I am in need of Clarification about the Mean & Variance Stationary for time series data..
I was reading this discussion about the importance of Stationary https://stats.stackexchange.com/questions/253917/why-use-differencing-and-box-cox-in-time-series.. that @Michael R. Chernick clarify atmost that ARIMA model may need to model a Clean time series from Nonstationary in every aspects (which is Differencing and Box-Cox Transformations),
and later I want to apply forecasting with Prophet and ETS (Exponential Smoothing Space Model).. which this article helps give insight to do it https://mode.com/example-gallery/forecasting_prophet_r_cookbook/
I noticed that the article did apply only Box-Cox Transformation on data, and then do a inverse Box-Cox Transformation after the forecast applied.
So my question:
1) I recall using UKgas data from datasets library, this is the results of Dickey Fuller test after Box Cox Transformation
library(tseries) library(forecast) library(prophet) library(datasets) data(UKgas) lambda <- BoxCox.lambda(na.contiguous(UKgas)) print(paste("Lambda = ", lambda)) "Lambda = -0.445702282821823" UKgas_transform_1 <- BoxCox(UKgas,lambda) adf.test(UKgas_transform_1) Augmented Dickey-Fuller Test data: UKgas_transform_1 Dickey-Fuller = -1.0813, Lag order = 4, p-value = 0.9218 alternative hypothesis: stationary
with high of p-values, the test implies that it may have unit root in the data after Box-Cox Transformations. So can this data be applied to other kind of forecast instead ARIMA?
2) if it cannot be applied, I may need to Difference the data again right? after the prediction done, so how to revert back the forecast data to actual data if I use both Differences and Box Cox Transformations?
Thank You in advance, Correct me also if my understanding are incorrect :)