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We consider strictly stationary heavy tailed time series whosefinite-dimensional exponent measures are concentrated on axes, and hence theirextremal properties cannot be tackled using classical multivariate regularvariation that is suitable for time series with extremal dependence. We recoverrelevant information about limiting behavior of time series with extremalindependence by introducing a sequence of scaling functions and conditionalscaling exponent. Both quantities provide more information about joint extremesthan a widely used tail dependence coefficient. We calculate the scalingfunctions and the scaling exponent for variety of models, including Markovchains, exponential autoregressive model, stochastic volatility with heavytailed innovations or volatility.

Heavy tailed time series with extremal independence