## Tuesday, November 1, 2011

### More on Reading a Graph

"Good sense is of all things in the world the most equally distributed, for everybody thinks himself so abundantly provided with it, that even those most difficult to please in all other matters do not commonly desire more of it than they already possess."
- Descartes

I am perfectly happy to look at graphs and determine trends by eyeballing them. The trouble with that is, well, I don't know but maybe not everybody would see the same trend that I see. And it is hard to agree on things, when you can't agree on things. So it might be good for me to put some thought into the process of trend determination, rather than always depending on one good eye.

My major in college was math, but not statistics, and not the determination of trends. I approach the problem of trends full of good sense but not resolute. The best place I have to start this review is with the thoughts of my friend Jazzbumpa. I will interrupt his remarks with my replies, to create a discussion of sorts.

Jazz writes in part:

A trend is determined by observing a series of {higher,lower} highs and lows.

The correct way to construct trend lines is across the troughs if the trend is upward, and across peaks if the trend is downward.

(Jazz says, "What I said about trend line construction comes from stock price analysis." That looks like a useful link, actually. But I want to look first at what I think.)

But I am left wondering why that is said to be the correct way to construct trend lines. The method seems probably a practical approach for evaluating trends and making decisions regarding a rising or falling stock price. Looking at the bottom of an uptrend, for example, seems a financially conservative (safe) approach.

Not sure why else one would look only at peaks or only at troughs... although I do remember Krugman using past peaks to evaluate the present course of GDP. But then, Krugman, too, was looking for a maximum return.

In regard to where the trend line is constructed, Jazz's LSOT link offers some useful tips. For the uptrend, where the line is drawn across the lows, "As long as prices stay above the trendline the uptrend is considered intact."

And for the downtrend, where the line is drawn across the peaks: "As long as prices stay below the trendline, the downward trend is considered intact."

Okay. Sure. But I think I can eyeball that. I don't think I need to actually draw a line there. (Though if I had money riding on it, I probably would draw the lines.)

Bearish trading strategies and downward trendlines are a great compliment to each other.

and

Bullish trading strategies and upward trendlines are a great compliment to each other.

and I don't doubt that at all. But it seems to confirm my thought about the financial aspect of the LSOT method of constructing trend lines. So I am left looking for a different method, or a better understanding. Have to take a good look at that LSOT link.

Watching the lows of an uptrend (or the highs of a downtrend) seems to be a way to minimize rather than exaggerate risk. And again, this may be the financially prudent choice. But if we set finance aside and consider only the trend, then I say we want neither to minimize nor exaggerate, but instead choose the middle ground.

Consider a number series that never goes below zero, and which has increasingly higher peaks. But each low is as long as the previous peak was high, and each peak is but momentary. The trend-of-troughs would be flat, at zero. The trend of peaks would be continuously upward. But the true trend would be near to the troughs:

If this graph represents a stock price -- and if you can find a buyer -- you might sell at one of those peaks and make a profit. But if the graph represents GDP, then surely economic growth has not been consistently good.

The trouble with this graph is that there is almost no area under the curve.

If we picture both a trend-of-peaks line and a trend-of-troughs line and create what I think is called a "channel", then I want to find the centers of the areas under the curve, the areas between the blue line and the trend-of-troughs. And I want to consider the relative sizes of those areas. And I want to show a trend line that takes into account both the center-point locations and the relative sizes. Sort of like calculating the center of gravity. Granted, that's a lot to do by eye.

The red line is Excel's linear trendline for the graph.

Jazz writes:

But the "quasi-midline" is exactly what I want to show: the line that is on average closest to the center of everything. Like Excel's trendline.

It seems to me that if the trend is flat, it's flat. Sure, you can reject the idea that a graph has three trends, and insist that it has only two. But either way, that seems to me a judgment call, not a determination of what the trends actually are.

You could put sixteen trend lines on the graph; it is still a judgment call made before the trend is known. This is part of my problem: How do we determine "how many" trends there are on a particular graph, and where the turning-points are? How do we determine this objectively, so that the decision does not falsify the outcome?

Jazzbumpa said...

I left a long comment that is not here. Please check spam.

Cheers!
JzB

The Arthurian said...

Dunno, Jazz. It's not in the spam and it's not in with my email. Will look again later.

Jazzbumpa said...

Attempt to reconstruct:

Your "Momentary Peaks" graph represents some phenomenon that defies trend analysis. You need a time series that exhibits either a sequence of higher highs and higher lows, or the inverse (unless the trend is sideways.).

Eyeballing a mid-line is highly uncertain. Even worse, a superimposed line can trick the eye into thinking it's valid - hence all your views of the Manufacturing Employment data.

If you can make a valid trendline off the peaks or valleys, that's good. If you can identify a channel, that's even better. A midline can be constructed half-way beween.

Using the trendline function in a spread sheet is OK, but you need to use some judgment. It will put the line in the graph without regard for its suitability.

Actually, this is not a reconstruction. It's about 50% new post and only half a long as the original. But it's been a few hours and I'm tired. I think I hit the important stuff.

Welcome back to the world of electricity.

Lo siento,
JzB

Jazzbumpa said...

I found it. Here it is.

My fault, not Blogger's. Slept really bad last night.

Your "Momentary Peaks" graph illustrates a phenomenon for which the concept of a trend line becomes close to meaningless. There is clearly a pattern to the graph, but some other methodology would be needed to comprehend it.

Your basic question is a good one, and your assessment of the conservatism of financial trendlines is valid. That is an artifact of the technique, though, as much as a goal of the method.

Defining the trend is not so hard, even by eyeball. Pinpointing when the trend direction changes is a lot more challenging. My thought is that as long as the values are contained in a channel, the trend is intact. When they veer outside, you can start looking for a new trend - though it might take some time before you can nail it down for certain.

If you like midlines more than channel boundaries, they're generally easy to construct, using the channel boundaries as reference points. OTOH, eyeballing the midlines is fraught with hazards and uncertainty. Your own multiple interpretations of the Manufacturing employment graph demonstrates this. And having a midline in place coaxes the eye into believing it is correct.

This idea is to find an objective method that eliminates guesswork. In the real world, you can reduce it, but elimination is probably not feasible.

Cheers!
JzB

Jazzbumpa said...

Here are a couple looks at trends, changes, and - in particular - midlines.

Wide Angle

Really Wide Angle.

Cheers!
JzB