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Author(s): Bolarinwa B. T., Yahaya H. U., Adehi M. U..

Volume/Issue: Volume 8, Issue 4 (2025)

Page No: 44-53

Journal: African Journal of Mathematics and Statistics Studies (AJMSS)

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Abstract:

This article investigates the robustness of ARIMA-GAS model to structural break and jumps, through simulation. It examines abrupt regime change by introducing a deterministic structural break at t=500 in both the ARIMA and GAS dynamics. The sample size is n=1000 with an 80/20 estimation–evaluation split; one-step-ahead forecasts are generated in a rolling fashion. For the jump process, this scenario injects discontinuous jumps into an otherwise Gaussian environment to test robustness to rare but large shocks. The data generating process is ARIMA (1,1,1) with score dynamics(A_1,B_1)=(0.35,0.55). Innovations are with jump intensity λ=0.05. We generate n=1000 observations with differencing order d=1 and evaluate one-step-ahead forecasts on the final 20% of the sample using rolling updates. The study utilizes ARIMA, GAS, LSTM and GARCH as benchmarks. For the pre-break regime, ARIMA outperformed the rest models on the basis of both the root mean square error (rmse) and mean absolute error (mae), closely followed by ARIMA-GAS. Pure GAS performs better than GARCH and LSTM which outperformed GARCH. Contrary to the pre-break case in which the classical ARIMA takes the lead, ARIMA-GAS takes the lead, achieves the lowest average loss (least rmse) in the post-break era beating ARIMA to the last position. LSTM is competitive, establishing its relevance in the competition, occupying the second position. GAS model maintains its third position, beating GARCH. Results of multi-horizon forecasting (h=1, 5, 10) reveal on the basis of rmse, ARIMA-GAS as best, followed by LSTM, although LSTM narrows the gap at longer horizons. An examination of the effect on model accuracy, of proportion of series length used for training reflects that all models experience improved accuracy with increased training data length; LSTM gains relatively more, yet ARIMA–GAS retains the lowest average RMSE. With jumps, ARIMA-GAS performed better than benchmarks having the least mse of 1.48562 and mae of 1.10234. The GAS model is next, confirming the capacity of GAS model to capture jumps. Classical ARIMA is next to GAS. Their combination has outperformed them individually and other benchmarks. This further confirms the appropriateness of combining GAS with ARIMA. ARIMA-GAS model outperforms benchmarks in multi-horizon forecasting comparison on the basis of rmse and mae— a feat repeated when two other jump intensity values (λ=0.01,0.1) are used to asses sensitivity, although relative performances of the benchmarks are altered. Based on the performance of ARIMA-GAS model over the benchmarks in the presence of structural breaks and jumps, the model offers a promising approach to modeling intradaily financial data with such features.

Keywords:

ARIMA-GAS, Structural break, Jumps, Poisson process, Robustness

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