An accurate cost estimate not only plays a key role in project feasibility studies but also in achieving a final successful outcome. Conventionally, estimating cost typically relies on the experience of professionals and cost data from previous projects. However, this process is complex and time-consuming, and it is challenging to ensure the accuracy of the estimates. In this study, the bivariate and multivariate transfer function models were adopted to estimate and forecast the building costs of two types of residential buildings in New Zealand: Low-rise buildings and high-rise buildings. The transfer function method takes advantage of the merits of univariate time series analysis and the power of explanatory variables. In the dynamic project conduction environment, simply including building cost data in the cost forecasting models is not valid for making predictions, because the change in demand must be considered. Thus, the time series of house prices and work volume were used to explain exogenous effects in the transfer function model. To demonstrate the effectiveness of transfer function models, this study compared the results generated by the transfer function models with autoregressive integrated moving average models. According to the forecasting performance of the models, the proposed approach achieved better results than autoregressive integrated moving average models. The proposed method can provide accurate cost estimates that can help stakeholders in project budget planning and management strategy making at the early stage of a project.