## 1. Introduction

[2] The Arctic has experienced some of the most dramatic environmental changes over the last few decades which includes the decline of land and sea ice, and the thawing of permafrost soil. These effects are thought to be caused by global warming and have potentially global implications. For instance, the thawing of permafrost soil represents a potential tipping point in the Earth system and could lead to the sudden release of methane which would accelerate the release of greenhouse gas emissions and thus global warming.

[3] Whilst the changes in the Arctic must be a concern, it is important to place them in context because the Arctic exhibits large natural climate variability on many time scales [*Polyakov et al.*, 2003] which can potentially be misinterpreted as apparent climate trends. For instance, natural fluctuations on a daily time scale associated with weather systems can cause fluctuations on much longer time scales [*Feldstein*, 2000; *Czaja et al.*, 2003; *Franzke*, 2009]. This effect is called climate noise. Even very simple stationary stochastic processes can create apparent trends over rather long periods of time; so-called stochastic trends [*Cryer and Chan*, 2008; *Cowpertwait and Metcalfe*, 2009; *Barbosa*, 2011; *Fatichi et al.*, 2009; *Franzke*, 2010, 2012]. On the other hand, a so-called deterministic trend arises from external factors like greenhouse gas emissions.

[4] Specifically, here I will ask whether the observed temperature trends in the Eurasian Arctic region are outside of the expected range of stochastic trends generated with three different null models of the natural climate background variability. Choosing the appropriate null model is crucial for the statistical testing of trends in order not to wrongly accept a trend as deterministic when it is actually a stochastic trend [*Franzke*, 2010, 2012].

[5] There are two paradigmatic null models for representing climate variability: short-range dependent (SRD) and long-range dependent (LRD) models [*Robinson*, 2003; *Franzke*, 2010, 2012; *Franzke et al.*, 2012]. In short, SRD models are the most used models in climate research and represent the initial decay of the autocorrelation function very well. For instance, a first order autoregressive process (AR(1)) has an exponential decay of the autocorrelation function. LRD models represent the low-frequency spectrum very well, have a pole at zero frequency and a hyperbolic decay of the autocorrelation function. One definition of a LRD process is that the integral over its autocorrelation function is infinite while a SRD process has always an integrable autocorrelation function [*Robinson*, 2003; *Franzke et al.*, 2012]. In general, both stochastic processes can generate stochastic trends but stochastic trends of LRD models can last for much longer than stochastic trends of SRD models. This shows that the rate of decay of the autocorrelation function has a strong impact on the length of stochastic trends. In addition to these two paradigmatic models we will also use a non-parametric method to generate surrogates which exactly conserve the autocorrelation function of the observed time series.Figure 1 displays the autocorrelation function for one of the used stations and the corresponding autocorrelation functions of the above three models. It has to be noted that there are a myriad of nonlinear stochastic models which can potentially be used to represent the background climate variability and the significance estimates will depend on the used null model. However, I have chosen the three above models because two of them represent paradigmatic models for representing the correlation structure and one conserves exactly the empirical correlation structure.