Time series degree of slope: calculating what I see 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. 
 A: This looks like an old question, but I'm surprised that nobody has pointed out that it's not even well-defined.
By basic trigonometry, the angle between one point of a time series, $y_i$ at time $t_i$, and the next, $y_{i+1}$ and time $t_{i+1}$, would be
$\theta = \arctan\left(\frac{y_{i+1}-y_{i}}{t_{i+1}-t_{i}}\right)$
but the quantity in parenthesis is not unitless.  The angle $\theta$ therefore changes, and not even linearly, if you change the scale of $y$ (e.g. from dollars to thousands of dollars, or meters to feet) or the scale of $t$ (e.g., from seconds to weeks).  
Worse, there is always some sort of scaling involved when translating from data to a graph (which is "what you see"), so even if $y$ and $t$ have the same units, the computed angle won't correspond to the perceived angle unless the graph is created with a 1:1 aspect ratio between the axes.
A: You'd better standardizing the slope coefficients (regression on standardized values produces standardzied coefficients) than this. The angle of a slope does not move in the same manner throughout the scale of -90 to 0 to 90deg (see when you switch x axis for y) and can't be vertical by definition of a function.
