This article introduces the Parabolic Variance (PVAR), a wavelet variance
similar to the Allan variance, based on the Linear Regression (LR) of phase
data. The companion article arXiv:1506.05009 [physics.ins-det] details the
Ω frequency counter, which implements the LR estimate.
The PVAR combines the advantages of AVAR and MVAR. PVAR is good for long-term
analysis because the wavelet spans over 2τ, the same of the AVAR wavelet;
and good for short-term analysis because the response to white and flicker PM
is 1/τ3 and 1/τ2, same as the MVAR.
After setting the theoretical framework, we study the degrees of freedom and
the confidence interval for the most common noise types. Then, we focus on the
detection of a weak noise process at the transition - or corner - where a
faster process rolls off. This new perspective raises the question of which
variance detects the weak process with the shortest data record. Our
simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in
all cases, exhibits the best ability to divide between fast noise phenomena (up
to flicker FM), and is almost as good as AVAR for the detection of random walk
and drift