Does ARIMA require normally distributed errors or normally distributed input data? I have two questions related to time series forecasting with ARIMA:


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*Does ARIMA require normally distributed errors or normally distributed input data ?

*Are there any assumptions on input time series data for ARIMA model and exogenous variables for ARIMAX model ?

 A: First, having normally distributed errors is equivalent to having normally distributed observations for any linear time series model.
Second, it is not necessary to assume normality of errors. Often, maximum likelihood is used to estimate the parameters of the model, and then a Gaussian likelihood is used, but it gives good results even with non-normal data. Where normality of errors is often assumed is in using the AIC for order selection, and in computing prediction intervals.
There are several specifications of ARIMA models with exogenous variables, and more than one such specification has been called an ARIMAX model, so it is not possible to precisely answer your second question without you specifying the model more accurately. For discussion of some of the models, see http://robjhyndman.com/hyndsight/arimax/
A: No -- the paper Maximum Likelihood Estimates of Non-Gaussian ARMA Models studies ARMA models with Student-t and Laplace distributed errors. Here is the abstract:
"We consider an approximate maximum likelihood algorithm for estimating parameters of possibly non-causal and non-invertible autoregressive moving average processes driven by independent identically distributed non-Gaussian noise. The normalized approximate maximum likelihood estimate has a global maximum which is consistent and ecient. The estimates and their associated asymptotic covariance matrix are calculated with a subroutine
implemented in FORTRAN 77."
A: To answer your first question and to quote from [1], 

Mathematics tell us that linear predictor can be optimal only when the
  process is Gaussian. When the process is non-Gaussian, a better
  predictor may be  given by a non-linear dynamic model (Masani and
  Wiener,  1959).

Why statisticians, both young and old, keep themselves silent about it I do not know.
References:
[1] Ozaki, T. & Iino, M. An innovation approach to non-Gaussian time series analysis Journal of Applied Probability, 2001, 38, 78-92
