Determinism, Holism, and Complexity pp 245-255 | Cite as

# Deterministic and Random Components of over Time Evolution of Milk Production Analysed by Time Series Methodology

## Abstract

Daily milk yield of dairy species shows a peculiar evolution over time from parturition to dry-off. In order to make correct comparisons among animals, lactation of standardised length are considered: in the dairy cow, for example, the standard lactation length has been fixed at 305 days. In official dairy recording schemes milk yields are measured on a large number of animals usually once a month: therefore, the maximum number of measurements per cow is 10, although lactations that end before 305 days or that show several missing data are quite frequent. A main problem in analysing the evolution of milk production over time is the separation of the regular and continuous component of the phenomenon from the random component, usually related to environmental short-term perturbations.

Actually, the deterministic component refers to genetic and physiological mechanisms that underlie milk secretion process, whereas the knowledge of the magnitude of the random component allow to define the range of an accurate forecasting for future yields or missing data, which represent a relevant technical problem for both the genetic improvement of the trait and the farm management.

Classical methodologies of time series analysis, particularly the box and Jenkins ARMA modelling, are able to identify the structure of the deterministic component and to estimate the relative magnitude of the random component. A major diagnostic tool is the autocorrelation function which is very useful to describe the nature of a process through time. Inference based on this function is often called an analysis in the time domain. At the same time, the analysis in the frequency domain, based on the spectral density function which describes how the variation in the time series may be accounted for by cyclic components at different frequencies, can be developed. Results of these analytic tools can be useful guidelines for the development of forecasting models able to reconstruct the original series in its pure deterministic component and in stochastic quota that follows Autoregressive (AR) or Moving Average (MA) probability models, whereas no inferences can be obviously made on the completely random (white noise) component.

## Keywords

Autocorrelation Function Time Series Analysis Milk Yield Time Series Model Random Component## Preview

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