In this study, we introduce a quantum computing method that incorporates Ridglet transforms into quantum processing pipelines for financial time-series forecasting with Quantum Approximate Optimization Algorithm (QAOA)-based portfolio optimization. We propose a Quantum Ridgelet Neural Network (QRNN) model for forecasting time-series data that integrates Parametrized Quantum Circuits (PQCs) with ridgelet-based feature transformations and QAOA-based portfolio optimization for asset selection. By breaking down financial time-series data into multi-resolution components, the ridgelet transform enables the identification of both local and global trends. Ridgelet-based features improve the scalability and accuracy of quantum computing by significantly reducing the number of qubits needed. However, the predicted results are turned into a QUBO-based mean-variance optimization problem and solved with QAOA to select the best stocks. Our study begins with a theoretical formulation of the single-qubit system for our proposed model. This formulation is further extended to a multi-qubit system, and we show that it captures a significant fraction of the predictive signal.