  We consider strictly stationary heavy tailed time series whose
finite-dimensional exponent measures are concentrated on axes, and hence their
extremal properties cannot be tackled using classical multivariate regular
variation that is suitable for time series with extremal dependence. We recover
relevant information about limiting behavior of time series with extremal
independence by introducing a sequence of scaling functions and conditional
scaling exponent. Both quantities provide more information about joint extremes
than a widely used tail dependence coefficient. We calculate the scaling
functions and the scaling exponent for variety of models, including Markov
chains, exponential autoregressive model, stochastic volatility with heavy
tailed innovations or volatility.
