An autoregressive exogenous model

Arima can be defined as an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. There models are fitted to time series data either to better understand the data and to predict future points in the series of forecasting

The answer will depend on the level of statistical knowledge that you have and, unfortunately, we do not know that. The regression model is based on the assumption that the residuals [or errors] are independent and this is not true if autocorrelation is present. A simple solution is to use moving averages (MA). Other models, such as the autoregressive model (AR) or autoregressive integrated moving average model (ARIMA) can be used. Statistical software packages will include tests for the existence of autocorrelation and also applying one or more of these models to the data.

Yes, if it is autoregressive.

Box-Jenkins Approach The Box-Jenkins ARMA model is a combination of the AR and MA models where the terms in the equation have the same meaning as given for the AR and MA model. Comments on Box-Jenkins Model A couple of notes on this model. # The Box-Jenkins model assumes that the time series is stationary. Box and Jenkins recommend differencing non-stationary series one or more times to achieve stationarity. Doing so produces an ARIMA model, with the "I" standing for "Integrated". # Some formulations transform the series by subtracting the mean of the series from each data point. This yields a series with a mean of zero. Whether you need to do this or not is dependent on the software you use to estimate the model. # Box-Jenkins models can be extended to include seasonal autoregressive and seasonal moving average terms. Although this complicates the notation and mathematics of the model, the underlying concepts for seasonal autoregressive and seasonal moving average terms are similar to the non-seasonal autoregressive and moving average terms. # The most general Box-Jenkins model includes difference operators, autoregressive terms, moving average terms, seasonal difference operators, seasonal autoregressive terms, and seasonal moving average terms. As with modeling in general, however, only necessary terms should be included in the model. Those interested in the mathematical details can consult Box, Jenkins and Reisel (1994), Chatfield (1996), or Brockwell and Davis (2002). Stages in Box-Jenkins Modeling There are three primary stages in building a Box-Jenkins time series model. # Model Identification # Model Estimation # Model Validation RemarksThe following remarks regarding Box-Jenkins models should be noted. # Box-Jenkins models are quite flexible due to the inclusion of both autoregressive and moving average terms. # Based on the Wold decomposition thereom (not discussed in the Handbook), a stationary process can be approximated by an ARMA model. In practice, finding that approximation may not be easy. # Chatfield (1996) recommends decomposition methods for series in which the trend and seasonal components are dominant. # Building good ARIMA models generally requires more experience than commonly used statistical methods such as regression. Sufficiently Long Series RequiredTypically, effective fitting of Box-Jenkins models requires at least a moderately long series. Chatfield (1996) recommends at least 50 observations. Many others would recommend at least 100 observations. source: http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc445.htm