Time series degree of slope: Calculating what I see

[expertalmost]

Good morning Crew Genius!

I want to calculate the degree of slope at each point in a time series. Different time series have different scales. The final number should be normalized in the range of +/-90 degrees. Basically, when I plot my time series in Excel, I can see the degree of slope up or down, 0=flat, 70=very steep up, -20=gradual slope down. I want to calculate the "number" for what I am seeing.

I thought using the arctangent(P-P1), P=current point, P1=previous point would work. Not at all. For example on one time series: atan(1.166031374-1.168266667) yields -0.00224. On another times series, atan(11373.92-11342.05) = 1.539431. Certainly not normalized across different value scales nor producing values between +/-90.

Visually, it’s so easy to see the degree of slope in my chart! Yet, over the last year I’ve tried more than a hundred work arounds, mostly complex. They approximate what I want but seem very convoluted and inelegant. I’d appreciate any insights into solving this problem.

Thank you very much!
alexander

 

[Bob Brown MSEE]

Simple

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The slope of a time series is simply a linear combination of points sampled near the point of interest. The weights depend only on the spacing of the samples near that point of interest.

Is your time series sampled at a uniform rate?
What rate?
How many data points do you want to consider?

 

[Bob Brown MSEE]

t-axis scaling

The distance between sample points will affect the visual slope. More distance, less absolute value of the slope.
You must be very careful about the units that you are using before applying the ArcTan function.

Can you give us a sample of your raw data, along with times at which the samples were taken?

EXAMPLE:
Suppose you have a time series of sampled voltage. You need to decide what 45 degrees of slope means.
Is it one volt per minute?
Is it one volt per hour?
Is it one milli-volt per second?