Quinoa (Chenopodium quinoa Willd.) has gained prominence worldwide over recent years and suddenly Peru has emerged as a major player in the global quinoa market. This study aims to analyze the expansion of quinoa farming in Peru in the period 1995-2014 and to discuss the changes in land-use the country has experienced as a result of the boom in the global demand for quinoa. Two statistical approaches, principal component analysis (PCA) and exponential smoothing, were applied in the data analysis to explore the evolution of the quinoa boom in Peru by periods and to forecast what the acreage expansion rate would have been if the boom had not occurred. The results show that the quinoa boom was responsible for an increase of 43% in the number of hectares planted with quinoa in 2014, in relation to the number predicted if there had been no boom. This provoked an acceleration of production in traditional quinoa farming areas and the extension of this activity to new regions. The consequences are already apparent in the land-use changes seen in Peru, namely the: (i) displacement; (ii) rebound; and (iii) cascade effects.

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A recent mathematical model has suggested that staying at home did not play a dominant role in reducing COVID-19 transmission. The second wave of cases in Europe, in regions that were considered as COVID-19 controlled, may raise some concerns. Our objective was to assess the association between staying at home (%) and the reduction/increase in the number of deaths due to COVID-19 in several regions in the world. In this ecological study, data from www.google.com/covid19/mobility/, ourworldindata.org and covid.saude.gov.br were combined. Countries with > 100 deaths and with a Healthcare Access and Quality Index of ≥ 67 were included. Data were preprocessed and analyzed using the difference between number of deaths/million between 2 regions and the difference between the percentage of staying at home. The analysis was performed using linear regression with special attention to residual analysis. After preprocessing the data, 87 regions around the world were included, yielding 3741 pairwise comparisons for linear regression analysis. Only 63 (1.6%) comparisons were significant. With our results, we were not able to explain if COVID-19 mortality is reduced by staying at home in ~ 98% of the comparisons after epidemiological weeks 9 to 34.

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In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval (0, 1). The proposed model accommodates a set of regressors and a long-range dependent time series structure. We derive the partial likelihood estimator for the parameters of the proposed model, obtain the associated score vector and Fisher information matrix. We also prove the consistency and asymptotic normality of the estimator under mild conditions. Hypotheses testing, diagnostic tools and forecasting are also proposed. A Monte Carlo simulation is considered to evaluate the finite sample performance of the partial likelihood estimators and to study some of the proposed tests. An empirical application is also presented and discussed.