  We outline the expected constraints on non-Gaussianity from the cosmic
microwave background (CMB) with current and future experiments, focusing on
both the third (f_{NL}) and fourth-order (g_{NL} and \tau_{NL}) amplitudes of
the local configuration or non-Gaussianity. The experimental focus is the
skewness (two-to-one) and kurtosis (two-to-two and three-to-one) power spectra
from weighted maps. In adition to a measurement of \tau_{NL} and g_{NL} with
WMAP 5-year data, our study provides the first forecasts for future constraints
on g_{NL}. We describe how these statistics can be corrected for the mask and
cut-sky through a window function, bypassing the need to compute linear terms
that were introduced for the previous-generation non-Gaussianity statistics,
such as the skewness estimator. We discus the ratio A_{NL} =
\tau_{NL}/(6f_{NL}/5)^2 as an additional test of single-field inflationary
models and discuss the physical significance of each statistic. Using these
estimators with WMAP 5-Year V+W-band data out to l_{max}=600 we constrain the
cubic order non-Gaussianity parameters \tau_{NL}, and g_{NL} and find -7.4 <
g_{NL}/10^5 < 8.2 and -0.6 < \tau_{NL}/10^4 < 3.3 improving the previous
COBE-based limit on \tau_{NL} < 10^8 nearly four orders of magnitude with WMAP.
