Hildreth-Lu Model for Autocorrelation Correction in Time-Series Regression of Shrimp Growth Perfomance

Abstract

Autocorrelation frequently occurs in time-series regression models, leading to inefficient estimators and biased inference when ignored. This study analyzed the relationship between water quality parameters and shrimp growth performance by applying the Hildreth–Lu iterative method to correct autocorrelation. The dataset consisted of Specific Growth Rate (SGR) as the dependent variable and three water-quality parameters—temperature, pH, and dissolved oxygen (DO)—as explanatory variables, with pond type included as a dummy factor. The initial Ordinary Least Squares (OLS) estimation revealed that temperature and pH significantly affected SGR, while the Durbin–Watson (DW) value of 0.878 indicated positive autocorrelation in the residuals. After applying the Hildreth–Lu correction, the estimated autocorrelation coefficient (ρ) was 0.64, and the DW statistic improved to 2.03, confirming that serial correlation had been successfully removed. The corrected model provided more efficient and unbiased parameter estimates without requiring data transformation or loss of observations. The results confirm that temperature is the most influential factor in shrimp growth, while pH, DO, and pond type showed no significant effects. The study highlights the importance of autocorrelation diagnostics in regression analysis and demonstrates that the Hildreth–Lu method is an effective and reliable approach for improving model efficiency in small-sample time-series data