons. As a result, when the monthly ayran production examined was evaluated, there was generally an increase in production between March and August, and a decreasing trend in production continued between September and February. The forecast results for 2025 also support this situation.