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Imagine that we collect time series data from a sensor. Due to measurement errors and let's say power outages, there are gaps in the time series that can be quite long. For example if data would be collected in five minute intervals, a two or three hour gap without any collected data is common.

The goal is to estimate the missing values to properly fill the time gaps and thereby reconstruct the time series.

There are some caveats: sometimes the sensor stops working for two hours, then it works again for 10 minutes, collects a few data points and then stops working again for another period. That is, there may be lots of data in a period A where the sensor works, then there is a data collection gap and then in period B only a single or a few data points are collected.

Sketch shows periods where data is collected (red points) and collection gaps (grey). Initial period has lots of data points, then large gap, then only two data points.

From my intuition, splining methods may not be appropriate to fill the gaps in the time series since the time gaps may be quite large and the periods where data is collected may sometimes only contain a single or few data points.

Alternatively, input sequences from periods with lots of data may be formed to predict future values ahead with a prediction model. Since we can be certain, that the sensor starts collecting data at some point in the future again, it may be possible to make use of that future data. That is, it may be useful to instruct the prediction model to predict ahead, knowing that at time t+x there is a collected data point and that the predictions should arrive at that point.

Q1: How can future known target values be incorporated in a prediction model?

Q2: Are there better ways of trying to reconstruct such a time-series than a forecasting model? E.g., would it be possible to use autoencoders to reconstruct the time-series?

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