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Probabilities in a Random Walk (Question about one CP's post)

  • #21
  • Mar 2, 2020 11:21am Mar 2, 2020 11:21am
Quoting artem_t
{quote} For me a trend is a move from point A to point B, where there are more either upward or downward movement. I remember the screenshot posted by some member here where he showed randomly generated chart. You won't tell the difference between real chart and that one.
Let me quote from an older post of mine:

'Why do people not realize that if trend-like patterns can be generated by a random walk, the inverse is nót necessarily true.'

Here with the inverse I mean the assumption that the market exhibits behavior that cannot be anything else than being fully described by random walks.

Of course people would be able to profit from trends in random data, but these temporary gains would all tend to be equalized after a statistically significant amount of trades.
  • #22
  • Mar 2, 2020 4:57pm Mar 2, 2020 4:57pm
Quoting artem_t
{quote} Hi Pip, Thanks for your reply! You're saying: {quote} But: {image} Source: https://www.investopedia.com/article...stationary.asp I'm not strong at math, so can't argue anything right now. But I've done several thorough researches in some other fields. And within CP's posts (that are not related to trading) I have found that he has deep knowledge in those same fields as well, and his conclusions correspond to mine. Of course, that doesn't automatically mean that all the rest of his statements are correct. But it gives...
Regarding differencing to remove a trend, that's literally just looking at the difference between each observation. Here's an example:

Gold prices
Attached Image (click to enlarge)
Click to Enlarge Name: Screenshot1.png Size: 49 KB


Differenced gold prices
Attached Image (click to enlarge)
Click to Enlarge Name: Screenshot3.png Size: 71 KB

Both are useful, but in very different ways.
Self-sufficiency is the greatest of all wealth. - Epicurus
  • #23
  • Mar 3, 2020 2:45pm Mar 3, 2020 2:45pm
Interested thread... Well apart of some DIRECT market effect, like (high economics news), "tweets" and even manipulation etc... there might be at least some form of random in the markets, right?

The theory (conclusion) that I find the most interesting is the one that says (apart of certain events) the markets are "random walk with left fat tail" or something similar Can not find the exact links but I think that below might be close...
http://ttswadvisory.com/2017/11/rand...ad-end-street/
https://forextraininggroup.com/rando...ncial-markets/
Can you afford to take that chance?
  • #24
  • Mar 4, 2020 1:54am Mar 4, 2020 1:54am
Quoting auricforecas
Interested thread... Well apart of some DIRECT market effect, like (high economics news), "tweets" and even manipulation etc... there might be at least some form of random in the markets, right? The theory (conclusion) that I find the most interesting is the one that says (apart of certain events) the markets are "random walk with left fat tail" or something similar Can not find the exact links but I think that below might be close... http://ttswadvisory.com/2017/11/rand...ad-end-street/...
When you have a lazy day or so, stroll into a casino with a pen and pad and find a high rotation roulette table (not one that only spins every 10 minutes). Take note of each red and black. 1 for red, -1 for black. With about 200+ observations, carefully plot it cumulatively. This is similar to what you can do in Excel, but more fun. It matters not if you take breaks, it is a random walk just as Craig and CP were talking about.

I keep going back to the law of large numbers - with sufficient data, in the long term the data can be proven to be random. Statistically, you could take an average of the minus and plus ones and see if they differ significantly from zero. Won't be exact zero, that would be a fluke. The same is true of financial data.

This is not to deny the existence of trends. In a casino, they are generated by a random process, so is true by definition - I think this may be what @kennerU was saying in post 21, above. The difference is that in markets, they are generated by the processes you describe, and anything else you can think of. You forgot the phase of the moon and planets bumping into each other.

The astute technical analyst will have the necessary tools which are freely available to be able to differentiate a trend from what is not a trend or what is persistent from what is not (edit - I have named one in a previous post here - note, I do not say random or not random, although that is getting semantic), knowing that in the end, it will all look random, like the chart of differences that EF5 provided.
  • #25
  • Mar 4, 2020 3:50am Mar 4, 2020 3:50am
Quoting LloydOz
This is not to deny the existence of trends. In a casino, they are generated by a random process, so is true by definition
This is not a trend. It is a fluke. A trend exists when there is a tendency (hence the name) to "push" the walk in a preferred direction. Nothing forces the roulette to choose red.
=> A long series of red at a roulette table is a spurious trend

Flipping a biaised coin that gives head says 51% of the time gives a preferrence to head. But you can still get long series of tails.
=> This is a stochastic trend

Modify your rule a little bit by adding 0.1 to the result = 1.1 for red and -0.9 for black.
=> You get a deterministic trend

http://hedibert.org/wp-content/uploa...4/DT-or-ST.pdf

What about the market? I think the three kinds happen together in proportion and magnitude that evolve over time.

The spurious part stems from the random time of the transations and their size vs the current state of the order book (liquidity) at that time. These can trigger cascade of stop orders.

The stochastic trend part comes, I guess, from the reaction and over-reaction of the traders, including algo.

The deterministic trend is due to the fundamentals.

Fundamentals come and go is a somewhat random fashion. Global crisis stays for years, interest rates can change by an amount decided by a central bank through a process you don't know completely (=random to us). A virus can pop up in China and spread around the world without a notice. Fundamentals create robust trends because they can persist a long time.
No greed. No fear. Just maths.
  • #26
  • Edited 5:46am Mar 4, 2020 4:52am | Edited 5:46am
Quoting PipMeUp
{quote} This is not a trend. It is a fluke. A trend exists when there is a tendency (hence the name) to "push" the walk in a preferred direction. Nothing forces the roulette to choose red. => A long series of red at a roulette table is a spurious trend Flipping a biaised coin that gives head says 51% of the time gives a preferrence to head. But you can still get long series of tails. => This is a stochastic trend Modify your rule a little bit by adding 0.1 to the result = 1.1 for red and -0.9 for black. => You get a deterministic trend http://hedibert.org/wp-content/uploa...4/DT-or-ST.pdf...
OK. It isn't a trend then.

Thankyou for clarifying, however a sharp eyed reader may have another question..

I did actually address the issue of the generating process as noted, albeit maybe in a flippant manner, and not as robust as yourself. Another process known and well acknowledged is the fractal process - that would be loosely stochastic, with modifications. There are others, well ensconced in the mirky corridors of academia..

I would like to add, though, that despite the generating process, the law of large numbers prevails. Black swans are included in this as outliers (one happened just about 20 hours ago, as I write this, by the Fed, sort of) and the well known fat tails propensity of markets (edit - what this means to readers unfamiliar, is that there will be more days/observations which are larger and happen more often than what would happen in the pages of a statistics text).

Explored by dudes such as Nicholas Taleb (and others) in his usual manner. But I digress.

Edit again - It also nearly goes beyond saying that cycles exist, but that is a whole other (off) topic.
  • #27
  • Mar 4, 2020 7:09am Mar 4, 2020 7:09am
From the data I analyzed, there is evidence of persistency in movements as compared to a random walk. However not too far off. A random walk will be 50/50 for every up and down whereas in the markets its like 57-58/43-42.Concluding that the participants are influenced by recent history and extrapolate the past into the future. But it is still incredibly hard to take advantage of. One must be very disciplined and patient because the edge is not that big.
When you see it, BET big.
  • #28
  • Mar 4, 2020 2:19pm Mar 4, 2020 2:19pm
Quoting PipMeUp
What about the market? I think the three kinds happen together in proportion and magnitude that evolve over time. The spurious part stems from the random time of the transations and their size vs the current state of the order book (liquidity) at that time. These can trigger cascade of stop orders. The stochastic trend part comes, I guess, from the reaction and over-reaction of the traders, including algo. The deterministic trend is due to the fundamentals.
Well put PipMeUp! That's a wise way of looking at the markets.
Self-sufficiency is the greatest of all wealth. - Epicurus
  • #29
  • Mar 4, 2020 3:07pm Mar 4, 2020 3:07pm
Quoting LloydOz
{quote} When you have a lazy day or so, stroll into a casino with a pen and pad and find a high rotation roulette table (not one that only spins every 10 minutes). Take note of each red and black. 1 for red, -1 for black. With about 200+ observations, carefully plot it cumulatively. This is similar to what you can do in Excel, but more fun. It matters not if you take breaks, it is a random walk just as Craig and CP were talking about. I keep going back to the law of large numbers - with sufficient data, in the long term the data can be proven to...
Yeah, that is whay I recommend (at cheetah thread also, for example) that should we STRIKE it big... we STOP Just in case it would random-out in the long-run
Within that LARGE numbers there are quite some SMALL numbers where some people DID get rich... the ones that KEPT that way were the ones that STOPPED... The rest though they "figured out the system" and gave everything back + adding whole fortune... some added quite some good debt (at high interest) to it

But with all being said, some people still APPEAR to have THE JUICE... therefore are banned from the casino
Can you afford to take that chance?
  • #30
  • Mar 7, 2020 11:30am Mar 7, 2020 11:30am
Quoting auricforecas
{quote} Yeah, that is whay I recommend (at cheetah thread also, for example) that should we STRIKE it big... we STOP Just in case it would random-out in the long-run Within that LARGE numbers there are quite some SMALL numbers where some people DID get rich... the ones that KEPT that way were the ones that STOPPED... The rest though they "figured out the system" and gave everything back + adding whole fortune... some added quite some good debt (at high interest) to it But with all being said, some people still APPEAR to have...
Super martingale.

May be we should look from a different prospective.
Everything I have calculated always confirms the efficient market but
The deviations which cannot be distorted in trend cannot be pre predicted but
The return to market efficiency is inevitable. That is the only point in which the probabilities change.

I think the majority are possibly looking at this conundrum from the wrong elevation
  • #31
  • Mar 7, 2020 11:37am Mar 7, 2020 11:37am
Quoting auricforecas
{quote} Yeah, that is whay I recommend (at cheetah thread also, for example) that should we STRIKE it big... we STOP Just in case it would random-out in the long-run Within that LARGE numbers there are quite some SMALL numbers where some people DID get rich... the ones that KEPT that way were the ones that STOPPED... The rest though they "figured out the system" and gave everything back + adding whole fortune... some added quite some good debt (at high interest) to it But with all being said, some people still APPEAR to have...
Super martingale.

May be we should look from a different prospective.
Everything I have calculated always confirms the efficient market but
The deviations which cannot be distorted in trend cannot be pre predicted but
The return to market efficiency is inevitable. That is the only point in which the probabilities change.

I think the majority are possibly looking at this conundrum from the wrong elevation

This can be prior to trend or returning to range.

The actual value of which is confusing everybody is actually irrelevant. Its the running black swan
  • #32
  • Mar 7, 2020 11:46am Mar 7, 2020 11:46am
And it from a viewd perspective is confusing. It only allows you to see a view point in a singular frame.

It needs to be viewd in multiple frames with considerations to all deviations on each frame.

Price will always return to market efficiency one frame at time.
  • #33
  • Mar 7, 2020 12:17pm Mar 7, 2020 12:17pm
Quoting PipMeUp
{quote} This is not a trend. It is a fluke. A trend exists when there is a tendency (hence the name) to "push" the walk in a preferred direction. Nothing forces the roulette to choose red. => A long series of red at a roulette table is a spurious trend Flipping a biaised coin that gives head says 51% of the time gives a preferrence to head. But you can still get long series of tails. => This is a stochastic trend Modify your rule a little bit by adding 0.1 to the result = 1.1 for red and -0.9 for black. => You get a deterministic trend http://hedibert.org/wp-content/uploa...4/DT-or-ST.pdf...
that's very well said.. but we must understand that when a system becomes too popular.. it is very likely to crash

with the increase of algorithmic trading I think only investors will survive.
  • #34
  • Edited Mar 8, 2020 1:20am Mar 7, 2020 2:03pm | Edited Mar 8, 2020 1:20am
Quoting HeyYou
{quote} that's very well said.. but we must understand that when a system becomes too popular.. it is very likely to crash with the increase of algorithmic trading I think only investors will survive.
BTW, we are all investors

for instance, if you have 100k Euro in your bank account, you are investing in Euro....

Now I don't think successful investing requires "discretion" at all...
  • #35
  • Mar 7, 2020 11:21pm Mar 7, 2020 11:21pm
Quoting EF5
{quote} Regarding differencing to remove a trend, that's literally just looking at the difference between each observation. Here's an example: Gold prices {image} Differenced gold prices {image} Both are useful, but in very different ways.
Can you explain your 2nd chart please?
I'm not a gold trader but the term "Differenced gold prices" or anything 'differenced' in the world of finance doesn't seem to really exist.
  • #36
  • Mar 8, 2020 1:21am Mar 8, 2020 1:21am
Quoting OutThere
{quote} Can you explain your 2nd chart please? I'm not a gold trader but the term "Differenced gold prices" or anything 'differenced' in the world of finance doesn't seem to really exist.
It just shows the daily change. That removes the trend like artem_t was talking about, but you wind up with a chart that's not really useful to traders.

Portfolio managers tend to use this kind of analysis in an effort to quantify risk.
Self-sufficiency is the greatest of all wealth. - Epicurus
  • #37
  • Jul 25, 2024 9:27am Jul 25, 2024 9:27am
Quoting artem_t
Does anybody know how to calculate properly the probability that Craig and CP mentioned?
Quoting PipMeUp
Because of the symmetry, each of the possible positive value has the same probability as its opposite. There is therefore exactly 50% chance to go up or down. Per construction it is independent of the path: it is memory-less.
It also triggered me when I read this the first time. However, the more often I read it, the more my perspective changed. Here is what Craig wrote: "We are looking at a stationary Gaussian random walk. When it gets away more than 2 standard deviations from the mean, the likelihood for being closer to the mean the next time is differs from 50 %". To imagine the overall scenario, consider a Bollinger band that's calculate over the last n values of the random walk. Since we have to look at the mean, we can imagine that the Bollinger bands are based on a simple moving average. And all moving averages lag, but the SMA lags most in comparison to more modern MAs. Therefore, it will continually push the upper band up during an up trend, even the random walk already "changed its direction". Therefore, you'll have a greater chance that the walk will go back into the bands once it left the bands. Below is an R example for a calculation periof of n = 10:

x <- cumsum(rnorm(1000000))
# x <- cumsum(sample(c(-1, 1), 1000000, replace = T))
n <- 10
m <- NULL
s <- NULL
for (i in n:length(x)) {
m[i] <- mean(x[(i-(n-1)):i])
s[i] <- sd(x[(i-(n-1)):i])
}
k <- which(x > m + 2*s)
dk <- diff(k)
length(which(dk > 1))/length(dk)

With n = 10 you have a 83 % that the walk will be closer to the mean once it hit mean + 2SD. With a random walk with (-1, +1) increments, the probability is a bit less (75 %).

BTW: If you increase n, the smaller these percentages get

But that's of course nothing you could use to make any profits in trading because you're trading away from a static point, your entry, and not towards a moving target (the moving average). (Just my 50 cents)
  • #38
  • Jul 26, 2024 5:34am Jul 26, 2024 5:34am
Quoting AntiCre
{quote} {quote} It also triggered me when I read this the first time. However, the more often I read it, the more my perspective changed. Here is what Craig wrote: "We are looking at a stationary Gaussian random walk. When it gets away more than 2 standard deviations from the mean, the likelihood for being closer to the mean the next time is differs from 50 %". To imagine the overall scenario, consider a Bollinger band that's calculate over the last n values of the random walk. Since we have to look at the mean, we can imagine that the Bollinger...

Very Cool!!! I may be mistaken but this goes towards the idea of "big money coming in"... and a Bollinger band measures the significance of price movement. The same happens with a zero lag MACD, a very reactive reference point: if price moves 5 pips above the DEMA it means it was faster than the reactive reference point therefore is significant and the breakout was real (= big money entered)

There is a Bayesian flavour to it...

Cheers
  • #39
  • Jul 28, 2024 8:32pm Jul 28, 2024 8:32pm
Quoting Swnlobo
{quote} Very Cool!!! I may be mistaken but this goes towards the idea of "big money coming in"... and a Bollinger band measures the significance of price movement. The same happens with a zero lag MACD, a very reactive reference point: if price moves 5 pips above the DEMA it means it was faster than the reactive reference point therefore is significant and the breakout was real (= big money entered)

There is a Bayesian flavour to it... Cheers
Yes, I agree. When I read the post of CP the first time in context with his other posts I also perceived it in the way you did: Fast price changes/high momentum causes further price changes in the same direction (somewhat like a landslide). But if you're using a static reference point, it seems to be 50/50, using a moving reference point, it shows the opposite, that a mean reversal is preferred.

Is there a Bayesian flavor to it? If so, I haven't seen it. Tbh, I personally couldn't see any momentum effect. It is equally likely to see a continuation in a move or a reversal, regardless of price moving 5 pips within a few ticks or within a few minutes/hours previously. But I'm open to being convinced that such a momentum effect exists – but please, with a quantitative analysis of market data (and not just some charts with lines drawn on them).
  • #40
  • Edited 11:08am Sep 2, 2024 10:58am | Edited 11:08am
Quoting AntiCre
With n = 10 you have a 83 % that the walk will be closer to the mean once it hit mean + 2SD. With a random walk with (-1, +1) increments, the probability is a bit less (75 %). BTW: If you increase n, the smaller these percentages get. But that's of course nothing you could use to make any profits in trading because you're trading away from a static point, your entry, and not towards a moving target (the moving average). (Just my 50 cents)
Hey AntiCre, care to explain more? do you mean your entry position is static, but the mean keeps moving? within certain limits, averaging can help

Statistics is not my field, however there should be conditions under which a stationary Gaussian random walk could exist. Of course, one must evaluate the applicability to the market


hint: check the Ornstein-Uhlenbeck process
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