Statistical anomaly
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The dataset contains two columns : the first column is the month info(represented by the first day of each month), and the second column is the number of passengers(in thousands). In such case, anomalous points are marked by values with irregularly large devivations in the random component, which correspond to unexplained large variations beyond trend and seasonality. In this blog post, we focus on anomaly detection for time-series that can largely be modeled by seasonal decomposition. In contrast, for additive decomposition, values in the random compoent are usually centered around 0, where the value of 0 indicates that the given time-series can be perfectly explained by the addition of its trend and and seasonal components. It should be emphasized that, for multiplicative decomposition, values in the random compnent are usually centered around 1, where the value of 1 means that the original time-series can be perfectly explained by the multiplication of its trend and seasonal components. multiplicative decomposition: X = S * T * R.To be formal, we let X be the given time-series, and S/T/R be its seasonal/trend/random component respectively, then The relation between the original time-series data and its decomposed components in seasonal decomposition can either be additive or multiplicative. the random component contains information that cannot be explained by seasonal and trend components(values assumed to be random, indicating time-independent).the trend component depicts the global shape of the time-series by smoothing/averaging out local variations/seasonal patterns.the seasonl component contains patterns that appears repeatedly between regular time-intervals(i.e.One such technique, also the main interest of this blog post, is seasonal decomposition.īasically, seasonal decomposition decomposes a given time-series into three components: trend, seasonal and random, where: However, with appropriated modeling, a roughly time-indepdent time-series can often be extracted/transformed from the original time-series of interest, in which case statistical tests becomes applicable. In other words, the applicability of statistical tests at least requires time-series data values to be time-independent, yet this is often not guaranteed. Because of this, traditional statististical tests or clustering-based methods for anomaly/outlier usually will fail for time-series data, because the time information of time-series is ignored by their design of nature. The natural association with time brings many unique features to time-series that regular 1D datasets, like time-dependency(via lagging), trend, seasonality, holiday effects, etc. The detection of anomalies from a given time-series is usually not an easy task. How detection of anomalies/outliers is done after seasonal decomposition is applied to the time-series data.
Statistical anomaly how to#
How to apply seasonal decomposition to the time-series data of interest and interpreting the statistics w.r.t.Basically, in this blog post you will learn: The seasonal decomposition method is provided in SAP HANA Predictive Analysis Library(PAL), and wrapped up in the Python Machine Learning Client for SAP HANA(hana_ml). Such time-series usually can be modeled well enough by seasonal-trend decomposition, or seasonal decomposition for simplicity. In this blog post, we will focus on the detection of anomalies/outliers in time-series that can be largely explained by a smoothing trend together with a single seasonal pattern. However, statistical tests for anomaly/outlier detection could become applicable to the time-series data if appropriate modeling is applied. Sometimes the detection of anomalous points in a time-series could be as simple as statistical tests, yet frequently the task will be much more difficult since there is no guarantee that the anomalous points are directly associated with extreme values. In this case, malfunction of the mornitoring system or unexpect local incidents(like fire-accident) can bring sudden changes of AQIs temporarily, causing the obtained values to appear anomalous.
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For example, an air-quality mornitoring system continously measures the air quality around it, and sends out the air-quality-index(AQI) values so we get the time-series of AQIs.
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A time-series is a collection of data points/values ordered by time, often with evenly spaced time-stamps.
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