The dataset is a tensor time series constructed from the Beijing multi-site air-quality data. The raw data contain six hourly air-pollution measurements, namely \(\textup{PM}_{2.5}\), \(\textup{PM}_{10}\), \(\textup{SO}_2\), \(\textup{NO}_2\), \(\textup{CO}\), and \(\textup{O}_3\), collected from 12 nationally controlled air-quality monitoring stations in Beijing from March 1, 2013 to February 28, 2017.
This dataset is not the raw data. It is a processed version constructed for studying the spatio-temporal dependence structure of air pollution in Beijing. Specifically, missing values and extreme values in the hourly observations were handled by interpolation. Then, for each monitoring station and each pollutant type, the hourly series were differenced to focus on concentration changes rather than levels. Finally, all series were standardized to remove the effects of different measurement scales across pollutants and stations.
After these preprocessing steps, the data form a tensor time series \(\mathcal{Y}_t=(y_{t,\ell_1,\ell_2,\ell_3})_{12\times 6\times 24}\) for \(t\in[1461]\), where \(y_{t,\ell_1,\ell_2,\ell_3}\) records the standardized concentration change of pollutant \(\ell_2\) at station \(\ell_1\) during the \(\ell_3\)-th hour of day \(t\).
data(BeijingAir)A 4-way array with dimension \(1461 \times 12 \times 6 \times 24\):
The day index, with 1461 daily observations from March 1, 2013 to February 28, 2017.
The 12 air-quality monitoring stations in Beijing.
The 6 pollutants: \(\textup{PM}_{2.5}\), \(\textup{PM}_{10}\), \(\textup{SO}_2\), \(\textup{NO}_2\), \(\textup{CO}\), and \(\textup{O}_3\).
The 24 hours within each day.