A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets

Abstract

Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984China ( -2009. Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods-e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.

Heterogeneous Space–Time Artificial Neural Networks for Space–Time Series Prediction

“…It has been found that the accuracy of the monitoring results obtained by the automatic gravimetric method meets the requirements of the standard manual monitoring method (Cheng, Gong, & Pan, ). To reduce the effect of missing data on the prediction results, a dataset with fewer missing values was selected, and some individual missing values were estimated using a spatio‐temporal interpolation method (Deng et al, ). Figure shows the spatial distribution of these monitoring sites.…”

“…The non‐separated approach aims to define a joint space–time covariance structure (Heuvelink & Griffith, ). When a space–time covariance structure is defined, kriging methods can be used to obtain the best linear unbiased prediction at a given location by computing a weighted average of the known values at its neighboring sites (Deng, Fan, Liu, & Gong, ). Although space–time dependence is considered in space–time geostatistics, the nonlinearities and nonstationarities of a space–time series cannot be well handled by space–time geostatistics.…”

Estimating missing values in China’s official socioeconomic statistics using progressive spatiotemporal Bayesian hierarchical modeling

“…To compare different imputation models with cross-validation, we used three indices to measure the actual prediction accuracy, namely, the standardized allocation error (SAE) 11 , the mean square error (MSE) and the coefficient of determination (R 2 ) 21 , 35 . All these indices compare the model-predicted values with observed values.…”

“…The R 2 is an index for assessing the agreement between observed and estimated values, with the value ranging from 0 for complete disagreement to 1 for perfect agreement. Scatterplots were created to compare the observed values and estimated values in the cross-validation 1 , 21 .…”

“…Thus large-scale official statistics data usually have spatial structures, particularly spatial autocorrelation 19 . Moreover, temporal autocorrelation, in which observations that are temporally close to each other tend to be similar, is also likely to be inherent in official statistics data 20 , 21 . On the one hand, information about spatial and/or temporal structures can be utilized for estimating missing values, especially when other information, such as that from samples and auxiliary data, is unavailable.…”