Application of AR, MA, and ARMA Models in Financial Time Series Analysis

This research analyzes and predicts the daily return on the SP500 and FTSE 100 indices from 2015 to 2023 using the autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) models. The AR model asserts that both indices have the mean reversion feature of returns, which means that past performances do not predict future results. The analysis of the findings in this paper demonstrates this. Nevertheless, it was evident that the FTSE 100's mean reversion was more reliable than that of the SP500, suggesting that the FTSE 100 has the capacity to promptly reverse such a situation. The MA model of the preceding period's return forecast discrepancy was used to adjust the subsequent returns by both indices. Market fluctuations, like those that occurred at the inception of the COVID-19 pandemic, exacerbate these effects. Therefore, as in previous analyses, ARMA derived advantages from the inclusion of errors and information about the prior returns. In contrast to the SP500, which is more sensitive and based on shocks, this index exhibits more accurate mean reversion and superior correction mechanisms than the FTSE 100. Consequently, the research confirms that the ARMA model can effectively forecast the financial markets by leveraging historical results and forecast error. These models may be beneficial to policymakers and investors due to their ability to capture the non-parametric characteristics of financial time series.