generate/simulate a single time series which "nests" several ARIMA(p,d,q) models

Machine Learning and Modeling
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Hi,

Using gratis Introduction to gratis, or otherwise, is it possible to generate/simulate a single time series which "nests" several ARIMA(p,d,q) models i.e. where those are easily estimated?

Also is there a "classic" time series known to fit well to several ARIMA(p,d,q) (and ETS) models?

Amarjit

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  1. I don't know what you mean by a time series nesting a model, or several models. You can generate data from an ARIMA model using the gratis package. You can then easily estimate an ARIMA model from the generated data using the forecast or fable packages.
  2. The AirPassengers data was famously modelled by an ARIMA(0,1,1) process by Box & Jenkins. An ARIMA(0,1,1) is sometimes called the "airline" model for that reason. Other examples of time series that are well estimated by ARIMA and ETS models are found in my textbook at Forecasting: Principles and Practice (3rd ed).
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I mean generate/simulate several time series, aggregate them (somehow) into a single, and estimate very good fits to all the individual, maybe even retrieve the coefficients of the individuals from the single.

All your textbooks are brilliant and strongly recommended. My question is: what "classic" time series (for (a) non-seasonal, and (b) seasonal) are known to fit to lots of time series models?