The effect of autocorrelation when performing theapproximated permutation test

Abstract: In meteorology, permutation tests are a commonly recommended tool because standard paramet-ric methods of inference often is insufficient when analysing weather. Therefore other methodswith less stringent assumptions like permutation testing is used. Time series data of weathercontains both temporal and spatial autocorrelation that may violate the exchangeability assump-tion of the permutation test. This paper explores the effect of autocorrelation in data on theapproximated permutation test. From a literary study it is found that the type I error of the test,i.e. rejecting the test while the null is true, increases when the assumption of exchangeability isviolated. A simulation study was then preformed on three meteorological variables, temperature,wind and precipitation in Iberia following a cold spell in the US. This increase in the type I er-ror was not found to be significant in the simulated data with autocorrelation ranging from 0 to 0.9.