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Time Series Functions

Below functions are used for series data analysis.

seriesOutliersDetectTukey

Detects outliers in series data using Tukey Fences.

Syntax

seriesOutliersDetectTukey(series);
seriesOutliersDetectTukey(series, min_percentile, max_percentile, K);

Arguments

  • series - An array of numeric values.
  • min_percentile - The minimum percentile to be used to calculate inter-quantile range (IQR). The value must be in range [2,98]. The default is 25.
  • max_percentile - The maximum percentile to be used to calculate inter-quantile range (IQR). The value must be in range [2,98]. The default is 75.
  • K - Non-negative constant value to detect mild or stronger outliers. The default value is 1.5.

At least four data points are required in series to detect outliers.

Returned value

  • Returns an array of the same length as the input array where each value represents score of possible anomaly of corresponding element in the series. A non-zero score indicates a possible anomaly.

Type: Array.

Examples

Query:

SELECT seriesOutliersDetectTukey([-3, 2, 15, 3, 5, 6, 4, 5, 12, 45, 12, 3, 3, 4, 5, 6]) AS print_0;

Result:

┌───────────print_0─────────────────┐
│[0,0,0,0,0,0,0,0,0,27,0,0,0,0,0,0] │
└───────────────────────────────────┘

Query:

SELECT seriesOutliersDetectTukey([-3, 2, 15, 3, 5, 6, 4.50, 5, 12, 45, 12, 3.40, 3, 4, 5, 6], 20, 80, 1.5) AS print_0;

Result:

┌─print_0──────────────────────────────┐
│ [0,0,0,0,0,0,0,0,0,19.5,0,0,0,0,0,0] │
└──────────────────────────────────────┘

seriesPeriodDetectFFT

Finds the period of the given series data data using FFT FFT - Fast Fourier transform

Syntax

seriesPeriodDetectFFT(series);

Arguments

  • series - An array of numeric values

Returned value

  • A real value equal to the period of series data
  • Returns NAN when number of data points are less than four.

Type: Float64.

Examples

Query:

SELECT seriesPeriodDetectFFT([1, 4, 6, 1, 4, 6, 1, 4, 6, 1, 4, 6, 1, 4, 6, 1, 4, 6, 1, 4, 6]) AS print_0;

Result:

┌───────────print_0──────┐
│ 3 │
└────────────────────────┘
SELECT seriesPeriodDetectFFT(arrayMap(x -> abs((x % 6) - 3), range(1000))) AS print_0;

Result:

┌─print_0─┐
│ 6 │
└─────────┘

seriesDecomposeSTL

Decomposes a series data using STL (Seasonal-Trend Decomposition Procedure Based on Loess) into a season, a trend and a residual component.

Syntax

seriesDecomposeSTL(series, period);

Arguments

  • series - An array of numeric values
  • period - A positive integer

The number of data points in series should be at least twice the value of period.

Returned value

  • An array of four arrays where the first array include seasonal components, the second array - trend, the third array - residue component, and the fourth array - baseline(seasonal + trend) component.

Type: Array.

Examples

Query:

SELECT seriesDecomposeSTL([10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34], 3) AS print_0;

Result:

┌───────────print_0──────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ [[
-13.529999, -3.1799996, 16.71, -13.53, -3.1799996, 16.71, -13.53, -3.1799996,
16.71, -13.530001, -3.18, 16.710001, -13.530001, -3.1800003, 16.710001, -13.530001,
-3.1800003, 16.710001, -13.530001, -3.1799994, 16.71, -13.529999, -3.1799994, 16.709997
],
[
23.63, 23.63, 23.630003, 23.630001, 23.630001, 23.630001, 23.630001, 23.630001,
23.630001, 23.630001, 23.630001, 23.63, 23.630001, 23.630001, 23.63, 23.630001,
23.630001, 23.63, 23.630001, 23.630001, 23.630001, 23.630001, 23.630001, 23.630003
],
[
0, 0.0000019073486, -0.0000019073486, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.0000019073486, 0,
0
],
[
10.1, 20.449999, 40.340004, 10.100001, 20.45, 40.34, 10.100001, 20.45, 40.34, 10.1, 20.45, 40.34,
10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.1, 20.45, 40.34, 10.100002, 20.45, 40.34
]] │
└────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘