Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Performance of state space and ARIMA models for consumer retail sales forecasting

Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts.

Delineating environmental groundwater vulnerability and protection zones mapping in fractured rock masses

Hard‐rock watersheds commonly exhibit complex geological bedrock and morphological features. Hydromineral resources have relevant economic value for the thermal spas industry. The present study aims to develop a groundwater vulnerability approach in Caldas da Cavaca hydromineral system (Aguiar da Beira, Central Portugal) which has a thermal tradition that dates back to the late 19th century, and contribute to a better understanding of the hydrogeological conceptual site model. In this work different layers were overlaid, generating several thematic maps to arrive at an integrated framework of several key‐sectors in Caldas da Cavaca site. Thus, to accomplish a comprehensive analysis and conceptualization of the site, a multi‐technical approach was used, such as, field and laboratory techniques, where several data was collected, like geotectonics, hydrology and hydrogeology, hydrogeomorphology, hydrogeophysical and hydrogeomechanical zoning aiming the application of the so‐called DISCO method. All these techniques were successfully performed and a groundwater vulnerability to contamination assessment, based on GOD‐S, DRASTIC‐Fm, SINTACS, SI and DISCO indexes methodology, was delineated. Geographical Information Systems (GIS) technology was on the basis to organise and integrate the geodatabases and to produce all the thematic maps. This multi‐technical approach highlights the importance of groundwater vulnerability to contamination mapping as a tool to support hydrogeological conceptualisation, contributing to better decision‐making of water resources management and sustainability.