Autoregressive (AR) Models Time Series (Part B) - Quantitative Methods Level II

An Autoregressive model can be estimated using ordinary least squares model (OLS) when the time series is covariance stationary and the errors are uncorrelated.


Detecting Serial Correlation in AR models: In AR models, Durbin-Watson statistic can not be used to test serial correlation in errors. In such cases, t-test is used.

The autocorrelations of a time series refers to the correlations of that series with its own past values.
· When autocorrelations of the error term is zero, the model can be specified correctly.
· When autocorrelations of the error term is significantly different from zero, the model can
not be specified correctly.

T-statistics = Autocorrelations / Standard Error
Decision Rule: If | T-Statistics | > 2 then autocorrelations differ significantly from 0 thus the residuals are serially correlated and the model cannot be specified correctly.


Correcting Serial Correlation in AR Models: The serial correlation among the residuals in AR models can be removed by estimating an autoregressive model by adding more lags of the dependent variable as explanatory variables.