Suppose we have different candidate models proposed for a time series based on ACF and PACF. Now the basic equation has the white noise term. In MATLAB, u have "randn" command to generate normal random numbers. The parameters can be estimated from "armax" command.
After parameter estimation (calibration), the validation involves comparing the observed data with the predicted values. Now the problem which I m facing is that figuring out whether the white noise should be generated of what length (data length or a bigger population). Secondly, the white noise sequence should be preserved for all candidate model validation or subject to change? If they are changed, then the performance indicators such as RMSE, ML, AIC, BIC will also change.
So what should i do?
i have no clear direct answer however if random provider proceeds by taking provided value back into matrix for future random provisions,it is effectively infinite , so using new random matrix is superfluous.Data length provision usual, but could try several lengths
and see if it matters, doubt it. if you do not preserve sequence for candidate model validation your performance indicators may well change. then you could conduct a sensitivity analysis by repetition ,and see if that matters.
I'd say that if your sample size / number of repetitions is small enough that you're worried about dramatic shifts in your summary statistics, then you should be looking at doing ensemble-type runs to ensure that you are in the realm of suitably-sized numbers. I would assume that you would want your results to be robust enough that they are reproducible without specifying your RNG scheme or seed.
data length or a bigger population? - data length;
the white noise sequence should be preserved for all candidate model validation or subject to change? - I do believe, that you need to do that for each sequence of numbers
Stochastic processes are nondeterministic dynamical processes passible of being described by mathematically supported models that typically include a significant contribute from random variable(s) along with their encompassing statistics theory. A conceptual observer monitoring such a system may acquire a time series of data which describes the stochastic process, hence the stochastic system dynamics. Time series of data can also be acquired by monitoring deterministic dynamical processes.
Application example relying on numerically generated Gaussian white noise ― While investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the recursive least squares algorithm (RLS) with forgetting factor (RLS-FF) to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...
Saving the generated set of random numbers or its seed is a critical step in ensuring the reliability of stochastic modeling results. It can help you reproduce results, perform model validation, and sensitivity analysis. If you don't save this data, you run the risk of not being able to validate the model's performance, especially if the model results are sensitive to randomness.
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