Aggregation of asynchronous electric power consumption time series knowing the integral

More and more data mining algorithms are applied to a large number of long time series issued by many distributed sensors. The consequence of the huge volume of data is that data warehouses often contain asynchronous time series, i.e. the values have been sampled and are not anymore observed at the same instants. This is a problem when applying data mining algorithms to such asynchronous time series. The standard way to solve this problem is to interpolate intermediate points. We present here two new interpolation approaches which take into account the knowledge of the integral of the time series between two points. The first approach is naive and uses the history of slope values. The second approach is stochastic and provides a confidence interval of interpolated values. The two methods have been assessed experimentally on a real dataset of electric power consumption time series issued from smart meters.