Photonic reservoirs have emerged as a promising complementary solution for computing hardware platforms, offering significant advantages in addressing time-dependent tasks and thus attracting substantial attention. Waveguide-based photonic reservoirs, in particular, have shown exceptional performance in time-series applications, such as communication and bit-level processing tasks. For more complex analog prediction tasks, studies have validated the efficacy of larger reservoirs, comprising up to 128 nodes, for the Santa Fe chaotic laser prediction challenge. However, this approach suffers from the limitation of requiring a large physical footprint. To overcome this constraint, the present study refines algorithmic techniques and input strategies, enabling accurate predictions using a more compact integrated photonic reservoir.First, to process the high-dimensional sampled data from the reservoir chip, the data processing algorithm was transitioned from linear regression to vector autoregression (VAR). VAR allows the incorporation of additional historical sample data as feature inputs in linear combinations, thereby alleviating computational limitations imposed by the restricted number of output nodes. Building on this improvement, a 32-node plum-shaped integrated photonic reservoir is proposed for predictive tasks. Finally, a multiple-dissimilar-input strategy is introduced to enhance data diversity at the input layer, further reducing computational errors in time-series prediction tasks.The results of research demonstrate that compact integrated reservoir computing, when combined with the VAR algorithm, achieves highly accurate prediction results. The prediction errors remain within the same order of magnitude as those in delay-based reservoirs, positioning the small integrated photonic reservoir as a strong competitor in this category. Building on this foundation, our investigation extended to the input strategy, demonstrating the effectiveness of a multiple-dissimilar-input approach. Compared to traditional methods, the root mean square error (RMSE) improves by an order of magnitude, while the normalized mean square error (NMSE) decreases by three orders of magnitude. Additionally, the mean absolute error (MAE) and dynamic systems (DS) evaluation metrics show substantial improvements. These findings suggest that the complexity of the reservoir's output signal is no longer solely determined by the chip's design and dynamic properties, significantly enhancing computational performance.This study demonstrates the feasibility of compact waveguide-based reservoirs for complex time-series prediction tasks, offering superior predictive performance compared to existing delay-based reservoirs. By integrating the reservoir chip with the VAR algorithm, the compact reservoir gains enhanced capabilities for handling intricate tasks, achieving performance levels comparable to current state-of-the-art methods. Additionally, a significant improvement in prediction accuracy is attained through the implementation of an optimized input strategy. The precise prediction of stock indices underscores the vast potential of photonic waveguide-based reservoir chips in various time-series prediction applications. Moreover, the advancements in reservoir chip design, training algorithms, and input strategies extend beyond a single reservoir configuration. These improvements can be applied to cascaded configurations of small reservoirs, such as those employed in classical ensemble combination techniques, broadening the scope of their application.