public double GetSlopeConfidenceInterval(double alpha)
{
if (this.n < 3L)
{
return(Double.NaN);
}
if ((alpha >= 1.0D) || (alpha <= 0.0D))
{
// throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL, Double.valueOf(alpha), Integer.valueOf(0), Integer.valueOf(1));
}
TDistribution distribution = new TDistribution(this.n - 2L);
return(GetSlopeStdErr() * distribution.inverseCumulativeProbability(1.0D - alpha / 2.0D));
}
/// <summary>
/// Args:
/// #' series: Time series to perform anomaly detection on.
/// #' max_Anoms: Maximum number of anomalies that S-H-ESD will detect as a percentage of the data.
/// #' alpha: The level of statistical significance with which to accept or reject anomalies.
/// #' num_obs_per_period: Defines the number of observations in a single period, and used during seasonal decomposition.
/// #' Returns:
/// #' A list containing the anomalies (anoms) and decomposition components (stl).
/// </summary>
private ANOMSResult detectAnoms(long[] timestamps, double[] series)
{
if (series == null || series.Length < 1)
{
throw new System.ArgumentException("must supply period length for time series decomposition");
}
int numberOfObservations = series.Length;
/// <summary>
/// use StlDec function
/// first interpolation to solve problem data to much
/// </summary>
// -- Step 1: Decompose data. This returns a univariate remainder which will be used for anomaly detection. Optionally, we might NOT decompose.
STLResult data = removeSeasonality(timestamps, series, config.NumObsPerPeriod);
double[] data_trend = data.Trend;
double[] data_seasonal = data.Seasonal;
// Mean mean = new Mean();
// Variance variance = new Variance();
// Median median = new Median();
// Remove the seasonal component, and the median of the data to create the univariate remainder
double[] dataForSHESD = new double[numberOfObservations];
double[] dataDecomp = new double[numberOfObservations];
QuickMedians quickMedian = new QuickMedians(series);
double medianOfSeries = quickMedian.Median; //median.evaluate(series);
// if the data of has no seasonality, directed use the raw_data into function S-H-ESD !!!
for (int i = 0; i < numberOfObservations; ++i)
{
dataForSHESD[i] = series[i] - data_seasonal[i] - medianOfSeries;
dataDecomp[i] = data_trend[i] + data_seasonal[i];
}
// Maximum number of outliers that S-H-ESD can detect (e.g. 49% of data)
int maxOutliers = (int)Math.Round(numberOfObservations * config.MaxAnoms);
if (maxOutliers == 0)
{
throw new System.ArgumentException("You have " + numberOfObservations + " observations in a period, which is too few. Set a higher value");
}
long[] anomsIdx = new long[maxOutliers];
double[] anomsSc = new double[maxOutliers];
int numAnoms = 0;
OnlineNormalStatistics stat = new OnlineNormalStatistics(dataForSHESD);
QuickMedians quickMedian1 = new QuickMedians(dataForSHESD);
double dataMean = stat.Mean; //mean.evaluate(dataForSHESD);
double dataMedian = quickMedian1.Median; //median.evaluate(dataForSHESD);
// use mad replace the variance
// double dataStd = Math.sqrt(stat.getPopulationVariance());//Math.sqrt(variance.evaluate(dataForSHESD));
double[] tempDataForMad = new double[numberOfObservations];
for (int i = 0; i < numberOfObservations; ++i)
{
tempDataForMad[i] = Math.Abs(dataForSHESD[i] - dataMedian);
}
QuickMedians quickMedian2 = new QuickMedians(tempDataForMad);
double dataStd = quickMedian2.Median;
if (Math.Abs(dataStd) <= 1e-10)
{
//return null;
throw new System.ArgumentException("The variance of the series data is zero");
}
double[] ares = new double[numberOfObservations];
for (int i = 0; i < numberOfObservations; ++i)
{
ares[i] = Math.Abs(dataForSHESD[i] - dataMedian);
ares[i] /= dataStd;
}
// here use std for the following iterative calculate datastd
dataStd = Math.Sqrt(stat.PopulationVariance);
int[] aresOrder = getOrder(ares);
int medianIndex = numberOfObservations / 2;
int left = 0, right = numberOfObservations - 1;
int currentLen = numberOfObservations, tempMaxIdx = 0;
double R = 0.0, p = 0.0;
for (int outlierIdx = 1; outlierIdx <= maxOutliers; ++outlierIdx)
{
p = 1.0 - config.Alpha / (2 * (numberOfObservations - outlierIdx + 1));
TDistribution tDistribution = new TDistribution(numberOfObservations - outlierIdx - 1);
double t = tDistribution.inverseCumulativeProbability(p);
double lambdaCritical = t * (numberOfObservations - outlierIdx) / Math.Sqrt((numberOfObservations - outlierIdx - 1 + t * t) * (numberOfObservations - outlierIdx + 1));
if (left >= right)
{
break;
}
if (currentLen < 1)
{
break;
}
// remove the largest
if (Math.Abs(dataForSHESD[aresOrder[left]] - dataMedian) > Math.Abs(dataForSHESD[aresOrder[right]] - dataMedian))
{
tempMaxIdx = aresOrder[left];
++left;
++medianIndex;
}
else
{
tempMaxIdx = aresOrder[right];
--right;
--medianIndex;
}
// get the R
R = Math.Abs((dataForSHESD[tempMaxIdx] - dataMedian) / dataStd);
// recalculate the dataMean and dataStd
dataStd = Math.Sqrt(((currentLen - 1) * (dataStd * dataStd + dataMean * dataMean) - dataForSHESD[tempMaxIdx] * dataForSHESD[tempMaxIdx] - ((currentLen - 1) * dataMean - dataForSHESD[tempMaxIdx]) * ((currentLen - 1) * dataMean - dataForSHESD[tempMaxIdx]) / (currentLen - 2)) / (currentLen - 2));
dataMean = (dataMean * currentLen - dataForSHESD[tempMaxIdx]) / (currentLen - 1);
dataMedian = dataForSHESD[aresOrder[medianIndex]];
--currentLen;
// record the index
anomsIdx[outlierIdx - 1] = tempMaxIdx;
anomsSc[outlierIdx - 1] = R;
if (R < lambdaCritical * config.AnomsThreshold || double.IsNaN(dataStd) || Math.Abs(dataStd) <= 1e-10)
{
break;
}
numAnoms = outlierIdx;
}
if (numAnoms > 0)
{
List <Pair> map = new List <Pair>();
for (int i = 0; i < numAnoms; ++i)
{
map.Add(new Pair(this, (int)anomsIdx[i], anomsSc[i]));
}
map.Sort(new PairKeyComparator(this));
long[] idx = new long[numAnoms];
double[] anoms = new double[numAnoms];
for (int i = 0; i < numAnoms; ++i)
{
idx[i] = map[i].key;
anoms[i] = map[i].value;
}
return(new ANOMSResult(this, idx, anoms, dataDecomp));
}
else
{
return(null);
}
}