The goal of this work is to extend the Time Series Data Mining (TSDM) framework [1-4] by developing techniques for measuring time series predictability. A time series X is Â¡Â°a sequence of observed data, usually ordered in timeÂ¡Â± [5, p. 1]. .
where t is a time index, and N is the number of observations. Time series predictability is a measure of how well future values of a time series can be forecasted, which will be studied in the context of the TSDM framework. Additionally, we see the possibility of integrating this work with two other parallel projects. These efforts aim to improve the computational performance of the TSDM methods by using alternative optimization techniques and developing distributed implementations of the TSDM methods.
Time series analysis is fundamental to engineering, scientific, and business endeavors. Researchers study systems as they evolve through time, hoping to discern their underlying principles and develop models useful for predicting or controlling them. Time series analysis may be applied to the prediction of welding droplet releases and stock market price fluctuations [1, 3].
Traditional time series analysis methods such as the Box-Jenkins or Autoregressive Integrated Moving Average (ARIMA) method can be used to model such time series. However, the ARIMA method is limited by the requirement of stationarity of the time series and normality and independence of the residuals . The statistical characteristics of a stationary time series remain constant through time. Residuals are the errors between the observed time series and the model generated by the ARIMA method. The residuals must be uncorrelated and normally distributed. .
For real-world time series such as welding droplet releases, stock market prices, or motor fault detection and prediction, the conditions of time series stationarity and residual normality and independence are not met.