Autoregressive T-Cell-Receptors Algorithm-Based Interventions for Multivariate Cointegration Estimation and Forecast

Abstract

Forecasting multivariate time series is difficult because such data often show non-stationarity, autocorrelation, and structural shifts. An added challenge is cointegration, where variables share hidden long-term synchronization trends even if they move differently in the short run. To address these issues, we propose the T-Cell Receptor (TCR) algorithm, a novel forecasting framework inspired by the immune system’s selective and adaptive behaviour. Mimicking TCR antigen recognition functions, the model employs Orthogonal Least Squares (OLS) for dynamic regressor selection and Inter-Cell Cohesion Factors (ICCF) to quantifies each regressor’s contribution to error reduction. This enables adaptive identification of cointegrated lag structures, gaining an advantage over traditional models that rely on fixed heuristics, in turn, performing adaptive forecasting across volatile regimes. TCR was evaluated on separate samples of daily adjusted closing prices from the S&P 500 (SNP) and Infosys (INFY), representing datasets with differing volatility but evident cointegration. Benchmarking against ARIMA, SARIMA, Single Exponential Smoothing (SES), and the Dendritic Neuron Model (DNM), shows that TCR captures the fluctuations more effectively, particularly in high-volatility series, and adapts better than smoothing-based models. ACF analysis confirms stationarity, while error boxplots highlight predictive stability. Quantitatively, TCR achieved the lowest RMSE and MAE on volatile SNP data, with statistically significant improvements (p < 0.05) over SARIMA, SES, and DNM. The study validates TCR’s novelty as an interpretable, biologically inspired, and cointegration-aware forecasting model. Future extensions may address high-dimensional, real-time, and hybrid learning scenarios.