This paper presents the standardized precipitation evapotranspiration index (SPEI)-based approach to agricultural drought monitoring (ADM-SPEI approach) combining well-known methods, expert’ critical opinions, and local agro-climatic specificities. The proposed approach has been described in detail in three phases. This allows its application in any region and modification according to different agro-climatic conditions. The application of the ADM-SPEI approach has resulted in obtaining a modified SPEI for different crops (agricultural drought SPEI (AD-SPEI_crop)) in the Vojvodina region. In the first phase of the proposed approach, analytical hierarchy process (AHP) was used to obtain an experts’ group decision regarding the most suitable method for calculating evapotranspiration for a particular analyzed region. In the second phase, SPEI was modified and adjusted to the conditions in Vojvodina, where ET₀ was replaced by ET_c. In the validation phase, the results of the application of AD-SPEI_crop were compared to crop yields and well-known indices and evaluated by the experts’ feedback. The statistically significant correlations were achieved between AD-SPEI_crop and crop yields. The highest correlations were achieved in the months when the analyzed crops were in the developmental stages when they are most sensitive to drought. The AD-SPEI_crop better correlates to the crop yields compared to SPEI. The comparison of AD-SPEI_crop to the standardized precipitation index (SPI), SPEI, and self-calibrated Palmer drought severity index (SC-PDSI) shows that it can successfully detect dry and wet periods. The results have indicated that the proposed approach can be successfully applied, and AD-SPEI_crop has shown a good performance for agricultural drought monitoring.

We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor ²²²Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.

The purpose of this paper was to choose an appropriate information dissimilarity measure for hierarchical clustering of daily streamflow discharge data, from twelve gauging stations on the Brazos River in Texas (USA), for the period 1989–2016. For that purpose, we selected and compared the average-linkage clustering hierarchical algorithm based on the compression-based dissimilarity measure (NCD), permutation distribution dissimilarity measure (PDDM), and Kolmogorov distance (KD). The algorithm was also compared with K-means clustering based on Kolmogorov complexity (KC), the highest value of Kolmogorov complexity spectrum (KCM), and the largest Lyapunov exponent (LLE). Using a dissimilarity matrix based on NCD, PDDM, and KD for daily streamflow, the agglomerative average-linkage hierarchical algorithm was applied. The key findings of this study are that: (i) The KD clustering algorithm is the most suitable among others; (ii) ANOVA analysis shows that there exist highly significant differences between mean values of four clusters, confirming that the choice of the number of clusters was suitably done; and (iii) from the clustering we found that the predictability of streamflow data of the Brazos River given by the Lyapunov time (LT), corrected for randomness by Kolmogorov time (KT) in days, lies in the interval from two to five days.

The impact of adverse weather conditions (AWCs) on crop production is random in both time and space and depends on factors such as severity, previous agrometeorological conditions, and plant vulnerability at a specific crop development stage. Any exclusion or improper treatment of any of these factors can cause crop models to produce significant under- or overestimates of yield. The analysis presented in this paper focuses on a range of agrometeorological indices (AMI) related to AWCs that might affect real yield as well as simulated yield. For this purpose, the analysis addressed four indicators of extreme temperatures and three indicators of dry conditions during the growth period of maize and winter wheat in Austria, Croatia, Serbia, Slovakia, and Sweden. It is shown that increases in the number and intensity of AWCs cannot be unambiguously associated with increased deviations in simulated yields. The identified correlations indicate an increase in modeling uncertainty. This finding represents important information for the crop modeling community. Additionally, it opens a window of opportunity for a statistical (“event scenario”) approach based on correlations between agrometeorological indices of AWCs and crop yield data series. This approach can provide scenarios for certain locations, crop types, and AWC patterns and, therefore, improve yield forecasting in the presence of AWCs.

The aim of this paper is to find distributions that adequately describe returns of the Belgrade Stock Exchange index BELEX15. The sample period covers 1067 trading days from 4 October 2005 to 25 December 2009. The obtained models were considered in estimating Value at Risk ( VaR ) at various confidence levels. Evaluation of VaR model accuracy was based on Kupiec likelihood ratio test.