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A: Measuring negative correlation of time series?

CarlJust plot them parametrically [see note}, that is, given for time t and for temperatures T; {t0,T0},{t1,T1},...,{tn,Tn} and snowboard sales S; {t0,S0},{t1,S1},{t2,S2},...,{tn,Sn}, plot temperature against snowboard sales {T0,S0},{T1,S1},{T2,S2},...,{Tn,Sn}. There is more to this question, as well...

whuber
whuber
What is "parametric plotting" as opposed to just "plotting"?
Carl
Carl
@NickCox Agreed, obvious.
@whuber reference.wolfram.com/language/ref/ParametricPlot.html Also, the discrete or functional plot of a parametric equation or relationship en.wikipedia.org/wiki/Parametric_equation I assumed that the average reader would know what parametric means. Was I incorrect?
whuber
whuber
Yours is not a parametric plot in that sense.
Carl
Carl
@whuber I do not understand your objection. What would you call it?
@whuber Also, reference.wolfram.com/language/StatisticalPlots/ref/…
whuber
whuber
A "parametric plot" is the graph of a function $f:\mathbb R^m\to\mathbb R^n.$ Usually $m=1$ (giving a curve) or $m=2$ (a surface) and $n=2$ or $n=3.$ Generally, $f$ is piecewise differentiable or at least piecewise continuous. You appear to describe what is known in statistics as a scatterplot. Referring to this as "parametric" is confusing. That suggests you are proposing some kind of interpolation among the data points.
Carl
Carl
03:00
@whuber See note above. It is not just a "scatter plot" but a list of y1 versus y2 discrete values coordinated by a parameter, e.g., time.
whuber
whuber
That's still not a parametric plot in any standard sense of the term.
Carl
Carl
@whuber OK, but it is plotted parametrically, so what to call it? A parametric list plot? It is a plot made by varying a parameter, that is, the independent variable is missing, and both plotted variables depend on that missing parameter. So I would argue that it is parametric, if discrete. That is, if both functions were known and continuous, and we only plotted a subset of those points, would that parametric plot cease being parametric? I would argue that it is a subset of a parametric plot. Do you have anything to else that is complete to call it?
whuber
whuber
I don't think the plot goes at all beyond a mere scatterplot. If, perhaps, you were to vary the symbols (e.g., shape, color, size, ...) according to a third variable, you might have some support for calling it "parametric" -- but nobody else would call it that anyway, AFAIK. When your objective is communication, it's usually best to know what conventions your intended audience employs. I have illustrated this approach at stats.stackexchange.com/a/1837/919. An interpolation of this plot (over time) would indeed be a parametric plot.
Carl
Carl
03:16
@whuber Your definition is incomplete. It would not rule out a scatterplot of some {X, f(X)} with a regression line through it being a parametric plot, and yet that is not what you mean to say. The term 'parametric plot' is in frequent usage to indicate {g(X), f(X)}, and I implore you to give a name to {g(X), f(X)} plots that is not omissive.
@whuber Would you settle for "parametric scatterplot"?