Automatic Time Series Modeling Package

When you specify the 'ARIMA' method for an OUTLIER instance, you can use two methods to add ARIMA models to the instance:

Add predefined models: You can use the SetArima('MODEL', Value) method to add predefined models. Value is a string array in which each element of the array can contain one of the model names from Table 64. For each model name, you can also use the name from the Alias1 or Alias2 column. For example, the following code adds the AIRLINE, ARIMA011100NOINT, and ARIMA200100 models to the OUTLIER instance named "outlier":

array models[3] $ 20 / nosymbols;
models[1] = 'AIRLINE';
models[2] = '_PSD1Q1';
models[3] = '_A5';
declare object outlier(OUTLIER);
outlier.SetOption('METHOD','ARIMA');
outlier.SetArima('MODEL', models);

Add a custom ARIMA model: You can define your own ARIMA model structure by using the ARIMASPEC object in the Time Series Models (TSM) package and add it by using the AddFrom() method. For example, the following code adds a custom ARIMA model:

array ar[2]     / nosymbols;
ar[1] = 2;
ar[2] = 24;
array ma[1]     / nosymbols;
ma[1] = 1;
array diff[2]   / nosymbols;
diff[1] = 1;
diff[2] = 12;

declare object myARIMA(arimaspec);

rc = myARIMA.Open();
rc = myARIMA.AddARPoly(ar);
rc = myARIMA.AddMAPoly(ma);
rc = myARIMA.AddMAPoly(ma,,1);
rc = myARIMA.SetDiff(diff);
rc = myARIMA.SetOption('noint', 1);
rc = myARIMA.Close();
...
declare object outlier(OUTLIER);
...
rc = outlier.addFrom(myARIMA);

Table 64 shows the lists of the predefined ARIMA models.

When you specify multiple ARIMA candidate models for the OUTLIER object, the OUTLIER object fits all those models. You can use the 'USEBEST' option to control which of the successful candidates the OUTLIER object uses to detect and report outliers. The following list describes the behavior for each possible 'USEBEST' setting:

The Hampel identifier, also known as the Hampel filter, determines whether an observation is an outlier by comparing its absolute deviation from the median to a configurable multiple of standard deviation, which is computed by using the median absolute deviation (MAD).

MAD is defined as the median of the absolute deviations from the data’s median. Formally, for a data set that contains the observations , let m denote the median. Then, MAD is defined as

MAD = median

The Hampel filter uses a sliding window of configurable size to go over the input data to calculate the MAD for each window. You can set the size as follows:

rc=obj.SetHampel('WIDTH', Value);

Each observation has a window centered on it. The window size is 2 * Value + 1.

The Hampel-based outlier detection method calculates the MAD and uses it as follows to compute a consistent estimate of the standard deviation :

= MAD

where is a constant scale factor, which depends on the distribution. Five distributions are supported; you can specify which one to use by setting the 'DISTRIBUTION' option in the SetHampel method:

rc=obj.SetHampel('DISTRIBUTION', Value);

The distributions and corresponding scale factors k for each possible Value are shown in Table 65.

The Hampel filter declares an observation to be an outlier if that observation differs from the window median by more than a configurable number of standard deviations. Let w be the width of the window that is centered around observation . For each observation , the main steps of the outlier detection algorithm are as follows: