Applying regression conformal prediction with nearest neighbors to time series data

Abstract

In this paper, we apply conformal prediction to time series data. Conformal prediction is a method that produces predictive regions given a confidence level. The regions outputs are always valid under the exchangeability assumption. However, this assumption does not hold for the time series data because there is a link among past, current, and future observations. Consequently, the challenge of applying conformal predictors to the problem of time series data lies in the fact that observations of a time series are dependent and therefore do not meet the exchangeability assumption. This paper aims to present a way of constructing reliable prediction intervals by using conformal predictors in the context of time series. We use the nearest neighbors method based on the fast parameters tuning technique in the weighted nearest neighbors (FPTO–WNN) approach as the underlying algorithm. Data analysis demonstrates the effectiveness of the proposed approach.

Keywords:

• Conformal prediction
• Time series
• Prediction intervals
• Exchangeability
• Nearest neighbors

Data availability statement

For our analysis, Cow’s Milk Production in the UK are provided by Eurostat, which are available at: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=apro_mk_colm&lang=en