  An exponentially weighted moving model (EWMM) for a vector time series fits a
new data model each time period, based on an exponentially fading loss function
on past observed data. The well known and widely used exponentially weighted
moving average (EWMA) is a special case that estimates the mean using a square
loss function. For quadratic loss functions EWMMs can be fit using a simple
recursion that updates the parameters of a quadratic function. For other loss
functions, the entire past history must be stored, and the fitting problem
grows in size as time increases. We propose a general method for computing an
approximation of EWMM, which requires storing only a window of a fixed number
of past samples, and uses an additional quadratic term to approximate the loss
associated with the data before the window. This approximate EWMM relies on
convex optimization, and solves problems that do not grow with time. We compare
the estimates produced by our approximation with the estimates from the exact
EWMM method.
