Least absolute deviations estimation for uncertain autoregressive moving average model with application to CO2 emissions

Based on the previous observations, uncertain time series analysis provides plausible description for experimental data, and predicts future values by characterized observations and disturbance as uncertain variables under the framework of uncertainty theory. Sometimes, the current observation is simultaneously impacted by the past observations and past disturbance terms. Uncertain autoregressive moving average (UARMA) model emerged as the times require. Due to the inevitable presence of unknown parameters in the model, it is crucial to estimate these unknown parameters robustly based on observed data. Motivated by this, a way to calculate least absolute deviation estimations for unknown parameter in UARMA model is studied by transformation this model into an uncertain autoregressive model. Forecast value and confidence interval for the future value are derived from the fitted model. Finally, two real data analyses with imprecise and precise observations of carbon dioxide emissions are given to show the effectiveness of our proposed method, and uncertain hypothesis is documented to test our model. Besides, it also explains why stochastic time series model is not applicable for this case.