Testing for independence in heavy tailed and positive innovation time series

For time series with positive innovations, a test is given to distinguish between data coming from a stationary process where the variables are dependent versus the model being independent identically distributed random variables. The techniques are suitable either when the innovation distribution has heavy right tails or regularly varying left tails and is based on linear programming estimators given by Feigin and Resnick (1992, 1994). Examples using teletraffic data and the lynx data are discussed. The method has applications to model confirmation where the fit of a model is also examined by gauging whether the residuals are independent or not