An autoregression model is a statistical model that uses past values of a variable to predict future values. It is based on the assumption that the current value of a variable is influenced by its previous values.
An autoregression model is different from a linear regression model in that it uses the variable's past values as predictors, rather than other variables. In other words, an autoregression model is a regression of a variable on its own lagged values.
An autoregression model and a moving average model are both time series models used for forecasting. The main difference is that an autoregression model uses past values of the variable itself, while a moving average model uses past forecast errors.
The appropriate lag order for an autoregression model can be determined using statistical tests such as the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). These criteria measure the goodness of fit of the model and penalize for including too many or too few lagged values.
Some limitations of using an autoregression model include the assumption that the data is stationary (constant mean and variance), and the inability to capture non-linear relationships between variables. Additionally, the model may not perform well with large datasets or when there are missing values.