stats::arima() estimates $\sigma^2$ using the MLE of the innovations variance, while forecast::Arima() uses the unbiased estimate $\sum e_i^2/(n-k)$ where $n$ is the number of observations available and $k$ is the number of parameters estimated.
stats::arima() does not count $\sigma^2$ as a parameter in the computation of the AIC, whereas forecast::Arima() ...
A regression model with ARIMA errors is estimated using maximum likelihood estimation. It will give different results from estimating a regression model using least squares estimation because the optimization criterion is different.
There was a bug in the fable package for computing regression residuals. Now fixed in the github version (https://github.com/...
You can define the following process:
Assuming an initial condition $Y_0=0$ for simplicity, recursive substitution yields
a so-called random walk with drift.
We always have autocorrelation. However, original ARMA model assumes white noise; so, the autocorrelation is dirac-delta function, i.e. $\delta_k=0$, if $k\neq0$. If whiteness is violated, it'd modify the original model and require a different analytical treatment. In other words, if an ARMA model in a statistical toolbox/or library allows autocorrelated ...
There are two questions in your post:
How do ARMA and ARMA-GARCH models relate?
Why do the AR coefficients differ?
The first question is answered extensively here.
The second has been discussed multiple times, see e.g. these threads. The basic insight is that the parameter estimates of the conditional mean part are related to the those of the ...
t tests require not only constant variance BUT independent observations ...thus they are not recommended/appropriate for time series data. I took ACCOUNT3 and analyzed it with the intent of not only dealing with memory (arima) but latent deterministic structure ... thus empirically detecting the fixed effects that might be present . 9 data points is a ...
Since my similar question was flagged as duplicate (good debate in the comments!), I came across Simon Kuttruf's explanation on Medium:
for integer orders of differencing only a (small) finite set of past
values is reflected in the resulting differenced series: the preceding
value in first order differencing, two preceding values for second
I know this is late but it seems to be a commonly occurring question. From my point of view, the main questions are:
(1) Are there any lagged effects of the exogenous variable? Or is it having only a simultaneous impact?
(2) Are there any potential mutual dependencies between the endogenous and exogenous variables? (e.g. a "chicken-and-egg" relationship)