What Is a Trend?

I can give you a few facts here:

1. Currency pairs tend to trend, their distribution of returns shows fat tails and their price series show autocorrelation. I advice you to run statistical tests before you "believe" a trend exists.
2. There are many ways to define a trend but you can look and test if a price series statistically resembles a random walk with a drift component. This will tell you the likelihood with which a trending component actually exists.
3. Hurst exponents and auto-correlations, these two are very important when measuring trend strength. You probably need about 10+ ways to measure trend statistically to make accurate decisions.
4. I worked for a large bank, we tracked +90 instruments from which we had +20 FX pairs. From these the best were pairs from Latin America, etc. Exotics sometimes trend much more than major currency pairs or crosses.

Finally. I advice you to learn statistics, if you don't, take a course on coursera for God sake. It will really help you out.

How do you estimate the Hurst exponent? I know two methods: Re-scale range and wavelet. I know there are a couple more but don't know how they work. Except for RS all of them break with fat tail distributions. Wavelet needs >50K samples to give a trustable reading. RS seems to be the fastest it only needs ~1000 samples to converge. Same issue with the autoregressive models. An ARIMA doesn't converge before hundreds of samples. GARCH needs thousands... That's a little bit too much of lag for my taste. If you know better methods which converge very fast, please post.

I use a Kalman estimator with a second order polynomial model (ax^2+bx+c+noise). The choice of this model was driven by the fact that it "encodes" the price, the velocity (trend) and the acceleration to catch up quickly after a shock. Because the market isn't Gaussian while Kalman relies on Normal distribution, I correct this estimator with another KF (A constant + noise model) which feedback the error (by increasing the elements of the variance matrix). That's because using a Cauchy or Student distribution makes the prior/posterior untractable (to me at least). Do you think this is a good or a bad way of doing things?

very good way of doing this. Part of our analysis involved Kalman estimators. However Hurst exponent and auto-correlations are key. Take ideas from here: http://ccsenet.org/journal/index.php...cle/view/18513.

Hmmm the paper clearly shows that H-values are found to vary widely from period to period (their words) with only 60 observations. Is it because the Hurst exponent does indeed vary that fast or because the samples size is too small? Like RS and wavelet, the DFA method expects a stationnary time series. Financial time series are fractionally integrated. The returns (1st diff) is still not stationnary in general. These series are also corrupted with non gaussian noise. It is very strange to me... How can a process be showing "long term memory" today if it didn't yesterday and will no more tomorrow?

Also the 12 indexes are highly correlated and tested over the same period of time. This is almost equivalent as a single observation. No random walk generated series was tested to create a witness null hypothesis. I highly suspect their conclusion.

To me, a trend is confirmed by using a combination of Ichimoku Kinko Hyo, ADX, SMA and Aroon's Oscillator over at least 85 periods. When those criteria is fulfilled, it would take a huge movement for anything to change the direction of the trend.

quote:
"You probably need about 10+ ways to measure trend statistically to make accurate decisions."

Can you name them and say some more info about them?
Thanks.

Erik, thanks for your comments.
It is well known that market distributions generally have fat tails. I presume you're talking about autocorrelation of price returns because autocorrelation of a price series would seem to be not very meaningful.
How does comparing the price series statistically to a Random Walk with Drift (Yt = α + Yt-1 + εt ) tell you the likelihood that a trending component exists? Which test(s) should be performed? Is this analysis also appropriate for shorter timeframes, i.e., sub-one hour periods?
What sort of accuracy are you talking about? I ask because autocorrelation is a fairly transitory phenomenon in price returns when attempting to use prior period autocorrelations on next period data. I have used an indiator called iVAR which may be related to Hurst and is a similar measure for trend/non-trend. The main difficulty with measures of this type is lag.
It's a shame retail traders don't have general access to most Latin American markets.
Good advice for anyone! I also highly recommend taking a machine learning course (also offered on coursera). Not for God's sake, but for your own benefit!

Yesterday I tried to improve my Kalman filter by adding another estimator of the trend and comparing it with the state of the Kalman filter. I then modulated the variance matrix based on how the two estimations were different (like I already do for the price). To make things short the result was very deceiving. As usual the lag could be reduced at the expense of the smoothness. That made me realize something. The problem doesn't come from the filter itself but the model used (here a 2nd order polynomial). Whatever model is used like a MA, linear/polynomial regression, a Kalman filter, a random walk with drift, an ARIMA model, spectral decomposition, etc... all of these models make the assumption that the trend is a stable drift of the price. This is quite true in the middle of the trend but the trend can change very suddenly. We have no way to detect this change quickly enough.

So I start wondering if it wouldn't be easier to have a phenomenological approach instead. We recognize that there are trends but without trying to understand if a given trend is a spurious movement or if it is statistically valid or where it is coming from. Just that it is a trend. Like Erik suggests, we use many models and/or heuristics to measure the trend with some confidence interval and mix them into a likelihood. We no more answer "what is a trend?" but "what is the most likely current estimation of the trend?" (for a given time scale).

Yes that's my takeaway from the statement:


It sounds like using an approach where many methods are used to identify the likely trend, and then bringing those estimates together to form a consensus opinion.

I tried the descriptive approach.

I used a Kalman filter (2nd order polynomial model). The result is shown on the first picture. This estimator is meant to denoise the signal it is given. Here it denoises the price quite correctly but this doesn't give a good estimation of the trend.

I gave another chance to the wavelet decomposition. On the second picture I show the smooth part with 32 (red), 16 (blue) and 8 (green) bars delay. The 32 and 16 are drawn back in the past. The green line (8 bars delay) is drawn at the time it is calculated. Adding more delay doesn't improve beyond what the red line shows. The red line gives a good estimate of what we would expect when we say "the trend". The green line is near (in value) of the red one but is so wavy that it makes it useless for a good estimation of the trend.

So I tried to feed the green line into a Kalman filter (constant model):

I also tried to feed the green line into the first Kalman filter (2nd order polynomial model), smooth but it overshoots:

I use two wavelet decompositions in parallel to form a Hilbert transform. I get the decomposition of the price as an analytic signal. The result of the first wavelet is the real part. The second gives the imaginary part. I estimate the instantaneous phase (red), the instantaneous frequency (black) which is the derivate of the phase and the amplitude of the 3rd level of details of the wavelet decomposition. The amplitude is draw above and below the trend line (blue). This is a kind of amplitude demodulation. It doesn't look much better than the Bollinger bands. Yet I used a Kalman filter to try to improve the results.

When the market is stable enough, that is when the red line is straight, you may notice that when the period (red) crosses 0 or ±π the price reached a top or a bottom ~3 bars earlier (depends on the frequency). Note that these angles are either a top or a bottom. They sometimes change their roles.

Really nice thread you made here guys, its very informative and good to see quality threads too

You guys use math way beyond my level of understanding, and i respect it very much, but i have to say and please don't get offended or angry on me, but i have to say it: ...You guys are just wasting your time by calculating all sorts of overcomplicated algorithms to detect the trend when infact it could be done with way less effort.

Ok i will share my view with you guys

I view the markets as a truly random collection of ticks with some biases over time.The market in itself is efficient by nature, so its a zero sum game, money cant be extracted from it if its in its equilibrium state.But, and this is important, sometimes it gets biased, and in this periods it is possible to extract money from it.An ineficciency comes, but due to the markets "healing" ability sometimes it gets back to equilibrium state very quickly.But if it supported by outside "forces" then it can stay inefficient much more time.I know i throwed here much information so lets break them down 1 by 1.

I view 2 types of inefficiencies, the ones which are hidden and the ones which are visible.

1. The visible ones are the ones which can be detected by naked eye and relatively easy to trade.In this group are the: news generated big long candles (which get pulled back immediatly, generating a hammer or shooting star pattern), candlestick patterns, chart patterns and volatility/breakout based patterns.These are easy to trade, but are rare and nearly impossible to trade it manually only with an EA.
2. The invisible ineficciency is the trend, it is invisible because its hard to detect it before coming, its only visible after its over ,ok , so the trend by my definition is the inefficiency which lasts much more longer than the other type, but its very hard to detect before coming, and its only, only generated by fundamental effects, so the only precise way to detect a trend before coming its to look at fundamentals, there is absolutely no way around that.

I`m also a TA and try to avoid fundamentals as much as i can ,but for detecting a trend you just simply cant ignore them.The other characteristics of a trend is that its only visible on higher timeframes like D1 or higher, because important economic decisions happen daily and are mostly spread out evenly during the current month, if you see a swing on low timeframes thats not necessarly a trend, even if it looks like, its only part of the trend if it moves in the direction of the main trend, else its just a random illusion.

The main trend forms on D1 and its visible here, for example the most important fundamentals affecting the USD in 2013 is the Quantitative Easing, this made the EUR/USD rally after september.

The gold's rally since the 2000s, specifically since 9/11, as the confidence in USD decreased:



Depreciation of the USD vs the CHF as being the second "haven" instrument after gold



Do you think this is random? I dont think so, the fundamentals do influence forex and cause ineficiency where money can be made, but they only become visible at high timeframes, that is why big investors like Warren would trade positions for years.But that doesnt mean that money cant be made on low timeframe, you just have to see the trend.

1. First you have to know the fundamentals which may influence the market
2. Decide on which timeframe you will trade (if you want to take advantage of the big yearly trend then intraday trading is not good, but if you want to trade intraday then look no further than D1 timeframe, and your entry can be anything below or equal to H1)
3. They you have to see the signs of the influence on the market
4. Then create an algorithm which detects the trend or if you trade manually use trendlines or whatever tools
5. Trade only when there are good signs that the trend will continue (again have to check the economic calendar)
6. And trade only in the direction of the trend to gain the edge, otherwise its no edge

This is my view and tutorial how to recognize and trade trending markets, of course they are only 1 type of inneficiency which can be traded but its the most reliable and safe to trade.

Again i`m sorry if i said anything bad but i think there is just no other way to gain edge in the trending perspective.Good luck guys and Merry Christmas!