Abstract— Prediction of time series data has been used extensively in engineering, economics, and many other areas, however, more precise models are always sought by scientists. In this research, the predictability of dynamic gray systems is studied on forecasting time series data. Modified dynamic gray system models are also proposed and compared. The criteria such as MAE, MSE, directional accuracy, and the Theil’s inequality coefficient are used to analyze the predictability of dynamic gray models with relationship to parameters of models, and compared with random walk model. Index Terms—Time series, dynamic system, gray model, random walk I. INTRODUCTION IME series data has been studied widely as a case of prediction problem and find ways to mine information from the date. However, these efforts have has less than successful results compared with the random walk rule. Traditional time series analysis models, such as ARIMA model, also known as Box-Jenkins method [1] are limited by the requirement of stationary property of the time series and normality and independence of the residuals. Osborne (1959)[2] proposed the random walk characteristic of stock market. Later, the random walk model has been widely considered as a statistical model for the movement of the logged stock price. Under such a model, the stock price is not predictable or mean reversing. A time series is a random walk if it satisfies P t = P t-1 + a t Where P t and P t-1 are data value at time t and t-1, and a t is a white noise. Artificial intelligence techniques such as artificial neural network (ANN) and genetic algorithms (GA) have been Junfeng Qu, Department of Information Technology, Clayton State University, Morrow, GA 30260. Email: jqu@clayton.edu Hamid R. Arabnia is with the University of Georgia, Athens, GA 30602. Email: hra@cs.uga.edu Yinglei Song is with the University of Maryland Eastern Shore, Princess Anne, MD 21853; email: ysong@umes.edu Khaled Rashed is with the University of Georgia, Athens, GA 30602. Email: khaled@cs.uga.edu Yong Wei is with the North Georgia College & State University, email: ywei@northgeorgia.edu applied to forecast time series data as the computation power increased dramatically[3, 4]. Those approaches are based on the training time data that includes those far away from the present to train the model and thus produce prediction. Thus the data are not fully considered as in the time series because the all data are treated without any preference. Kim and Han[9] also showed that ANNs had some limitations in learning the patterns because some time series data such as financial data has tremendous noise and complex dimensionality and the sheer quantity of financial time series data sometimes interferes with the learning of patterns. The technical difficulty of the financial forecasting problem is due to low signal-to-noise ratio, non-Gaussian noise distribution, non-stationary, and non-linearly[5]. The other problem with predicting stock prices is that the volume of data is too huge to influence the ability of using information [6] Due to these controversies and difficulties in the stock market time series forecasting, a different approach is desirable that does not depends on the stationary and Gaussian distribution of the data and owns a certain accuracy and ability to forecast. The gray system theory is based on the assumption that a system is uncertain and that the information regarding the system is insufficient to build to construct a model to depict the evolution of the system exactly. The gray system was first introduced by Deng[7,8]. The gray predicting model is the essential of the gray system theory and it has been successfully used in geography, hydrology, management, engineering, agriculture, ecology, medicine, and social science because of its computational simplicity and effectiveness. The advantage of the gray predicting system is that only a few discrete data are sufficient to characterize an unknown system that depicted by the first-order differential equation. Thus, the gray predicting system is suitable for predicting the system that historical data is limited and a quick and reliable resolution for the decision-makers reference. The gray theory avoids the inherent defects of conventional statistic methods such as regressive analysis or traditional time series analysis that requires the certain constrains on the data. It provides an opportunity for the time series data analysis to establish a non-function model with a limited amount of data to estimate the behavior of gray system. In this paper, we use Time Series Predictability Analysis with Modified Dynamic Gray Systems Junfeng Qu, Hamid R. Arabnia, Yinglei Song, Khaled Rashed, Yong Wei T