mathematics Article Deterministic Chaos Detection and Simplicial Local Predictions Applied to Strawberry Production Time Series Juan D. Borrero * ,† and Jesus Mariscal †   Citation: Borrero, J.D.; Mariscal, J. Deterministic Chaos Detection and Simplicial Local Predictions Applied to Strawberry Production Time Series. Mathematics 2021, 9, 3034. https:// doi.org/10.3390/math9233034 Academic Editor: Manuel Alberto M. Ferreira Received: 3 October 2021 Accepted: 23 November 2021 Published: 26 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Agricultural Economics Research Group, Department of Management and Marketing, University of Huelva, Pza. de la Merced s/n, 21071 Huelva, Spain; jesus.mariscal@dem.uhu.es * Correspondence: jdiego@uhu.es † These authors contributed equally to this work. Abstract: In this work, we attempted to find a non-linear dependency in the time series of strawberry production in Huelva (Spain) using a procedure based on metric tests measuring chaos. This study aims to develop a novel method for yield prediction. To do this, we study the system’s sensitivity to initial conditions (exponential growth of the errors) using the maximal Lyapunov exponent. To check the soundness of its computation on non-stationary and not excessively long time series, we employed the method of over-embedding, apart from repeating the computation with parts of the transformed time series. We determine the existence of deterministic chaos, and we conclude that non-linear techniques from chaos theory are better suited to describe the data than linear techniques such as the ARIMA (autoregressive integrated moving average) or SARIMA (seasonal autoregressive moving average) models. We proceed to predict short-term strawberry production using Lorenz’s Analog Method. Keywords: time series; nonlinear forecasting; yield production; chaos theory; Lyapunov exponents JEL Classification: Q11; C15; C22; C53; C65 1. Introduction The strawberry of Huelva (strawberry from Spain) belongs to the select group of agricultural activities in which Spain is the absolute leader in the European Union [1]. Huelva accounts for 9% of world strawberry production and 25% of that of the European Union; it is the second-largest area of production, technology, and research in the world in this sector behind California [2] and contributes more than 400 million euros to the province in direct total agricultural production value [3]. On the other hand, the evolution of strawberry production is sensitive to price fluc- tuations [4,5]. Strawberry is a free-market crop with no entry or exit barriers, without intervention prices or production controls. The price of strawberries is determined strictly by the free interaction of supply and demand. Knowing the future productions of these time series could mean a considerable increase in profitability for the strawberry-producing sector [1], since a large distribution usually results in sales programs with heavy penalties for non-compliance. Yield forecast approaches are basically divided into single-factor time series models and multi-factor models. The former considers time as an independent variable and builds up mathematical models based on the yield time series to produce future predictions; the latter also considers the main influential factors in the system under study. As a first approach to the study of strawberry yield predictions, we considered only single-factor models. Multi-factor models are generally more time consuming and require extensive user intervention. In addition, external factors such as prices, costs, crop characteristics, consumer behavior, or climatic conditions often require data that may be unavailable or difficult to obtain. Finally, to use the forecasting model in the future, predictions for such Mathematics 2021, 9, 3034. https://doi.org/10.3390/math9233034 https://www.mdpi.com/journal/mathematics