HYBRID AUTOREGRESSIVE INTEGRATED MOVING AVERAGE-GENERALIZED AUTOREGRESSIVE SCORE MODELLING OF JUMPS IN INTRADAILY FINANCIAL DATA

Abstract

frequency intraday financial data, using 159,000 1-minute observations from FirstRate Data (Sept 2022–Sept 2023). Jump detection was performed via the Barndorff–Nielsen and Shephard test, identifying significant jumps on three dates in 2023. Stationarity of log returns was confirmed using ADF and KPSS tests.The ARIMA(1,0,1) structure was selected for its optimal AIC/BIC values and paired with a GAS(1,1) layer to capture time-varying volatility. Model parameters were statistically significant (p < 0.01). Optimization used maximum likelihood estimation under a Gaussian density and the BFGS algorithm.The return distribution showed leptokurtosis and mild negative skewness, typical of equity data. Benchmark models included GAS-Normal, GARCH (1,1), ARIMA (1,0,1), and LSTM. ARIMA-GAS outperformed all, achieving the lowest RMSE and MAE in out-of-sample tests and best AIC/BIC in-sample. It consistently excelled across MSFT Open and Close prices, demonstrating superior adaptability in modelling short-term dynamics and volatility.