TS_GARCH Function [Aggregate]

Used to analyze and forecast volatility in time series data. TS_GARCH computes the estimates of the parameters of a GARCH(p, q) model. GARCH (generalized autoregressive conditional heteroskedasticity) is a generalized model of ARCH; the ARCH computation relates the error variance to the square of a previous period's error.

Syntax

TS_GARCH (timeseries, garch_count, arch_count, xguess_binary_encoding[ , <max_sigma> ] ) 
OVER (window-spec)

Licensing Prerequisites

Available only with RAP – The Trading Edition Enterprise.

Parameters

timeseries_expression – a numeric expression, generally a column name, containing an element in a time series to be differenced.
garch_count – the constant integer number of the p GARCH parameter for the GARCH(p,q) calculation.
arch_count – the constant integer number of the q ARCH parameter for the for the GARCH(p,q) calculation. GARCH count plus ARCH count cannot exceed 9.
xguess_binary_encoding – represents the seed values for the model determination (also known as the xguess array), encoded as a constant binary expression generated by a call to the TS_DOUBLE_ARRAY scalar function. The array has a length of p + q + 1, and contains the initial values for the x parameter used in TS_GARCH_RESULT_USER. The first element (the seed for the sigma squared value) must be a non zero positive double-precision floating point value that is less than the value for max_sigma. The remaining p and q seed values must be double-precision floating point values that are greater than or equal to zero. Their sum must be less than 1.0.
max_sigma – (optional) a constant double precision floating point upper bound on the sigma squared value. Must be a positive value. The default is 10.0.
window-spec – TS_GARCH 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

As an OLAP-style aggregate function, TS_GARCH produces a single SQL result—a specially encoded variable-length binary result value. Supporting scalar functions accept the binary composite output value and return individual scalar result values from it.

Since an OLAP-style aggregate function returns one result value per input tuple, the same binary composite result is returned for each row within a partition. If you do not specify a PARTITION BY clause in the OVER clause, use SELECT FIRST to reduce the results to a single tuple containing the binary composite result. If you do specify a PARTITION BY clause in the OVER clause, use SELECT DISTINCT to eliminate all but one tuple per partition.

IMSL Mapping

Mapping to the parameters of the IMSL C functions in the external VNI library is performed by TS_GARCH_RESULT supporting scalar functions.

Example

This example computes a GARCH(1,2) model independently for the stock price for each of four specified companies stock prices. The query then uses the DISTINCT qualifier to reduce the set of tuples to one tuple per stock symbol. Finally, one output row is returned containing the stock symbol and all the relevant information describing the GARCH(1,2) model computed for that stock.

The second and third arguments to the TS_GARCH function are the p and q values specifying the GARCH(p,q) type of model is to be used. These values must be positive integer constants or constant expressions.

The fourth argument is the set of seed values for determining the GARCH(p,q) model encoded as a binary constant expression that must be generated via the supporting scalar function TS_DOUBLE_ARRAY.

select stock_symbol,
	TS_GARCH_RESULT_A( garch_res ) as log_likelihood, 
	TS_GARCH_RESULT_AIC( garch_res ) as akaike_info, 
	TS_GARCH_RESULT_USER( garch_res, 1) as sigma_squared, 
	TS_GARCH_RESULT_USER( garch_res, 2) as q_1,
	TS_GARCH_RESULT_USER( garch_res, 3) as p_1,
	TS_GARCH_RESULT_USER( garch_res, 4) as p_2
from ( select distinct 
		 stock_symbol,
		 TS_GARCH(stock_price, 1, 2,
			   TS_DOUBLE_ARRAY(1.2, 0.3, 0.2, 0.3), 4) 
		    over (partition by stock_symbol 
				    order by stock_trade_time) as garch_res
	from stock_trades
	where stock_symbol in (‘XYZ’, XZZ’, ‘ZXZ’, ‘ZZZ’)
	as dt1

Standards and Compatibility

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