Compare the slopes of two lines plotted on different scales

(sorry, this is a "How to?" question but I couldn't fit that into the title)

By slope I probably mean rate of change, as angle doesn't mean much on a trading graph (it depends on how big the chart window is!). But let's say I have two line graphs plotted in two sub-windows below the main price window (one graph per sub-window), and in the top graph the y-scale goes from a large negative number (e.g. -100,000) to a large positive number (e.g. +600,000), and in the bottom graph the y-scale goes from a small negative number (e.g. -20) to a small positive number (e.g. +200).

Because the y-scales are different, it's obvious that I need to normalise the scales somehow so that I can compare the slopes like for like. Is there a best-practice way of doing this? Some ideas I have are:

1. Use the difference between the min and max points on the graph as the range, and divide by that to get the rate of change.

Or:

2. Use an average of the last n bars (SMA? SMA/SD?), and divide by that to get the rate of change.
The problem with this is that as the line swings from positive to negative there will be a time when the average approaches zero, which will distort the calculation when you divide by it.

I'm doing this in C# but any code snippets in any language would be welcome if that's easier than typing the explanation in English!

Thanks very much.

If your 1st need is to be able to compare both graphs, then rate of change should do the job ...

Thanks Ferru. Have you ever done something like this? If so, which method did you use? I can see a pitfall to my first method too, that is when the line makes a new high (or low), the range suddenly increases so the RoC (rate of change) of the current bar will be less than the previous one even if the slope looks exactly the same for both bars on the graph! Maybe there isn't a perfect way to do this, I don't know.

... To be frank, I'm not sure to understand ... Maybe a chart will help ...

1. Normalize the values (y-scale) of the 2 lines using one of them as a reference.

In your example, the range for the first line is (+600,000- -100,000) = 700,000. the range for the second line is +200 - -20 = 220.
ratio of 1st line to 2nd is 3181.8
ratio of 2nd line to the 1st is 220/700000 = 0.00314.

It is better to use the 1st line as a reference in order to not lose details of the first line.
So to normalize the 2nd line values we multiple by 3181.8.

2. Slope Difference line then can be calculated by subtracting one line values from a the other (like MACD indicator).

Slope Difference line can be zero if the 2 lines have the same slope (values).

Sure. On the chart below, I have two lines plotted below the price panel: Line 1 and Line 2. These are actually the same indicator with different inputs, but that's not important right now.

You can see that the y-axis (vertical scale) of each line graph is different. I've highlighted the top and bottom of the scales in yellow.

What I'd like to do is compare the slope of each graph bar by bar, and plot the difference in slopes on a new panel below. So if the top line went up and the bottom line went down for a particular bar, that would be a big difference and the new plot would show a large spike for that bar. If the top line went up more than the bottom line went up, then that would be a smaller difference. If the two lines went up or down about the same (similar slope angles) then the new plot would show almost zero because there wasn't much difference.

Hence my question about the best-practice method of normalising the two graphs in order to calculate and compare the rate of change of each line effectively.

Thanks for your time Ferru

Thanks abokwaik. I think that's basically my Method 1 above. This works great most of the time but loses accuracy when new highs or lows are made by the lines, i.e. the range increases, particularly if one line's range changes and the other one doesn't (because they diverged).

Actually I coded this method up earlier and it seems to works well, so maybe I'll stick to it. I was just wondering if there was a better or more official method known to people with a better understanding of stats than me!

I'm now wondering whether to plot the difference in RoCs, or the ratio of RoCs. I'll have a play around with that and see which one looks more useful.