**4. Conclusions**

We have examined nine time series in this paper corresponding to snowpack percentages in Colorado, investigating if there has been a significant decline over time in the series in the context of long memory processes. For this purpose, we have tested for the significance of the time trend coefficient in a model where the regression errors are fractionally integrated or integrated of order d. Long memory occurs then if d is a positive value.

Our results indicate that there is no evidence of long memory behavior since all the orders of integration are close to zero or below it, implying short memory or anti-persistence behavior. Focusing on the time trend coefficients, these are significant in 15 of the 27 series examined, and in all these cases, they are found to be significantly negative, supporting thus the hypothesis of a decline in the amount of snow in Colorado watersheds probably as a consequence of global climate warming.

Future work should focus on alternative modeling approaches including for example non-linear structures which are clearly related with long memory and fractional integration models [26]. Thus, non-linear deterministic terms like those based on Chebyshev polynomials in time [27] or Fourier transforms [28], in both cases based on I(d) models, can also be implemented on these or on similar data.

## **Acknowledgements**

The author gratefully acknowledges financial support from the MINEIC-AEI-FEDER ECO2017-85503-R project from 'Ministerio de Economía, Industria y

Competitividad' (MINEIC), 'Agencia Estatal de Investigación' (AEI) Spain and 'Fondo Europeo de Desarrollo Regional' (FEDER).

Comments from the Editor and an anonymous reviewer are also gratefully acknowledged.
