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The stock market presents a formidable challenge for prediction due to its non-stationary and non-linear data dynamics. Consequently, precise prediction of stock dynamics has become a pivotal topic for researchers and investors alike. This paper addresses this challenge by proposing a method to derive precise predictions of stock closing prices through the utilization of the Time-Varying Auto-Regressive (TVAR) model alongside error analysis. Unlike traditional approaches, the TVAR model offers adaptability to the dynamic nature of stock prices by incorporating coefficients that evolve over time. This adaptability enables the model to provide precise predictions that are continuously updated with each new data point. Moreover, the integration of error analysis with the TVAR model enhances its predictive capability by offering valuable insights in the form of upper and lower bounds, thus providing users with estimations of potential closing prices. The proposed algorithm is validated through numerical simulations on the Bank Central Asia (BBCA), Bank Republik Indonesia (BBRI), and Bank Mandiri (BMRI) datasets. Results indicate that the algorithm is capable of predicting stock dynamics with errors of less than 2%. These findings underscore the potential of the TVAR model in facilitating investment decision-making by empowering investors to anticipate stock movements and trends.