Modeling Non-Stationary Processes Through Dimension Expansion

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field

Exploring the trend of New Zealand housing prices to support sustainable development

The New Zealand housing sector is experiencing rapid growth that has a significant impact on society, the economy, and the environment. In line with the growth, the housing market for both residential and business purposes has been booming, as have house prices. To sustain the housing development, it is critical to accurately monitor and predict housing prices so as to support the decision-making process in the housing sector. This study is devoted to applying a mathematical method to predict housing prices. The forecasting performance of two types of models: autoregressive integrated moving average (ARIMA) and multiple linear regression (MLR) analysis are compared. The ARIMA and regression models are developed based on a training-validation sample method. The results show that the ARIMA model generally performs better than the regression model. However, the regression model explores, to some extent, the significant correlations between house prices in New Zealand and the macro-economic conditions