The research aimed to describe the quarterly data of Rice Production in Nueva Vizcaya from 1987 to 2018 and the trend of rice production using the time series models It sought to determine the best Mathematical Model that best fit the trend of Rice Production in the province and to forecast the quarterly value of Rice Production of Nueva Vizcaya for 2019. Gathered from the Philippine Statistics Authority (PSA), the quarterly volume of total rice production will be predicted using four mathematical models which were the Traditional Time Series Analysis, Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), and Seasonally Autoregressive Integrated Moving Average (SARIMA). The study used the Time Series Analysis Model under Number Cruncher Statistical Software (NCSS 12) and Time Series Analysis in Microsoft Excel Analysis for Traditional Time Series. The researcher used the Microsoft Excel to compute for the r², mean absolute error, root mean square error, mean absolute percentage error and generate the different graphs in the study. To determine the best Mathematical Model that will fit the trend of Rice Production in Nueva Vizcaya by comparing the r², mean absolute error, root mean square error, mean absolute percentage error of the four models. The selected model will be used to predict the quarterly Rice Production of Nueva Vizcaya. Among the four models, the ARIMA (3,1,0) was chosen as the best fit model since it has the highest correlation coefficient 0.830, moreover, it has the lowest value of MAE that is 4,996.40 and the lowest value for RMSE with 6,385.98. In addition, the forecast accuracy on the mean absolute percentage error (MAPE) using the ARIMA (3,1,0) is 11.47% and for the year 2018, only ARIMA (3,1,0) follows the trend of the actual rice production. Using ARIMA (3,1,0) model the following quarterly Rice Production of Nueva Vizcaya for 2019 were obtained: (January March) 67,079.48 metric tons, (April-June) 58,022.09 metric tons, (July-September) 64,218.80 metric tons and (October-December) 75,986.69 metric tons

Keywords: Rice Production, Mathematical Model, Mean Absolute Error, Mean Absolute Percentage Error, Root Mean Square Error, Traditional Time Series Analysis

Thesis (Master of Science Teaching - Mathematics)

Includes appendices and bibliographical references.