Vertical federated learning (VFL) is a promising area for time series forecasting in industrial applications, such as predictive maintenance and machine control. Critical challenges to address in manufacturing include data privacy and over-fitting on small and noisy datasets during both training and inference. Additionally, to increase industry adaptability, such forecasting models must scale well with the number of parties while ensuring strong convergence and low-tuning complexity. We address those challenges and propose 'Secret-shared Time Series Forecasting with VFL' (STV), a novel framework that exhibits the following key features: i) a privacy-preserving algorithm for forecasting with SARIMAX and autoregressive trees on vertically partitioned data; ii) serverless forecasting using secret sharing and multi-party computation; iii) novel N-party algorithms for matrix multiplication and inverse operations for direct parameter optimization, giving strong convergence with minimal hyperparameter tuning complexity. We conduct evaluations on six representative datasets from public and industry-specific contexts. Our results demonstrate that STV's forecasting accuracy is comparable to those of centralized approaches. They also show that our direct optimization can outperform centralized methods, which include state-of-the-art diffusion models and long-short-term memory, by 23.81% on forecasting accuracy. We also conduct a scalability analysis by examining the communication costs of direct and iterative optimization to navigate the choice between the two. Code and appendix are available: https://github.com/adis98/STV

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