12/9/2019 Department of Veterinary and Animal Sciences Advanced - - PDF document

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Department of Veterinary and Animal Sciences

Advanced Quantitative Methods in Herd Management Autocorrelation

Leonardo de Knegt Dan Børge Jensen

Outline

Definition Non-autocorrelated data Autocorrelated data with no trend Autocorrelated data with simple trend Autocorrelated data with systematic trend (seasonality) Real examples in herd monitoring

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Definition

• Milk yield on day 1 more similar to day 2 or day 250 ?

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• If milk yieldt is more similar to milk yieldt+1 or milk yieldt-1

than to milk yieldt+1+n , the data is said to be autocorrelated. “The degree of correlation between values of the same variables across different observations in the data”

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Definition

• Just as correlation measures the linear relationship

between two variables, autocorrelation measures the linear relationship between lagged values of a time series.

• Most often discussed in the context of time series data
• Same animal/object/herd observed at different

times

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Definition Autocorrelation coefficients measures the relationship between yt and yt−k, where k is the length of the lag. ∑

• ∑
• , where T is the length of the time series.

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Non-autocorrelated versus correlated Examples in R

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Trend and seasonality

• For data with simple, non-systematic trend
• autocorrelations for small lags are large and positive

because observations nearby in time are also nearby in size.

• the ACF of trended time series tend to have positive

values that slowly decrease as the lags increase.

• You can reduce correlation using filters (EWMA)
• For seasonal data (systematic trend)
• autocorrelations are larger for the seasonal lags
• e.g. 24 hours for pigs drinking behavior
• Shewart on raw data and on forecast errors both useless
• For data both trended and seasonal, you see a combination of

these effects.

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