# 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 [0.02,0.98]. The default is 0.25.
• max_percentile - The maximum percentile to be used to calculate inter-quantile range (IQR). The value must be in range [0.02,0.98]. The default is 0.75.
• 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. 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], 0.2, 0.8, 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. NaN when number of data points are less than four. 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. 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    ]]                                                                                                                   │└────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘