  Data compression often subtracts prediction and encodes the difference
(residue) e.g. assuming Laplace distribution, for example for images, videos,
audio, or numerical data. Its performance is strongly dependent on the proper
choice of width (scale parameter) of this parametric distribution, can be
improved if optimizing it based on local situation like context. For example in
popular LOCO-I \cite{loco} (JPEG-LS) lossless image compressor there is used 3
dimensional context quantized into 365 discrete possibilities treated
independently. This article discusses inexpensive approaches for exploiting
their dependencies with autoregressive ARCH-like context dependent models for
parameters of parametric distribution for residue, also evolving in time for
adaptive case. For example tested such 4 or 11 parameter models turned out to
provide similar performance as 365 parameter LOCO-I model for 48 tested images.
Beside smaller headers, such reduction of number of parameters can lead to
better generalization. In contrast to context quantization approaches,
parameterized models also allow to directly use higher dimensional contexts,
for example using information from all 3 color channels, further pixels, some
additional region classifiers, or from interleaving multi-scale scanning - for
which there is proposed Haar upscale scan combining advantages of Haar wavelets
with possibility of scanning exploiting local contexts.
