A State Space Model Exhibiting a Cyclic Structure with an Application to Progesterone Concentration in Cow Milk

Progesterone is a hormone linked to the reproductive status of dairy cows. Hence, with the increasing availability of on-line records of the concentration of progesterone in cow milk, there is a need for new tools to analyse such data. The aim is to find techniques for better determination of the time when cows are in oestrus to increase the rate of succesful inseminations. In this paper we propose a state space model for data with a continuous and cyclic trend in the mean. Furthermore a matching Kalman filter is developed. The model is tested on progesterone data from 112 cow-lactations with the purpose of evaluating the use of progesterone for detection of oestrus.