Analysis of an Adaptive ARMA Model for Time Series Prediction

This paper introduces and evaluates an adaptive Autoregressive Moving Average (ARMA) model designed for enhanced time series prediction in dynamic and non-stationary financial markets. Traditional ARMA models, constrained by static parameters, often struggle to capture the evolving underlying dynamics and sudden shifts characteristic of highly volatile assets. Our proposed adaptive ARMA(1,1) model addresses these limitations by incorporating a recursive parameter estimation mechanism, resembling a Least Mean Squares (LMS) algorithm, which allows its coefficients to continuously adjust to new observations. Through empirical backtesting on historical stock price data for Tesla (TSLA) and Google (GOOGL), the adaptive model demonstrates significantly improved predictive accuracy. Specifically, it achieved a Mean Absolute Error (MAE) of 7.78 for TSLA and 1.61 for GOOGL, outperforming a traditional ARIMA model which yielded a Mean Squared Error (MSE) of 58.78 for GOOGL compared to the adaptive model's 4.47 MSE. These results underscore the robustness and practical utility of the adaptive ARMA framework for forecasting in volatile financial environments, offering a promising approach for real-time applications.