Efficient estimation for the conditional autoregressive model

Methodological approaches to exploring the spatial variation in social impacts of protected areas: An intercomparison of Bayesian regression modeling approaches and potential implications

Protected Areas (PAs) are widely used to conserve biodiversity by protecting and restoring ecosystems while also contributing to socio-economic priorities. An increasing number of studies aim to examine the social impacts of PAs on aspects of people's well-being, such as, quality of life, livelihoods, and connectedness to nature. Despite the increase in literature on this topic, there are still few studies that explore possible robust methodological approaches to capturing and assessing the spatial distribution of impacts in a PA. This study aims to contribute to this research gap by comparing Bayesian spatial regression models that explore links between perceived social impacts and the relative location of local residents and communities in a PA. We use primary data collected from 227 individuals, via structured questionnaires, living in or near the Peak District National Park, United Kingdom. By comparing different models we were able to show that the location of respondents influences their perception of social impacts and that neighboring communities within the national park can have similar perceptions regarding social impacts. Simulation based on existing data using the Bootstrap sub-sampling was also conducted to validate the association between social impacts and mutual proximity of residents. Our findings suggest that this type of data is better treated, in terms of accounting for potential spatial effects, using models that allow for proximity effects to be stronger between people living nearby, e.g. between neighbors in the same community and have minimum effects otherwise. Understanding the spatial clustering of perceived social impacts in and around PA, is key to understanding their causes and to managing and mitigating them. Our findings highlight therefore the need to develop new methodological approaches to assessing and predicting accurately the spatial distribution of social impacts when designating PAs. The findings in this paper will assist practitioners in this regard by proposing approaches to the consideration of the distribution of social impacts when designing the boundaries of PAs alongside typical ecological and socio-economic criteria.

Model Selection and Post Selection to Improve the Estimation of the ARCH Model

The Autoregressive Conditionally Heteroscedastic (ARCH) model is useful for handling volatilities in economical time series phenomena that ARIMA models are unable to handle. The ARCH model has been adopted in many applications that contain time series data such as financial market prices, options, commodity prices and the oil industry. In this paper, we propose an improved post-selection estimation strategy. We investigated and developed some asymptotic properties of the suggested strategies and compared with a benchmark estimator. Furthermore, we conducted a Monte Carlo simulation study to reappraise the relative characteristics of the listed estimators. Our numerical results corroborate with the analytical work of the study. We applied the proposed methods on the S&P500 stock market daily closing prices index to illustrate the usefulness of the developed methodologies.