Comprehensive interval‐valued time series model with application to the S&P 500 index and PM2.5 level data analysis

In this study, we develop comprehensive symbolic interval‐valued time‐series models, including interval‐valued moving average, auto‐interval‐regressive moving average, and heteroscedastic volatility models. These models can be flexibly combined to adapt more effectively to various situations. To make inferences regarding these models, likelihood functions were derived, and maximum likelihood estimators were obtained. To evaluate the performance of our methods empirically, Monte Carlo simulations and real data analyses were conducted using the S&P 500 index and PM2.5 levels of 15 stations in southern Taiwan. In the former case, it was found that the proposed model outperforms all other existing methods, whereas in the latter case, the residuals deduced from the proposed models provide more intuitively appealing results compared to the conventional vector autoregressive models. Overall, our findings strongly confirm the adequacy of the proposed model.