An Exploratory Comparison of Process Capability Indices: Analyzing Autocorrelation in Seasonal and Non-Seasonal Moving Average Model

Abstract The impacts of autocorrelation on process capacity indices in the setting of time series data are investigated in this research. Using several moving average models, such as , and , we explore the behavior of three common indices, namely , and , under auto correlated circumstances. By using the Python programming language, this study employs Monte Carlo simulations to compare and contrast seasonal and non-seasonal moving average models. The findings emphasize the significant influence of autocorrelation on the distributional characteristics of sample process capacity indices, particularly in the context of the multiplicative seasonal moving average model. Additionally, the analysis demonstrated that the empirical distributions had a tendency towards positive skewness. The results of this study provide a challenge to the conventional understanding that process data is independent and normally distributed. These findings highlight the need of adopting a more nuanced approach when generating capacity indices for data that exhibits autocorrelation. The research emphasizes the need of taking autocorrelation into account when analyzing time series data, as well as the requirement for adequate modeling and parameter selection to appropriately assess process performance. Abstract Cryptocurrency price movements may be examined with the use of time series analysis, which is the process of applying statistical models to time series data. In this study, we examine and analyse the performance of several approaches for predicting the closing price of Bitcoin and Ethereum. In order to foretell what the Bitcoin and Ethereum prices will be at the end of the day, the time series model Auto-Regressive Integrated Moving Average (ARIMA) is used and it was applied to the research dataset's historical trading data. In order to forecast the nightly closing prices of Bitcoin and Ethereum, this cross-sectional research used the Auto-Regressive Integrated Moving Average (ARIMA) model. Bitcoin price forecasts based on ARIMA have shown a high degree of accuracy for horizons up to seven days in the future. The researchers tried many alternative models, but the ARIMA model (4, 1, 4) yielded the most reliable results when predicting the future value of bitcoin and Ethereum. On the first day of predicting (1 June 2019), Mean absolute percentage error (MAPE) generated an output value of 0.87, whereas on the seventh day, it generated a value of 5.98. (7 June 2021).