TS_AUTO_ARIMA_OUTLIER Function [Aggregate]

Syntax

TS_AUTO_ARIMA_OUTLIER( <time_value>, <timeseries_expression>              [ , <max_lag> [ , <critical	>              [ , <epsilon> [ , <criterion>              [ , <confidence> [, <model> [ , <delta>]]]]]]] )
OVER (window-spec)

Licensing Prerequisites

Available only with RAP – The Trading Edition Enterprise.

Parameters

• time_value – the time value for each input time-series data point.
• timeseries_expression – a numeric expression, generally a column name, containing an element in a time series to be differenced.
• max_lag – (optional) represents the maximum lag allowed when fitting an AR(p) model. Must be a positive integer constant or constant expression. The default is 10.
• critical – (optional) critical value used as a threshold for outlier detection. The value must be greater than 0, and must be a double-precision floating point constant or constant expression. The default is 3.0.
• epsilon – (optional) positive tolerance value controlling the accuracy of parameter estimates during outlier detection. Must be a double-precision floating point constant or constant expression. The default is 0.001.
• criterion – (optional) the information criterion used for optimum model selection. Must be an integer constant or constant expression valued at 0, 1, or 2. The default is 0.
  

  • 0 – (default) Akaike's Information Criterion (AIC)

  • 1 – Akaike's Corrected Information Criterion (AICC)

  • 2 – Bayesian Information Criterion (BIC)

• confidence – (optional) confidence level for computing forecast confidence limits, taken from the exclusive interval (0, 100). Typical choices for confidence are 90.0, 95.0, and 99.0. Must be a double-precision floating point constant or constant expression. The default is 95.0.
• delta – (optional) the dampening effect parameter used in the detection of a temporary change outlier. Must be a double-precision floating point constant or constant expression. The default is 0.7.
• model – (optional) represents a binary-encoded integer array, with a length of four integers, containing the ARIMA values for p, q, s, and d, in that order. If the model argument is specified in the TS_INT_ARRAY function, then the TS_AUTO_ARIMA_OUTLIER function determines the p, q, s, and d, values using the method 3 (Specified ARIMA) parameter of the (IMSLS_METHOD, int method) argument of the imsls_d_auto_arima function in the IMSL library. If the model parameter is NULL, then the TS_AUTO_ARIMA_OUTLIER function automatically calculates an ARIMA(p,0,0)X(0,d,0) model, which minimizes the specified error criterion. The default is NULL.
• window-spec – TS_AUTO_ARIMA_OUTLIER is an OLAP function requiring an OVER() clause containing an ORDER BY clause. ROWS or RANGE specifiers are not allowed in the OVER() clause

Usage

The inputs to TS_AUTO_ARIMA and TS_AUTO_ARIMA_OUTLIER are nearly identical. However, TS_AUTO_ARIMA_OUTLIER returns different values for each input row within a partition, while TS_AUTO_ARIMA returns the same value for every row. Because of these differences in result data type and result value scoping, you need not use SELECT FIRST or SELECT DISTINCT to eliminate the duplicate output values. TS_AUTO_ARIMA_OUTLIER does not have any supporting scalar functions for decoding results.

Like TS_AUTO_ARIMA, TS_AUTO_ARIMA_OUTLIER requires the TS_INT_ARRAY supporting scalar function. TS_INT_ARRAY provides the binary composite input.

The function returns an integer value for each input tuple, specifying the type of outlier for the time and data value within each tuple. If the time and data value is not an outlier, the function returns NULL. The integer values are:

• 0 – innovational outlier (IO).
• 1 – additive outlier (AO).
• 2 – level shift (LS).
• 3 – temporary change (TC).
• 4 – unable to identify (UI).

See IMSL C Numerical Library User’s Guide: Volume 2 of 2 C Stat Library for detailed information on the five outlier types.

IMSL Mapping

Maps to the outlier identification logic of imsls_d_auto_arima.

Example

This example computes the ARIMA model for the time series of the stock prices for XYZ, and then uses that model to identify which of the trades are statistical outliers. For rows which are not identified as outliers, TS_AUTO_ARIMA_OUTLIER returns NULL. For rows which are identified as outliers, TS_AUTO_ARIMA_OUTLIER returns an integer value between 0 and 4 representing the specific type of outlier for the current row.

select stock_trade_time,
	stock_price,
	stock_trade_shares,
	TS_AUTO_ARIMA_OUTLIER(stock_trade_time,
	stock_price) 
		over (order by stock_trade_time) as outlier_type
from stock_trades
where stock_symbol = 'XYZ'

Standards and Compatibility

• SQL – ISO/ANSI SQL compliant
• Sybase – not compatible with SQL Anywhere or Adaptive Server Enterprise

See Also