# Wildebeest's  Instablog

Wildebeest
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Wildebeest is a PhD MBA who invests primarily in resource stocks such as base metals, iron ore and coal.
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May 21, 2010 10:34 AM

Is it valid to rule a line like this on charts?

Why is it valid to rule a straight line on a logarithmic scaled chart?

These two charts are IDENTICAL.

Disclosure: not relevant

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• W - - -

What you have drawn is a visual smoothing of the noisy data. The question I think you mean to ask is: what is the mathematical significance of either line?

The issue is how much of the drawing is quantitative and how much is qualitative. As I have said in previous discussion, I think a rigorous analysis is in order. Before I start I am biased to think that the lines you have drawn here are judgmental and arbitrary and therefore very much qualitative.

It would become quantitative if every point on the noisy curves (the "data points" curve) is fitted to a regression which would define the "mid point" of the data set. The standard deviation (or any other mean variance measure) can be used to define tolerance bands for the data, the upper band being related to "resistance" and the bottom band being related to "support". Bollinger has defined such a process to define the "mean seeking" behavior of prices that is observed so often. By calculating a moving average of variance Bollinger Bands, his method shows the variability of mean seeking to a trend rather than to a fixed value. (Note: The variance of the mean seeking tendency can vary dramatically. You see this in the wide variations in the shapes of Bollinger bands over time.)

This is something that might make a very good discussion. It would cover the analysis aspects and the "artistic license" aspects of looking at trends. I expect that there are probably some very good text books that address this from both the qualitative and quantitative approach. My favorite tech analysis text is the very comprehensive "Technical Analysis of Stock Trends" by Robert D. Edwards and John Magee. It is very much in the qualitative camp. I don't have a good quantitative reference.

By the way, a degree of quantitative characterization can be achieved with the "artistic" approach by trying to balance the total of areas under the curve that do not include data points with the total of areas above the curve that do contain data points.

Developing a complete array of "eyeball quantitative analysis" and "regression quantitative analysis" methods (and their limitations) would be a worthwhile project. It is not a project to be undertaken lightly. However, I am not a very good authority on what has been written on the subject. Perhaps, rather than doing some original work, we just need to be pointed to the right existing references.
21 May 2010, 03:08 PM Reply Like
• Author’s reply » Hi John,

Neither line has any significance. They weren't lines of best fit or anything like that. I just drew a straight line of the log scale and the equivalent line on the linear scale.

The purpose was to show that a straight line on a log scale is an exponential line on a linear scale. That may sound obvious but not every reader has studied math. Given that I have never seen exponential lines drawn on charts before I am still puzzled about the justification of using log scales. It appears to be entirely arbitrary designed to give a preordained--optical illusory--result.

The bottom line is that I could use all sorts of mathematical functions to draw lines on charts but any departure from a linear scale seems very contrived, designed solely to achieve a pre-determined end.

It appears that none of the commenters to your instablog had a solid explanation/justification for log scales either.
22 May 2010, 09:26 AM Reply Like
• W - - -

Maybe it is not what you are looking for because it is rather obvious, but here is my justification:

Log scale (y-axis) is used to show the same magnitude for a given ratio of change. In other words, doubling from 50 to 100 has the same vertical scale as doubling from 500 to 1,000.

If you are looking for something more profound we should keep on talking because I may be missing something important in my simple view.
22 May 2010, 09:40 AM Reply Like
• Author’s reply » John this comment that I posted to your article sums up what I am asking:

"Doug, to summarize my objections another way, over a long period you cannot assume some sort of constant growth which is what is implicit in using an exponential trend line. You really should be normalizing the data and the most obvious things to choose to try would be CPI, GDP, or M2 money supply. I've noticed Dow/Gold charts. John put a link above and it was mentioned again on SA this morning. There are still underlying non-constant things that lead to changes in the value of gold and the dow so the 3 things I listed would be better choices to normalize the data and then look for trend lines. "

So essentially I don't see how you can have exponential trend lines i.e. linear trend lines on a log scale chart. To me it makes more sense to normalize long time span data.
23 May 2010, 05:38 PM Reply Like

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