The HPFUCMSPEC Procedure
CYCLE Statement
CYCLE <options>;
The CYCLE statement is used to specify a cycle component 
in the model. The stochastic equation that governs a cycle component of period p and damping factor 
is as follows:
where 
and 
are independent, zero-mean Gaussian disturbances with variance 
and 
is the angular frequency of the cycle. Any p strictly larger than 2 is an admissible value for the period, and the damping factor can be any value in the interval (0, 1), including 1 but excluding 0. The cycles with the frequency zero and 
, which correspond to the periods equal to infinity and two respectively, can be specified using the AUTOREG statement. The values of smaller than 1 give rise to a stationary cycle, while 
gives rise to a nonstationary cycle. As a default, values of , p, and are estimated from the data. However, if necessary, you can fix the values of some, or all, of these parameters.
There can be multiple cycles in a model, each specified using a separate CYCLE statement. Currently, you can specify up to 50 cycles in a model.
The following examples illustrate the use of the CYCLE statement:
cycle;
cycle;
These statements request that two cycles be included in the model. The parameters of each of these cycles is estimated from the data.
cycle rho=1 noest=rho;
This statement requests inclusion of a nonstationary cycle in the model. The cycle period p and the disturbance variance are estimated from the data. In the following statement a nonstationary cycle with fixed period of 12 is specified. Moreover, a starting value is supplied for .
cycle period=12 rho=1 variance=4 noest=(rho period);
The following options can be specified in the CYCLE statement.
-
NOEST=PERIOD
NOEST=RHO
NOEST=VARIANCE
NOEST= ( <RHO> <PERIOD> <VARIANCE> ) fixes the values of the component parameters to those specified in the RHO=, PERIOD=, and VARIANCE= options. This option enables you to fix any combination of parameter values.
- PERIOD=value
supplies an initial value for the cycle period during the parameter estimation process. Period value must be strictly larger than 2.
- RHO=value
supplies an initial value for the damping factor in this component during the parameter estimation process. Any value in the interval (0, 1), including one but excluding zero, is an acceptable initial value for the damping factor.
- VARIANCE=value
supplies an initial value for the disturbance variance parameter
to be used during the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting value.