Phase and Amplitude Variation in Montreal Weather

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Fitting criterion The fitting criterion was the smallest eigenvalue of the matrix ⎡ ⎢ ⎢ ⎣ ∫ ∫ 2 x () () () 0 t dt ∫x0 t x ⎡⎣ h t ⎤⎦ dt⎤ ⎥ () () 2 x () 0 t x⎡h t ⎤dt x ⎡h t ⎤dt ⎥ ⎣ ⎦ ∫ ⎣ ⎦ ⎦ This criterion measures the extent to which a plot of x[h(t)] against x 0 (t) is linear, and thus whether the two curves are in phase.
The warping function h(t) Every smooth strictly monotone function h(t) such that h(0) = 0 can be represented as t ht () C exp wvdvdu ( ) u = ∫ ∫ 0 0 We represent unconstrained function w(v) by a B-spline expansion. Constant C is determined by constraint h(T) = T.
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Phase and Amplitude Variation in Montreal Weather

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