What Is a Trend?

What is a trend? The question sounds simple enough but if you do any amount of research, you will find that the definitions are varying, sometimes vague and oftentimes contradictory or illogical. The most common answer given to the question, what is a trend is that an up trend consists of higher lows and highs and that a down trend consists of lower highs and lows.

Wikipedia, under its entry for Trend (technical analysis) says the following:


The general direction is certainly broad enough and general enough to cover most aspects of a trend. But I think we can and should do better. The CFTCs definition is no less ambiguous:


There are a number of books that talk about the trend but few of them give a concrete and objective definition beyond those nonspecific descriptions just mentioned. One book that claims to provide a concrete trend definition, and offers mathematical proof as to its exactitude is Trends and Trendlines by the author, who happens to post on this forum from time to time under the user name twoblink. Without turning this into a single book review or a survey of the existing definitions let me state in general terms that the truth of a particular set of premises rests on the underlying truth of the premises. If you start with incorrect initial premises, it is nearly impossible to reach the correct conclusion. But if you start with sound initial premises, you have a much better chance to arrive at the truth.

I shall endeavor to describe in an objective and statistically measurable way how I define the trend or one way you can do it too. It is important to define the terms properly so that a statistically valid trading methodology can be built up from this base. But first Im going to describe why everybody seems to have the wrong idea about trends and lay a foundation for the identification of trends.

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Note: this is not an open discussion on what you think defines trend. Please keep the discussion on the topic of trends presented in the statistical framework here. I placed a 3 voucher minimum so hopefully the more experienced will chime in on the subject after reading the material. Those who can't post feel free to PM me your questions though I can't guarantee a response due to time restrictions and I think this material pretty well explains itself.

It is unfortunate but some will undoubtedly question my motives so let me put it here in the first post. What is my motivation for posting this information? I'm sick and tired of all the misinformation that is perennially passed around under the guise of TA "truth" and accepted without any question by the masses. How many books have regurgitated this misinformation? How can anybody possibly get the right answer if they are basing their inquiry on false assumptions? Nowhere have I seen information regarding how to statistically define a trend. I get nothing other than the good feeling from knowing that I have made my one small attempt to shine some light on the subject of trends. This thread will either become the least popular and most forgotten or the most popular thread on FF. I doubt it will be the latter given the quality I see on these boards every day but I hope that at least one person learns something. Maybe that person will be me.

I've attached an Excel sheet. It will be used throughout the discussion and you won't be able to follow along unless you download it and study it when reading some of the sections.

Why is there a lack of clear and objective definitions of trend in the various books and articles on the subject? Why are the same old, tired, and vague definitions thrown around on forums and in books by even experienced traders and educators, those who should know better? It seems that the definition of trend is either so self evident or so generic and elusive as to escape the grasp of all but a few.

Why doesn’t the average trader who is seeking a profitable trading strategy tend to dig any deeper than the surface definition of trend as a general direction or tendency? It seems to me that you can’t develop a consistently profitable trading strategy without having a statistically valid definition of trend. Perhaps Frank Sinatra got it right.

It seems to me that a statistically valid definition of trend and a consistently profitable trading strategy must go together and that trying to separate them is an illusion as the song says. It seems to me that if consistency of returns is the goal, then consistency in defining the trend is a prerequisite.

When trend is defined in objective terms, the underlying premise or premises must also be defined. When trend is defined concretely it opens up the possibility to poke holes in the definition by taking issue with the underlying premises or with the reasoning used to arrive at the definition. In other words, the contradictions stand out like a sore thumb to anyone who understands logic. And it is my premise that the existing definitions of trend (as used by trading practitioners and trading educators) are illusory. Let’s define the underlying assumptions necessary for a statistically valid definition of trend.

The field of research has much more rigorous rules for inferring trend vs. the field of technical analysis. Allow me then to raise the bar and provide some basic assumptions that I feel will move the discussion forward with regards to “What is a trend?” drawn from the field of research.

A trend cannot be derived from two points. Two consecutive days of cold weather don’t constitute global (or even local) cooling. A trend requires a statistically significant number of observations, and as such we will determine a minimum number of observations to give us statistical significance. Most traditional TA fails by this rule because it allows for the connection of two points into a line, called a trend line with the inference that the connection of two data points defines a support or resistance area.

As has been discovered from the uproar over the hacked climate research emails at East Anglia University and the now infamous hockey stick charts, picking arbitrary start and end dates gets researchers into trouble. You can’t cherry pick start and end dates & times to make the data prove your thesis. It is bad science and it is bad analysis, so we will only use objective means of picking start and end times for our market studies.

Single data points (or prices) contain error. I realize that this flies in the face of commonly held economic theory which claims that all available information is contained in the last price. I will attempt to provide a simple logical argument for this point from modern quantitative finance theory and a way to statistically measure this error.

Because you need a statistically significant number of data points to infer a trend, you can’t draw a line between the start and end points and call it a trend. If single data points contain error, a single data point is neither an accurate nor sufficient measure of the variable’s (in this case price) trend . Trend lines should be drawn with a statistical technique in order to be statistically valid.

And since we are using statistical methods to determine trend, no change in trend will be determined until or unless statistics says so. I may have to expand my bag of statistical tools to pull this off but I hope you will come along for the ride and learn a thing or two in the process. Some of the known methods are regression, correlation and covariance tests. And then there are the more math sophisticated nonlinear methods. It is time to dust off Excel and start using some of the functions that only a few have ever used. Will it improve our concept of trend? Let’s find out!

A trend cannot be derived from two points. Two consecutive days of cold weather don’t constitute global (or even local) cooling. A trend requires a statistically significant number of observations, and as such we will determine a minimum number of observations to give us statistical significance. Most traditional TA fails by this rule because it allows for the connection of two points into a line, called a trend line with the inference that the connection of two data points defines a support or resistance area.

In geometry a line can be drawn between any two points. It is time to depart the geometry definition of a line, and look at a statistically valid definition of a trend line by looking at more than two data points.

Sample size is the subject of our inquiry. Wikipedia states that, “all else being equal, a larger sample size leads to increased precision in estimates of various properties of the population.” Additionally,


We will set 30 as our absolute minimum number of data points to give us statistical significance according to this simple rule which allows us to still compute the 95% confidence interval which may or may not prove useful to us. Sample sizes larger than 30 will tend to give us better results according to the law of large numbers by reducing sampling error. This is important because according to one of our initial premises, single data points (or prices) contain error. So no more will we pick two data points (lows or highs) and play the connect the dots game. Geometry class is over. Connecting two points isn’t statistically the way trends are determined and so we’ll use the right type of analysis to derive the best solution for the trend.

Now that we know the minimum number of data points that we can choose, we can go about determining where to start our trend tests and where to end those tests. The criteria that I stated previously is that the start and end times need to be objective. Part of objectivity implies that given the same data, anyone performing the same analysis would come to the same result, including a computer program. This makes the determination of trend an objective exercise and not a judgmental one.

Logic states that you could theoretically begin your analysis anywhere, and end it anywhere as long as both start and end time were determined objectively. Market data is divided into daily, weekly, monthly, hourly, minute by minute and even down to the second or single transaction for high frequency data. For instance, if you select hourly data and decide that you want to test 50 data points for possible underlying trend, it is possible to walk forward over the entire data series point by point, testing blocks of 50 data points each, and use the analysis as a basis for comparison. The “trend” that you determine is merely going to represent a historical subset of the data, and whether it proves to be forward looking or not mostly depends on the underlying market’s continuing serial correlation and the algorithm you use in determining the mean. So we need either a simple rule or a complex algorithm to determine the start and end times for our measurement. Since the selection of the start and end points can dramatically impact whether we identify an up trend, a down trend or a more sideways trend, testing multiple time slices might give us better estimation of underlying trend.

One way to accomplish this is as follows. You might determine that you want to test 100 data points. This number might have certain significance, such as 100 minutes of data, or you might observe that in the data you’re testing 100 data points represents the minimum average range you’re looking to exploit – such as 20-30 pips on average. Having selected our sample size of 100 we might come up with the following simple rule. We will test a series of 100 data points at 25 point intervals for a total of 4 tests, and determine that we have an up trend if and only if the angle of our trend line in each successive test is positive and increasing. So if our four measured trend angles are 0.01, 0.014. 0.02, 0.021 we shall determine that the trend is upward. By inverting this simple rule to read a down trend consisting of four successive down angles at 25 unit test intervals we can test additional data. For the following set of data points we will not determine that the trend is downward: -0.05, -0.052, -0.051, -0.0065 due to the rising temporary angle at –0.051 by our simple rule.

As we start testing our observations of trend against real data it is very likely that we will need to alter our simple rules to provide us with simple algorithms that better identify when a trend exists and which direction the identified trend is moving. Some examples on this will follow after we nail down some of the other fine points with regards to our underlying assumptions. In particular, we should determine if it is possible to measure error in our data points and reduce the effect that these sampling errors have on our determination of underlying trend.

Each price that is recorded in the case of a transaction based market, like the futures market, represents actual transactions that have taken place at a given price, time and volume. In quote driven markets such as in the spot currency market, prices represent active or historical levels where market makers willingly offer or offered to buy or sell. For the sake of simplicity, from this point on I will refer to both of these price changes as transactions.

As markets are quoted and order flow comes in to a given price driven or quote driven market, transactions take place at varying prices. The high and low price, such as a 1 hour period, reflect the range of buying and selling extremes for that hour. Is there a true fair value on a given price bar, which has a given high-low?

It could be stated that every price or transaction was “fair” at the time it occurred because buyer and seller both agreed and were matched at a price of their mutual choosing – one participant demanding liquidity and the other providing it in a sort of symbiotic relationship. In this respect those who believe that the current price or the last price represent all available information can justifiably make an economic argument.

However, the reality of the markets is that they are constantly changing and dynamic in nature and in price movement. But fundamental information about value does not change at the same rate that prices change. What could account for this disparity?

In the book “Trading and Exchanges” Larry Harris provides a possible explanation for the phenomenon of price changing more rapidly than its underlying fundamentals would dictate. He states, “Total Volatility is the sum of fundamental volatility and transitory volatility.” Harris defines fundamental volatility as the price changes that occur when fundamental values change.

An example of a fundamental change in values might be a drought that causes less grain to come to market, reducing supply and leading to an increase in grain prices. The distinguishing characteristic of fundamental volatility is that it consists of seemingly random price changes that do not revert. Mean reversion or its lack then becomes our identifying characteristic for dividing volatility up into its two main components.

Transitory volatility might arise when impatient buyers take the posted offers on EUR/USD, driving prices up as a result of their order flow. The distinguishing characteristic of transitory volatility is that it consists of price changes that do ultimately revert. This reversion can happen within seconds, minutes, hours, days, weeks or even months.

This is all fine, you say, but why you should care about splitting volatility up into its components? It all comes back to value. If you can correctly identify the portion of price change that is mean reverting and the portion of price change that is not mean reverting, then it is possible to derive from this true underlying value. And if you understand the true underlying fundamental value of the market you’re trading, then it is possible to develop a strategy to exploit deviations from underlying value or to trade in the direction of the shifting underlying fundamental value.

It is possible to analyze a given data series for serial covariance to determine to what extent its price changes are a result of fundamental volatility, and transitory volatility. We will develop a simple model in Excel to test for the two types of volatility. This will provide us with a statistically based way to measure the strength of an underlying trend, rather than the ADX indicator which relies on no statistical measures and doesn’t differentiate the underlying volatility components. More on this later.

If price’s only function were the discounting of all available fundamental data we would expect prices to only change when the underlying fundamental values change. Price would move horizontally over time at a given equilibrium or “agreement” price until fundamental values changed. At which time price should make a dynamic vertical move to realign with the new fundamental values. Then a new agreement level would set up and price would again move horizontally and to the right. It would look something the picture below:

This simplistic and static model of price movement is a far cry from the reality seen in the markets every day. Prices oscillate almost constantly and disagreements exist about the fundamental values as well as the interpretation of those values.

Price may in fact move based on anticipated future discounted fundamental values. However the degree of overshoot, overreaction, and general disagreement as to actual value, points to the fact that much of the time, the anticipated future fundamental values are simply WRONG. In other words, much of the transitory price movement is carried about by uninformed agents who may have no idea about the true underlying value. One academic research paper estimated that the markets are out of alignment from fundamental values around 80% of the time (citation needed).

Persistent deviation from underlying fundamental value tells us that on the very short term, price fluctuations are primarily as a result of short term order flow. (Short term order flow can be motivated by a number of factors, but examining the motivations of market participants is beyond the scope of this work.) Because these order flow imbalances can persist for seconds, minutes, hours and in some cases months, profiting from order flow deviations from fundamental values isn’t as simple as fading every deviation from fundamental values. Persistent order flow based on anticipated future fundamental values can cause persistent trends that may cause price to deviate from fundamental values for an extended period of time and with deviations of such large magnitude as to cause most/all adversely leveraged holders to be unable to maintain their position. Yes, it is a dog eat dog world in financial markets.

If price deviations due to order flow are persistent enough, it is possible that new fundamental information is released to the public that confirms the anticipations of the market participants order flow. This is known as discounting news and is happening all the time and in all markets. But because our definition of fundamental volatility is that it doesn’t mean revert, by using serial covariance (which is mostly commonly examined by looking at a bounded statistic, correlation) to identify the fundamental and transitory components of volatility, the fundamental component will actually consist of price changes based on both actual fundamental values and anticipated fundamental values. In this way it should allow us to shadow the participants who trade on good (but private) information in advance of the release of new fundamental information to the markets. This persistent non-mean reverting order flow should be measurable and identifiable as part of the trend component.

This leaves us with two statistically identifiable components of market movement that can be potentially exploited: the trend component could be played via trend following methods for continuation due to the persistent nature of trends. And the non-trend or transitory component could be played via a reversion to the mean strategy for a return to the underlying fundamental value. Depending on which market or markets you follow, one or the other of these components might be dominant and so any strategy should take the characteristics of the target market into account. But before the discussion can turn to strategies, we must first be able to answer the underlying question: “What is a trend?” To that end the next section reviews what we have learned thus far about how to statistically define a trend, and brings it all together into some simple definitions of trend and drawing trend lines on the underlying data.

From the underlying assumptions laid out previously regarding more statistically sound ways of determining trend, it can be stated that:





One additional common misconception with regards to trend is that it must consist of a straight line. This misconception probably comes from the fact that most trend lines drawn by traders start as the connection of two progressively higher lows, or two progressively lower highs. If a trend is a general price tendency, is it always best defined by a straight line? Statisticians have ways of measuring how well a given trend line fits the data. One statistical tool is R squared.

The simplest way of measuring how well a drawn trend line fits the underlying data is to figure the coefficient of determination or R squared (R^2). This calculation gives an objective means of determining how well a given trend line conforms to or describes the underlying data by minimizing the error or deviation from the defined trend line. The values of R^2 vary from 0 to 1 where 0 represents maximum variability of price from the underlying trend line, and 1 represents zero variance between price and our trend line or a perfect fit. If you would like to read more on how R^2 is calculated or used in statistics, please see this article on Wikipedia:

http://en.wikipedia.org/wiki/Coeffic..._determination

The basic rule of thumb is that a higher number for R^2 indicates a better fit, and a lower value for R^2 indicates an inferior fit. Given two possible trend lines with two measures of R^2 the trend line with the larger value for R^2 will do a better job of characterizing the underlying trend. We can use this basic rule of thumb as an objective and statistically sound underlying technique for drawing and selecting the proper trend line, thus meeting the above condition:
For our purposes and to simplify things the best strategy is to allow modern technology to work the computations in our behalf. This should cut down on errors in calculation and provide us with an objective means of determining the trend and for drawing the correct trend line.

As was alluded to previously, trend lines don’t have to be lines. Trends aren’t always best defined by a straight line. Trends might be better characterized by a curved line. I will refer to curved or straight lines as trend lines for simplicity but keep in mind that a “trend line” could refer to a straight line with no curves, or a line with one or more curves. This distinction will prove to be important as the examination turns to drawing trend lines within Excel and determining via an objective and easy to replicate method which trend line best fits the data.

There are a number of different ways to draw trend lines within Excel. Rather than turn this into a primer on how to use Excel to draw simple trend lines, please download and refer to the attached spreadsheet for the following discussion. If you need extra help, please skip to the end and follow the link below to the “Quick’n’ Dirty Regression Tutorial.”

Now let’s refer to the attached Excel spreadsheet “Sample Trend Lines” that contains 10 minute bar data from EURUSD starting 10/5/2009 on the tab “EUR_USD”. I created a chart that should be self-explanatory on the tab “EU 10 Min Chart.” Go there now if it isn’t already selected. You’ll see a chart with 400 data points consisting of 10 minute close prices, or in other words 4000 minutes worth of data or a period of about 67 hours or 2.8 days of 10 minute data.

Let’s quickly go through our checklist: 1) More than 2 data points. Check! We’re going to use all 400 data points to draw our trend line. 2) An objective way of picking start and end times. I take a mulligan on this one as I simply *objectively* picked the first 400 data points in the series but as 3) sample size > 30 we score one point. We’re using Excel to determine our trend lines so we meet the last criteria 4) Statistical technique to draw a trend line.

Now that we’ve ascertained that our methodology is statically sound, let’s start drawing trend lines. You can do this very simply while viewing the “EU 10 Min Chart” tab by right clicking directly on the dark blue data points in the middle of your chart. If you right clicked on the data point you should get a menu with an option that says “Add Trendline”. Fantastic! Upon selection of the “Add Trendline” menu item, a box should pop up with various types of trend lines on the “Type” tab, and various options on the “Options” tab. We want a way to measure how well our trend line fits the data so go to the “Options” tab and check the box that says “Display R-squared value on chart.” Next from the “Type” tab let’s select our first trend line – the linear trend line, and press the OK button to close the dialog.

You should see a black trend line now running through the data. Also note that there is a value “R^2 =” on your chart. You can use your mouse to drag that number off the data series if you have trouble seeing it. If you did it correctly, you should see a line that is gradually pointing upward. But our R^2 value is only 0.3094 which doesn’t inspire a lot of confidence. Go back and change your trend line and note the changes in the R^2 value and how well the line visually fits the data. If you have questions about how the different trend lines are computed, press F1 while the “Format Trendline” dialog is open, then search for “trendline” and you should see the “Equations for calculating trendlines” help topic. Follow topic entitled “Choosing the best trendline for your data” and you will see helpful descriptions of Linear, Logarithmic, Polynomial, Power, Exponential and Moving average. Take some time to read through and understand each of the descriptions and when you might use each. Understanding which type of trend line will best fit the data under consideration is very important. After reviewing the choices, I settled on the Polynomial method of trend line drawing because:


Our time series data certainly fluctuates. You could state that fluctuation is one of the core characteristics of market generated time series data. Of the selections the Polynomial type of trend line will usually be the best fit for our data. But don’t take my word for it, run through the other types of trend lines and make note of the highest R^2 value to determine which line is objectively better based on a statistical measure. You can alter the trend line by right clicking (exactly on the trend line – this might take some practice) and selecting “Format trendline” from the popup menu. Do this now. Logarithmic has a higher R^2 than the linear trend line but at 0.4891 it is still sub-optimal. The power trend line is similar at 0.4898 while the exponential trend line is in the same category as the linear trend line for this data set. If you pick Moving average you’ll notice that you can also alter the periods from 2 to whatever you choose for a simple smoothing factor. This moving average is a simple moving average. You will notice that when you pick moving average, the R^2 value disappears from your chart. This should be a lesson for you – moving averages ARE NOT statistically sound measures of trend but are designed with data smoothing in mind rather than trend identification. So choose the correct tools for the job.

Finally, let’s look at the polynomial trend lines. (make sure to check Options, Display R-squared value on chart again as it comes unchecked when you select moving average). You will notice that you can vary the order of the polynomial. As the help file states, a 2nd order polynomial allows for one hill or curve. A 3rd order polynomial allows for two hills or curves and so forth. Perform a visual inspection of the data. How many trends does your eye identify? This will vary from person to person but my eye identifies a starting up trend, then a slow and jagged down trend, followed by a resuming up trend. So two curves making a 3rd order polynomial likely ideal. Let’s start out and just go through all the order polynomials first though, starting with 2nd order. With a 2nd order polynomial our R^2 value is higher than any of the previous readings at 0.6211, but the trend line fails to accurately describe the final up trend that my eye sees. This is to be expected because a 2nd order polynomial can only have one curve maximum. Let’s look at a 3rd order polynomial next. The R^2 value increases to 0.7148 but the final up trend is only identified by a slight rise in the curve.

Let’s look at the 4th order next. As an aside, each higher order of polynomial introduces something called a degree of freedom in the calculation – allowing the trend line more room to wiggle. If we are trying to characterize data with lots of wiggles then higher order polynomials will do a better job of characterization than lower order polynomials. For 4th order polynomial I get an R^2 of 0.8695 and a curve that (to my eye) does a much better job of identifying the underlying trends in the data series. I have found that 4th order polynomials often do a very good job of identifying the underlying trend in a limited data series like the one we’re examining. The 5th order polynomial draws exactly the same on my data and the R^2 value stays exactly the same.

There is some slight improvement in R^2 with the 6th order polynomial trend line (0.8882) but not significantly so. To my view the 4th, 5th, and 6th order polynomial trend lines all do a good job of identifying the underlying trends in the data series on the chart. Take some time to experiment with different settings, and perhaps with different chunks of data. You might figure out some interesting things. The lesson we can learn is that maximizing for R^2 does a pretty good job of identifying the best underlying trends in a given data series.

If you need more information on the topic of drawing trend lines within Excel, this page, titled “Quick’n’ Dirty Regression Tutorial” contains some very good introductory information on the types of statistical tools available and how to access them through Excel. I learned a thing or two about some of the built-in statistical capabilities of Excel that I have never used before. It is worth a look:

http://www.udel.edu/johnmack/frec834...sion_intro.htm

In the next section, I'm going to sum up the basic steps for drawing a statistically sound trend line within Excel

This is a summary of steps that can be taken to draw a statistically sound trend line on a chart from within Excel. Here are the basic steps:


You might find as you start testing different data ranges that determining the right trend is a bit more tricky than maximizing R^2. Often the lines drawn when using different order polynomials will contradict. Additionally, sometimes you get overshoot when the polynomial order used is too high. In this case the best bet is to reduce the order down until the trend line plot is within the data range. To resolve any possible conflicts in trend direction we need another way to check that the trend lines are accomplishing what they are intended to accomplish.

What are you trying to accomplish with your trend lines and with your characterization of the data by drawing statistically sound trend lines? If you’re like me then you’re interested in a metric that is forward looking or predictive. But this comes down to specific methodology and logic as well as the type of tools used for the task.

In general, a trend line that points upward indicates an up trend. A trend line that points downward indicates a down trend. But is this information that can be acted upon in a consistent manner with consistent results? Next, an examination of the “trend paradox” and one metric that might help alleviate this problem.

There is a bit of a paradox with regards to drawing the ideal trend line. When a trend line fits the data perfectly (or nearly perfectly) according to our previous metric, R^2, we get a very high value that approaches 1 for R^2. However the underlying trend can change at any time. And when a trend is too easy to define, often it reverses itself or tends to be more prone to reversal. So very high values for R^2 might do a better job of identifying how well a trend line matches the historical trend, but might fail in looking forward to the possible future trend. This “trend paradox” is well known to most experienced traders. We need another way to determine not only the general direction of the trend (slope of the trend line), and the fit of the trend line to the underlying data (R^2), but to determine the strength of the underlying trend.

An up trend that is increasing in strength should continue higher. And a down trend that is increasing in strength should continue lower. But how can we measure the strength of the underlying trend? If the trend is identified by the slope, then one way to determine if the underlying trend is strengthening might be to determine if the slope of the underlying trend line is up and increasing or down and decreasing on the most recent data.

Another way that delves deeper into the way price is moving to determine the strength of the trend is through calculating the serial covariance. The key is to determine if it is increasing or decreasing on the most recent data. By converting serial covariance to correlation, it is possible to essentially measure the average tendency to mean revert, a tendency that shows up as a negative correlation approaching –1. When the correlation is a positive number approaching 1, it could be said that the trend is strong or strengthening.

Let’s assume that our maximum desired holding period for a given trade is 400 minutes. On the 10 minute data provided in the previously referenced Excel workbook, this equates to a maximum of 40 data points. 400 minutes might be determined based on the desire to end the trading session flat coinciding with the U.S. stock market session, or time constraints on a trader.

Correlation is a comparison between two series. If reversion to the mean is an indication of transitory volatility and continuation away from the mean is an indication of fundamental volatility, we can measure these metrics using simple tools in Excel. Note columns G through N contain calculations for the simple moving averages of lengths 40 down to a length of 5. Since we don’t know the optimal average length for our data series, I take the correlation of the last price vs. all of these averages, and compute the results in columns O through V. In column W, I take an average of the correlation figures computed in columns O through V.

This correlation calculation then is really an average correlation of the 10 minute last price verses a range of means ranging in length from 40 periods down to 5 periods with a 5 period step for a total of 8 means. This should give us an indication of the strength of the trend. When the average correlation is rising, we can state that the price trend is strengthening. And when the average correlation is decreasing, we can state that the price trend is weakening. I plot a series of charts within the worksheet starting at cell X80. Please refer to the worksheet for the charts and the discussion.

In the worksheet I progress forward 10 data points at a time with a series of three charts each as a sort of step forward function. In this way time lapse is simulated and a discussion is provided of how a sample decision process could work based on the available data at given intervals. The charts show the fourth order polynomial trend line drawn over the correlation, last price, and a combined X= correlation, Y= last price chart, so we have several different views of the data.

No trading system is being presented here. The purpose of this presentation is to show additional tools and how to use them within Excel to identify statistically valid trends. The specific method you use will be up to you but I hope you think about the information presented here and that it helps you in your trading.

Please refer to the worksheet for a more detailed analysis of the time slice progression and a possible way to interpret the data. Also, please discuss amongst yourselves your own interpretations of the provided charts and let me know if you have alternative/differing analysis of the data.

Although it is an extraordinarily time consuming process of putting a worksheet together with its related charts, it is nice to see that the price can in fact be used in conjunction with the correlation to indicate strengthening price trends as a possible use for this type of analysis.

I hope you’ve enjoyed following along on this journey into “What is the trend” and that you have a better idea about how to answer that question and to statistically identify the trend and a metric that you can use to gauge the strength of the trend to possibly identify high probability opportunities for trend following.

Although the specific application of this information will be left to you, the trader I hope you have learned something about statistics, and trends and that this will help to elevate the discussions here on this forum away from indicator chasing and faulty TA to focus more on the fundamentals of price movement. And I hope that I have given each of you tools whereby you may identify the underlying trends in the markets you trade and the strength of those trends. Please explore the tools available in Excel and develop your own methodology. The spreadsheet should be taken as one of many possible paths, not as THE path.

There are other avenues of exploration that I wanted to take but the time involved up to this point no longer provides a positive expectancy for future effort. Best of luck to all of you in your trading and feel free to ask questions and to start a discussion on this topic using the tools presented here.