  A multivariate, stationary time series is said to be jointly regularly
varying if all its finite-dimensional distributions are multivariate regularly
varying. This property is shown to be equivalent to weak convergence of the
conditional distribution of the rescaled series given that, at a fixed time
instant, its distance to the origin exceeds a threshold tending to infinity.
The limit object, called the tail process, admits a decomposition in
independent radial and angular components. Under an appropriate mixing
condition, this tail process allows for a concise and explicit description of
the limit of a sequence of point processes recording both the times and the
positions of the time series when it is far away from the origin. The theory is
applied to multivariate moving averages of finite order with random coefficient
matrices.
