Vertical federated learning (VFL) is a promising area for time series forecasting in many applications, such as healthcare and manufacturing. Critical challenges to address include data privacy and over-fitting on small and noisy datasets during both training and inference. Additionally, such forecasting models must scale well with the number of parties while ensuring strong convergence and low-tuning complexity. We address these challenges and propose ``Secret-shared Time Series Forecasting with VFL'' (STV), a novel framework with the following key features: i) a privacy-preserving algorithm for forecasting with SARIMAX and autoregressive trees on vertically-partitioned data; ii) decentralised forecasting using secret sharing and multi-party computation; and iii) novel N-party algorithms for matrix multiplication and inverse operations for exact parameter optimization, giving strong convergence with minimal tuning complexity. We evaluate on six representative datasets from public and industry-specific contexts. Results demonstrate that STV's forecasting accuracy is comparable to those of centralized approaches. Our exact optimization outperforms centralized methods, including state-of-the-art diffusion models and long-short-term memory, by 23.81% on forecasting accuracy. We also evaluate scalability by examining the communication costs of exact and iterative optimization to navigate the choice between the two. STV's code and supplementary material is available online: https://github.com/adis98/STV.