Design an FPGA-based system for real-time analysis and prediction of stock prices, incorporating various financial indicators and time series data. The system should efficiently process large volumes of data, apply advanced statistical and machine learning techniques, and provide accurate and reliable predictions for various market conditions. Design a high-level block diagram of the system, including the key components and their interconnections. Describe the function of each component Select appropriate FPGA technology and device family, justifying your choice based on the required processing capabilities, power consumption, and cost considerations. Implement a data processing pipeline using hardware description languages (HDLS), such as VHDL or Verilog. The pipeline should include the following stages: a. Data input and pre-processing b. Feature extraction and selection c. Statistical analysis and machine learning model training d. Prediction generation and post-processing Design and implement a scalable memory hierarchy to handle the storage and retrieval of financial time series data, intermediate processing results, and metadata efficiently. Choose suitable statistical methods and machine learning models for stock price prediction, considering their accuracy, computational complexity, and resource requirements. Discuss the trade-offs involved in selecting these methods and models. Implement advanced techniques, such as the GARCH model for volatility forecasting and Long Short-Term Memory (LSTM) neural networks for time series prediction, as shown in the equations below: GARCHLp, a) model: * 0^2_t = w + ai + ^z_{ti}) + (_j * 0^2 _{ tj } ) the model orders, & represents the error terms, and where p and of are 0^2 denotes the conditional variance. LSTM neural network equations: it f_t = (w_f+[h_{t_1}, p_t] + b_f_ ot gt t - = ow_ox[h_{t1}, p_t] + b_o) tanhcw_gh_{t1}, p_t] + b_g) * c_ { t 1} + i t * g t htot tank (c_t) = where i, f, o, and g represent input, forget, output, and cell gates, respectively; h denotes the hidden state; c is the cell state; and p is the input. Implement techniques for handling data quality issues, such as missing values, outliers, and non-stationarity, to ensure the system's reliability and accuracy. Design a graphical user interface (GUI) or mobile application for monitoring and controlling the system, providing real-time feedback on stock price predictions and the performance of the models. Develop a testbench to validate the functionality and performance of the implemented design, ensuring that it meets the desired. specifications. optimize the design for power, area, and latency, providing a detailed analysis of the trade-offs involved in achieving the optimal configuration. Discuss the potential for scaling the design to accommodate larger datasets, more sophisticated models, or additional financial indicators and market factors.