Multivariate time series forecasting of abortion incidence rate in New Zealand livestock populations using deep learning models : a thesis presented in partial fulfilment of the requirements for the degree of Master of Information Science in Computer Science at Massey University, Albany, New Zealand

Abstract

Livestock abortion counts are important indicators of population health and productivity. In practice, however, obtaining timely and accurate abortion incidence data and producing reliable forecasts remain challenging due to factors such as reporting delays, incomplete records, and substantial observational noise. Abortion dynamics are influenced by multiple interacting factors, including production history, seasonal variability, climatic conditions, and socio-behavioural effects. As a result, the monthly abortion time series exhibits both long-term trends and short-term fluctuations that reflect complex underlying processes. Modelling such heterogeneous, multi-source time-series data while maintaining appropriate control over model complexity remains a central challenge in applied forecasting research. This study focuses on livestock abortion incidence data in New Zealand and applies time-series forecasting at both national and regional scales. Multiple data sources are incorporated, including historical abortion records, livestock population statistics, climatic variables, and Google Trends search information. These data are aggregated at a monthly resolution to construct a unified time series for forecasting. In the national-level analysis, two time-series forecasting models are considered to address the characteristics of multivariate inputs. One model builds on the standard Long Short-Term Memory (LSTM) architecture by incorporating an attention mechanism, whereas the other employs a Mixing-Channel Patch Time Series Transformer (PatchTST) framework with a parallel LSTM branch. These models are evaluated with respect to their architectural design and predictive performance, and their results are compared with those obtained from other baseline deep learning approaches. For the regional-level analysis, New Zealand’s 16 administrative regions are grouped into seven study areas based on the livestock demography and geographical adjacency. Both model configurations are subsequently applied to each region, and differences in predictive performance are analysed alongside regional patterns in livestock abortion counts. Overall, in national-level prediction tasks, the proposed Mixing-Channel PatchTST parallel LSTM framework achieved superior results compared to several well-established baseline models (RMSE=6.0062, MAE=4.6993, 𝑅²=0.9784). Compared with the strongest baseline model (LSTM with attention mechanism; RMSE=7.4426, MAE=6.0720, 𝑅²=0.9668), this method achieved a 19.3% relative reduction in RMSE, a 22.6% relative reduction in MAE, and an absolute increase of 0.0116 in 𝑅². Further experiments at the regional level showed that the framework achieved varying levels of error reduction in most regions, demonstrating more robust predictive behaviour and a more consistent capability in trend characterisation. In conclusion, the model proposed in this thesis provides a robust and effective modelling framework for predicting livestock abortion numbers and can provide practical technical support for pasture management and risk-related decision analysis.