پیش بینی رده زمانی با استفاده از شبکه بیزی پویا Time series prediction using dynamic Bayesian network

1. Introduction Recently, time series forecasting is concerned by many researches, most of time prediction models focus on one-stepahead prediction, the multi-step-ahead prediction is still a challenge topic. We can divide the multi-step-ahead time series forecasting into two kinds of ways [1–3]: direct-based and iterate-based approaches. The direct-based approaches always build prediction models to estimate multi-step-ahead values directly. The iterate-based approaches often first constructs one-step-ahead forecasting framework, and the predictions are usually used as known information to estimate the next ones. In iterate-based approaches, the prediction accuracy is great influenced by cumulative errors, on the other hand, for direct-based methods, time cost of methods always is an important element to be considered. In split of aforementioned two main trend approaches, other time series forecasting approaches are also concerned, for example, such as, multi-input several multi-outputs (MISMO) forecasting framework [6,7], the multi-input multi-output (MIMO) approach [5], and DirRec method [4], and so on. The MIMO and the MISMO strategy usually concern to get higher predictionaccuracy,however,itis often withthehigher time cost. TheMISMO approachesdivide originalforecastingproblem into subtasks, using optimal solution or cross-validation, to estimate system outputs [8], on the one hand, the forecasting performance is usually not bad, however, the time cost of computation still need to be improved. In this article, a new graph-based approach is proposed for improving performance of time series forecasting, and the algorithm is based on combination of the echo state network (ESN) [9,10] and Kalman filtering frame. The prediction system is described by the dynamic Bayesian network (DBN), the DBN can present random sequence signals entirely. Our motives can be described as follow. Firstly, in last years, many scholars have proved that the ESN is promising time series prediction system. In many fields, the ESN has been used to predict sequence information [9,10], hence, in this paper, the ESN model is selected as one part of our forecasting frameworks. Secondly, in split of the ESN method has good prediction performance, only short-time sequence information is used to estimate the coming information. Such as, for the ESN real-time forecasting [9], only previous part of short-time data is utilized as input signals to predict data, if all previous sequence data is used to estimate the coming data, the forecasting performance would be further improved.