## 1 Introduction
Although stock price fluctuations cannot be determined precisely, combining different models reduces the risk of failure and provides more accurate results than using them individually. Different kinds of hybrid models have been investigated. A new combination of ARIMA and ANN was proposed by [PERSON] and [PERSON] [24], which proved to be more accurate than ARIMA, ANN, or the [PERSON] model. Hybrid models combining GARCH and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) with different ANN structures have been investigated by [PERSON] and [PERSON] [25; 26]. Despite the fact that ANN-based models outperform linear statistical models and some hybrid statistical-ANN models, it would be unwise to rely only on them without incorporating risk analysis [9; 14]. Technical analysis (TA) provides a number of tools that can support investment decisions. [PERSON] and [PERSON] [27] proposed a hybrid methodology combining these analytical models and ANN for future value forecasting of the WIG20 index on the Warsaw Stock Exchange. Another trend is to combine TA and fundamental analyses with ANN for stock price forecasting [28; 29]. Hybrid models combining TA and ANN have also been used in previous works by the authors for close values prediction [22; 30]. The hybrid analytical-neural approach for stock price prediction was inspired by the authors' previous studies in the field of engineering, in which hybrid modeling yielded better results than \"pure\" ANN solutions [31; 32]. In our early work, hybrid models combining TA with ANN were compared only with the ANN-based approach [22]. We then reported our initial research into hybrid models containing fractal analysis (FA) [30]. Hybrid ANN-based models with technical and fractal analyses were applied in the core module of a decision-making information system supporting investor decisions on the Warsaw Stock Exchange [33; 34; 35]. The system was designed to analyze stock prices trends and choose the assets that will achieve the highest expected profit in the next day. The system was tested offline on historical data from 70 companies over a period of 6 months. The investment decisions were correct 60% of the time, and a profit of 17.2% was made, while the major Polish growth indices for the same time period were \(-0.99\%\) for WIG20 and \(5.69\%\) for mWIG40 [35]. These results proved the effectiveness of the hybrid models and ANN-based decision algorithms. In the present study, new hybrid models combining technical and fractal analyses with ANN are proposed for the short-term prediction of close values on the Warsaw Stock Exchange. Novel structures for hybrid models are presented, along with new fractal analysis indicators, and we compare the accuracy of the new hybrid models. Fractal analysis is based on the fractal market hypothesis, which was formulated in 1994 by [PERSON] [36] and derived from chaos theory [37]. Fractal shapes can be formed in many ways. The simplest is the multiple iteration of a generating rule (e.g., the Koch curve or Sierpinski triangle) [38; 39]. Fractals are generated in a deterministic way and all have a fractal, i.e., non-integer dimension. There are also random fractals, which can be generated using probability rules [40]. These ideas inspired the authors to implement fractal theory in the hybrid models and apply the fractal dimension to modify the TA indicators.