Causal analysis for non-stationary time series in sensor-rich smart buildings

Advances in low cost sensor and networking technologies in smart buildings have given researchers access to a multitude of time series data, including temperature, humidity, real and reactive power consumption of specific nodes or devices, occupant presence and activities, etc. Time series generated by sensor networks reflect various phenomena in buildings and are naturally related to each other. Hence quantitative techniques are required to exploit dependence among different types of sequences in order to allow smart applications such as non-intrusive activity detection, energy usage prediction, demand side management and control. Past research of relational analysis has focused on symmetric correlative statistics. On the other hand, asymmetric causal relations can capture more dynamic and complex relationships and is able to reveal directed influence among series. However, most traditional causal analysis relies on stationarity, while the statistics of real sensor measurement in smart buildings is rarely time invariant. In this paper, a statistical time series analysis framework is proposed to examine causal relationships among time series that are highly non-stationary. The Granger causality identification is extended to sensor data in buildings and the issue of non-stationarity is initially addressed by using modified Hodrick-Prescott (HP) filter which is able to extract simpler trend components. Subsequently, Autoregressive Integrated Moving Average model with exogenous variables (ARIMAX) model is trained for different components of two series. Finally, Granger causality is tested for both directions by F-statistics. The above procedure is performed on actual energy-consumption time series to exploit potential causal relations.