hubao666/Time-Series-Analysis-Central-African-Republic-Exports

## Topic The study analyzes the Central African Republic's export data (1960–2017) using time series analysis to identify trends and forecast future values, supporting economic planning. ## Methodology - Data Preprocessing: Cleaned data and confirmed no missing values. - Stationarity: ADF tests showed the data was non-stationary. First-order differencing achieved stationarity. - Model Selection: - ACF/PACF plots suggested MA(1) and AR(2) on differenced data. - Diagnostics (AIC, BIC, and Ljung-Box test) favored AR(2). - Machine Learning Method: Split data into training/testing sets; ARMA(1,2) was chosen based on the lowest MSE. ## Tools - Python for analysis and visualization. - Models: AR(2), MA(1), ARMA(1,2). - Metrics: AIC, BIC, MSE (for ARMA(1, 2)). ## Results - AR(2) and ARMA(1,2) were selected as the best models. $$ y_t = -0.505033 y_{t-1} -0.289666 y_{t-2}+ w_t $$ $$ y_t = 0.337728 y_{t-1} -0.883232 w_{t-1}+ 0.441870w_{t-2} + w_t $$ where $$ y_t = x_t - x_{t-1} $$ is the first-order difference on original data. - Forecasts for 2018–2021 show export values stabilizing around 12.6 million USD.