Hydrological extremes experience an increase in some regions and a decrease in other zones. The objectives of the present work were (i) to introduce Class A pan evaporation data and virtual temperature-based potential evapotranspiration (PET v hereafter) into the Standardized Precipitation–Evapotranspiration Index (SPEIm hereafter) computation and (ii) to describe small and large fluctuations of SPI and SPEIm through multifractal detrended fluctuation (MF-DFA) and multifractal detrended cross-correlation (MF-DCCA) analyses. We used 40 years data (1974–2013) of monthly rainfall (P), mean, minimum and maximum air temperature, pan evaporation (E), relative humidity (RH) and relative sun brightness (RSB). Meteorological variables were collected from Puyo meteorological station, Pastaza Province, Ecuador. SPI time series for 1 and 6 months timescales were determined following two approaches. We computed SPI values using precipitation as the only input variable. Additionally, we incorporated pan evaporation and virtual temperature-based potential evapotranspiration into the standard SPEI computation (SPEIm). The SPEIm revealed some differences as compared with the classical SPI methodology. Five out of fifteen Asymmetry Index (AI) values were positive (0.095 ≤ AI ≤ 0.419).This indicates the relevance of high fluctuations at different time scales. Joint multifractal spectra between SPI (1,6)/SPEIm(1,6) versus RH and RSB rendered negative AI values which suggests the importance of low fluctuations at shorter time scales. The DCCA cross-correlation coefficient allows one to identify those time scales where SPI and SPEIm are influenced by other meteorological variables. Long-term correlation and sub-Gaussian behaviour of meteorological variables (apart from air temperature) are the main causes of multifractal structures.