General questions fpp3, fable and tidyverts


I have general questions regarding fpp3/tidyverts:

[1] For the 4 simple methods: mean, naive, snaive and rw_drift in 5.2 Some simple forecasting methods | Forecasting: Principles and Practice (3rd ed)
(a) Can all 4 simple methods be estimated/used with ANY series, e.g. rawdata as is: no transformations, no differencing?
(b) For all 4 simple methods are bootstrap PI's applicable to ANY series? 5.5 Distributional forecasts and prediction intervals | Forecasting: Principles and Practice (3rd ed)

[2] Are bootstrap forecasts valid for ARIMA models including MA terms, as in 9.8 Forecasting | Forecasting: Principles and Practice (3rd ed) ? I have read elsewhere, that simple shuffling of residuals is NOT completely appropriate for a model with MA terms for an entire sample.

[3] Non-Gaussian forecasting using fable is described in: Rob J Hyndman - Non-Gaussian forecasting using fable.
Non-normality within the modelling framework arises due to,
(a) transformations: normal if no transformation used, non-normal if transformation applied i.e. box-cox.
(b) non-normality of residuals.
Are there any other sources of non-normality?

For forecasting in COMBINATION and ENSEMBLE models:
(i) COMBINATION: if both (a) and (b) are normal, use either simulate or bootstrap, or none i.e. simulate = FALSE, bootstrap = FALSE.
(ii) COMBINATION : if either (a) or (b) are non-normal, NOT use simulate as that draws from independent N(0,sigmasq) shocks over the forecast period i.e. NOT use fabletools:::forecast.model_combination() as this applies the formula Var(aX + bY), based on the normality assumption. Likewise, NOT use bootstrap.
(iii) ENSEMBLE: if both (a) and (b) are normal, use either simulate or bootstrap, or none i.e. simulate = FALSE, bootstrap = FALSE.
(iv) ENSEMBLE: if either (a) or (b) are non-normal, use bootstrap as these are more representative of the series, NOT use simulate as that draws from independent N(0,sigmasq).


Further, if [2] is true i.e. I cannot bootstrap forecasts from an ARIMA model, can I mix an ETS with bootstrap forecasts and an ARIMA with no shocks, in an ENSEMBLE? If so how?

[4] Formal normality tests, used for residuals, are NOT included in tidyverts. Why? However, in R there are:
etc, etc

Importantly, which test is the most appropriate/recommended for use with fable (e.g. Jarque-Bera tends to be sensitive) as this will determine whether to bootstrap PI's or not?

[5] Seasonal Characteristic Roots:
I understand non-seasonal characteristic roots, but am confused with seasonal characteristic roots.

In Forecasting Methods,3e, by Makridakis, Wheelwright, and Hyndman p.346, specification ARIMA(1,1,1)(1,1,1)[4], quarterly data, it's simple to multiply out the factors, but the general model has 8 AR terms at lags 1,2,4,5,6,8,9 and 10 (implying 8 roots) and 3 MA lagged terms at 1,4,5 (implying 3 roots).

Based on, Rob J Hyndman - Plotting the characteristic roots for ARIMA models plotting an ARIMA(1,1,1)(1,1,1)[4] should have 5 AR roots and 5 MA roots. Yet, for an ARIMA(1,1,1)(1,1,1)[4] there are only 2 AR coeffs (1 non-seasonal, 1 seasonal) and 2 MA coeffs (1 non-seasonal, 1 seasonal), implying 2 AR roots and 2 MA roots. Please can a BY-HAND example be provided, algebraically and in fable, as to why?

many thanks,

This topic was automatically closed 21 days after the last reply. New replies are no longer allowed.

If you have a query related to it or one of the replies, start a new topic and refer back with a link.