Time series analysis
In this chapter, we introduce the methods and techniques of stochastic time series analysis which we will use for the load forecasting model in the subsequent part of the thesis. Time series analysis appears to be among the most popular approaches to load
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3.1. Dealing with outliers When it comes to analyzing time series, the input data should be checked for missing values and outliers in a first step. The poorer the data is, the more difficult it gets to create an accurate forecast. While single missing hours are not a big deal (as long as the number holds within normal limits), missing days or even weeks can, depending on the data history, cause a loss of information which cannot be compensated. That means the forecast is distorted to a certain extent, leading to a higher forecast error and thus a higher risk. In Germany, a common gap in automatically recorded load data is the missing hour caused by the switch from standard time to daylight saving time. Other missing values could be caused by power outages, for example. However, it depends on the metering hard- and software if these gaps are closed automatically or if it has to be done by hand. A more challenging task is the identification of outliers in a time series. Obviously, the definition of “outliers” or “abnormal load” is quite subjective and depends on the personal opinion and the type of load profile which is considered. For instance, an anomalous load pattern on a particular weekday should not be recorded as an outlier if the weekday is a public holiday. A high level of load on saturday is not abnormal for many customers in retail industry, but it would be remarkable if the customer usually does not work on saturdays. But not only anomalous load sequences are of interest, also “unusual” single (positive or negative) load peaks should be investigated. As K. Berk, Modeling and Forecasting Electricity Demand, BestMasters, DOI 10.1007/978-3-658-08669-5_3, © Springer Fachmedien Wiesbaden 2015
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3. Time series analysis
we already mentioned, load profiles often show hourly peaks due to reasons like machine starting in the morning. The question is, how can we tell these normal load peaks from abnormal ones? 250 200 150 100 50 0 Mo
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Figure 3.1.: Two weeks of load. The weekend between is Easter weekend in Germany with Friday and Monday being public holidays.
Consider the two weeks of load displayed in figure 3.1. Comparing these two weeks without any further information, one could detect three conspicuous features. Most obvious is the low load on Friday and Monday. Given more information, the explanation is quite easy: the weekend between the two weeks is Easter weekend in Germany, i.e. Friday and Monday are public holidays. Another abnormality is the peak on saturday of the first week, which seems to be quite high compared to the corresponding day of week two. This peak comes without any intuitive explanation. It therefore depends on personal assessment if one would refer to it as an outlier or not. Detection of outliers through visual inspection is not an efficient procedure, though. Therefore we need an adequate method for automatic detection. Statistical methods suggest to use moving average or running median filter bands. We will use the running median technique s
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