How to run multiplicative winters and what does "run simulation" do when we run it using JMP
I'm going to post a little different question here, and a response that I found helpful in understanding what the simulator does.
How does JMP simulate a time series model?
JMP simulates possible trajectories of future time series using fixed parameters and random noise.
Maybe something a little less abstract:
lets say I run an 1,1,1 ARIMA on Log Passengers from seriesg.jmp
And then save the prediction formula
ARIMA Forecast(
:Actual Log Passengers,
144,
ARIMA( 1, 1, 1 ),
{AR Coefficients( {-0.582604336951054} ),
MA Coefficients( {-0.850222562210878} ), Intercept( 0.00425609524103588 )},
Row() - 144,
Row() - 144
);
Does simulate use this expression to simulate k periods?
What effect does the seed have? (is it just a random seed?)
Where does the random noise get added?
For this example, the expression of the model is
and
- y 's are observed time series data with time indices as subscripts.
- Capital B’s are so called backward operators.
- Lower cases a’s are JMP doc notations of noises, indexed by time as well.
The general form is in the “Statistical Details for ARIMA Models” in the documentation.
The platform reports parameter estimates of the models in that general form.
A non-expert friendly form of the above model is ,
where beta’s involve additional calculations of the parameter estimates from the above model. JMP does NOT report this parameterization.
For ARIMA Forecast JSL, the calculation only needs,
by making all a’s zeros, i.e. the expectation of noises are zeros.
For simulation, the calculation needs,
and needs simulated values for a’s. Each seed will generate different series of a’s.
(huge shout out to Peng Liu for help here)
Thanks Byron, my question is what kind of simulation is run? MCMC etc? Its a black box right now...want to understand some details around what happens when I click that button run 1 simulation for 10 time periods with a seed of 100, what does it do if I am using a ARMA(1,1) model.
From the Model Comparison help:
Simulate Once Provides one simulation of the model out k time periods. The simulation is shown on the Model Comparison time series plot. To change k, use the Number of Forecast Periods option in the Time Series red triangle.
