Phase and Amplitude Variation in Montreal Weather. Jim Ramsay McGill University. The Data. 34 years of daily temperatures, 1961-1994 inclusive Values are averages of daily maximum and minimum 12410 observations in tenths of a degree Celsius
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The registration process requires that we smooth the data two ways:
The fitting criterion was the smallest eigenvalue of the matrix
This criterion measures the extent to which a plot of x[h(t)] against x0(t) is linear, and thus whether the two curves are in phase.
Every smooth strictly monotone function h(t) such that h(0) = 0 can be represented as
We represent unconstrained function w(v) by a B-spline expansion. Constant C is determined by constraint h(T) = T.
Plotting this allows us to see when the seasons come early (negative deformation) or late (positive deformation).