Outliers detection using Tramo

Tramo is an efficient tool for the detection of outliers. We describe below the steps for processing an automatic outliers detection and for analysing the likelihood of the last observation(s) (TERROR-like).

Outliers detection.

Creation and initialisation of the specification (enabling the OutliersDetection sub-entity) .
Execution of the processing
Retrieval of the outliers

Predefined outliers are:

AO: additive outlier
LS: level shift
TC: transitory change
SO: seasonal outlier
DO: displacement outlier (shift between two adjacent periods).

Note that it is also possible to define new kinds of outliers (see User-defined outliers detection)

Check of the last observation(s).

Creation and initialisation of the specification (enabling the OutliersDetection sub-entity) .
Truncation of the series
Execution of the processing on the truncated series
Retrieval of the forecasts, and comparison between the observed value and of the predicted value (relatively to the prediction error).

C#:

References:

NbbUtilities.dll

NbbTs.dll

NbbTramoSeats.dll

Code:

using Nbb.TimeSeries.SimpleTS;
using Nbb.TramoSeats;

...

// External trade statistics: exports
double[] data =
{
    9568.3,9920.3,11353.5,9247.5,10114.2,10763.1,8456.1,8071.6,10328,10551.4,10186.1,8821.6,
    9841.3,10233.6,10794.6,10289.3,10513.4,10607.6,9707.4,8103.5,10982.6,11836.9,10517.5,9810.5,
    10374.8,10855.3,11671.3,11901.2,10846.4,11917.5,11362.8,9314.5,12605.9,12815.1,11254.5,11111.8,
    11282.9,11554.5,12935.6,12146.3,11615.3,13214.8,11735.5,9522.3,12694.8,12317.6,11450,11380.9,
    10604.6,10972.2,13331.5,11733.1,11284.7,13295.8,11881.4,10374.2,13828,13490.5,13092.2,13184.4,
    12398.4,13882.3,15861.5,13286.1,15634.9,14211,13646.8,12224.6,15916.4,16535.9,15796,14418.6,
    15044.5,14944.2,16754.8,14254,15454.9,15644.8,14568.3,12520.2,14803,15873.2,14755.3,12875.1,
    14291.1,14205.3,15859.4,15258.9,15498.6,15106.5,15023.6,12083,15761.3,16943,15070.3,13659.6,
    14768.9,14725.1,15998.1,15370.6,14956.9,15469.7,15101.8,11703.7,16283.6,16726.5,14968.9,14861,
    14583.3,15305.8,17903.9,16379.4,15420.3,17870.5,15912.8,13866.5,17823.2,17872,17420.4,16704.4,
    15991.5,16583.6,19123.4,17838.8,17335.3,19026.9,16428.6,15337.4,19379.8,18070.5,19563,18190.6,
    17658,18437.9,21510.4,17111,19732.7,20221.8
};

TS series = new TS(TSFrequency.Monthly, 1995, 0, data);

// Creation of the specification.
TramoSpecification spec = new TramoSpecification();
// Initialisation of the OutliersDetection part.
spec.OutliersDetection.AO = true;
spec.OutliersDetection.LS = true;
spec.OutliersDetection.SO = true;
// The threshold for the outliers detection, as defined in Tramo. Set to 0 to use the predefined value, that depends on the length of the series)
spec.OutliersDetection.VA = 3;

// Other initialisation... (for instance)
spec.ModelIdentification.IsEnabled = true;

Tramo tramo = new Tramo();
tramo.Specification = spec;
tramo.Process(series);

// iterating through the outliers collection
foreach (OutlierEstimation outlier in tramo.OutliersEstimation())
{
    String desc = outlier.Code;
    TSPeriod period = series.Domain[outlier.Position];
    double value = outlier.Value;
    double tstat = outlier.TStat;
}

// TERROR-like.
// drop the last n observations
int n = 3;
TS truncatedseries = series.Drop(0, 3);
tramo.Process(truncatedseries);

// drop the last n observations
TramoForecast fcast=tramo.Forecast(n);

for (int i = 0; i < n; ++i)
{
    double lastobs = series[series.Domain.Count - n + i];

    if (tramo.UsedSpecification.Transformation.Option == DataTransformation.Log)
        lastobs = Math.Log(lastobs);

    // relative prediction error
    double error = (lastobs - fcast.Forecast(i)) / fcast.ForecastStdev(i);
}