# A Forecast Model Applied to Monitor Crops Dynamics Using Vegetation Indices (NDVI)
## 4 Conclusions  
The results of this study presented above show a forecast model constructed as a combination of models applied to monitor crop dynamics, more specifically, a forecast algorithm applied to vegetation indices (NDVI) time series data closely related to the type and crop state derived from optical remote sensing. The combination of predictions improves the precision of the individual predictions, and this work analyzed predictions associated with different univariate methods (smoothed and ARIMAX) and their combinations, comparing their behavior. Figure 16: Subfigures (**a**–**d**) presents maize crop types (1)–(4) forecast intervals with the associated \(\alpha=0.05\). Subfigure (**e**) presents aggregateMaze crop types (1)–(4) forecast intervals with the associated \(\alpha=0.05\). Subfigure (**f**) presents olive crop type forecast intervals with the associated \(\alpha=0.05\). By comparing the different forecast models combinations, it was found that the equations of the models present a positive contribution of the climatological parameters of T, P, H and R for the growth of the plants. The considered climatological parameters are within the favorable ranges for the growth of the crops. Extreme climatic situations that could affect the normal development of the crops were not considered. This issue will be further developed in the future. Following this, the equation models revealed that the temporal variable (\(Y_{t-1}\), \(Y_{t-2}\), \(Y_{t-12}\), \(Y_{t-24}\)) included in each model depends on the type of crop, the interval being greater in the case of maize crops because they are seasonal crops and have a faster evolution. Furthermore, the weighting from the double smoothing model is high (\(\alpha\) = 0.85). In the case of olive trees, as it is a perennial crop with fewer transformations, the dependence on the temporal variable is lower.Finally, considering the results obtained in this study, we highlight the following conclusions:  
(1) Because each prediction method is capable of capturing different aspects of the information available for prediction, in this study, we offered a forecast algorithm combining different univariate methods (smoothed and ARIMAX) and their combinations for forecasting vegetation indices (NDVI) time series derived from optical remote sensing data. (2) The accuracy of the prediction of the results, estimated as a weighted average of the predictions resulting from the selected relevant estimation models, was proved to be relevant in the final forecast. (3) The considered climatological variables (temperature, air humidity, precipitation and solar radiation) have a positive and coherent contribution with the temporal evolution of the vegetation indexes but with different influence weights, according to the type of cultivation. Although in this work, we only explored data from two types of crops, four maize crops of different cycles, one aggregate for all maize crops and one plot of olive trees, in the future, it would be important to extend our methodology to other agricultural areas with other types of crops. (4) The results of the prediction models were validated for a time series of one year and are very useful to be applied in the short term, in the management and planning of agricultural activities or availability of water resources for irrigation. In order to incorporate these forecasting models into climate models or hydrological models that require time series of tens of years, more data must be collected (NDVI and environmental conditions) to advance in longer forecasting models. All authors made a significant contribution to the final version of the paper. Conceptualization, F.C.-C., and A.E.S. ; Methodology, F.C.-C., A.E.S., C.S., and D.M.-C.; Supervision, F.C.-C., A.E.S., C.S., and D.M.-C.; Processing remote sensing data: F.C.-C., and D.M.-C.; Weather variables data, D.M.-C. and F.C.-C.; Forecast models, A.E.S. and C.S.