  In a first-of-its-kind study, this paper proposes the formulation of
constructing prediction intervals (PIs) in a time series as a bi-objective
optimization problem and solves it with the help of Nondominated Sorting
Genetic Algorithm (NSGA-II). We also proposed modeling the chaos present in the
time series as a preprocessor in order to model the deterministic uncertainty
present in the time series. Even though the proposed models are general in
purpose, they are used here for quantifying the uncertainty in macroeconomic
time series forecasting. Ideal PIs should be as narrow as possible while
capturing most of the data points. Based on these two objectives, we formulated
a bi-objective optimization problem to generate PIs in 2-stages, wherein
reconstructing the phase space using Chaos theory (stage-1) is followed by
generating optimal point prediction using NSGA-II and these point predictions
are in turn used to obtain PIs (stage-2). We also proposed a 3-stage hybrid,
wherein the 3rd stage invokes NSGA-II too in order to solve the problem of
constructing PIs from the point prediction obtained in 2nd stage. The proposed
models when applied to the macroeconomic time series, yielded better results in
terms of both prediction interval coverage probability (PICP) and prediction
interval average width (PIAW) compared to the state-of-the-art Lower Upper
Bound Estimation Method (LUBE) with Gradient Descent (GD). The 3-stage model
yielded better PICP compared to the 2-stage model but showed similar
performance in PIAW with added computation cost of running NSGA-II second time.
