Discussion of article "What is a trend and is the market structure based on trend or flat?" - page 2
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In econometrics, a trend is a function of price over time. I.e. the dependence can be any, including random or linear/nonlinear.
In the case of SB the trend is stochastic, i.e. the function of time is random. In the case of quotes, it can be deterministic (non-random), but it still needs to be proved.
The shift of average increments is called drift and it describes the tendency of a time series to be directed in one direction or another.
I.e. trend is the f-ya of price from time, minus drift and noise component, and there is no such concept as flat in econometrics.
It is difficult to say whether a trend is stochastic or deterministic from the probability distribution density function, because different densities describe different stochastic functions, which, in turn, are also random (describe a random trend).
In other words, you have reinvented the Hurst indicator in another interpretation, which determines persistence/antipersistence of a time series, but says nothing about functional dependence (trend). And the trend itself is always there.
Actually, it's not that hard.
Formula for calculating the theoretical price of stock futures
// F = S * (1 + r * n/365) - DIV
// F - theoretical futures price
// S - SPOT price
// r - Central Bank Rate
// n - number of days until expiry
// DIV - Dividends
Added
You may find the following functions useful:
It will not work on demo as there is no SPOT on demo
That's not good at all. A trend is not a probability density distribution of increments (quote), it is just a straight line. It has to be constructed with skill.
In econometrics, a trend is a function of price over time. I.e. the dependence can be any, including random or linear/nonlinear.
In the case of SB the trend is stochastic, i.e. the function of time is random. In the case of quotes, it can be deterministic (non-random), but it still needs to be proved.
The shift of average increments is called drift and it describes the tendency of a time series to be directed in one direction or another.
I.e. trend is the time-price function minus drift and noise component, and there is no such thing as flat in econometrics.
It is difficult to say whether the trend is stochastic or deterministic based on the probability distribution density function, because different densities describe different stochastic functions, which, in turn, are also random (describe a random trend).
In other words, you have reinvented the Hurst indicator in another interpretation, which determines persistence/antipersistence of a time series, but says nothing about functional dependence (trend). And the trend itself is always present.
Not disparaging your work. You have done a good job, but more logical ways of identifying trends have been devised for the financial markets. They're still valid today. They accurately characterise a trend. There is a sketched example in my thread.
Forum on trading, automated trading systems and testing trading strategies.
Uladzimir Izerski page
Uladzimir Izerski, 2020.07.22 11:33 AM
Here is an example of a classic way to determine the trend up. Which I use. Sequence of wave tops.
The tops of the waves are marked with icons. The current impulse wave is marked with a blue channel. The red channel shows thatthere is a pullback in the wave. It isnot a wave yet, but it may be a new corrective wave . We will know after the "N1" icon appears at the bottom of the pullback instead of N0.
But the trend now is up!!!
Don't linear and (more generally) non-linear regression show the same relationship?
PS. "Random dependence" sounds like an oxymoron in common trader's language. ;-)
Don't linear and (more generally) non-linear regression show the same relationship?
PS. "Random dependence" sounds like an oxymoron in common trader's language. ;-)
Random Walk with Drift and Deterministic Trend (Y t = α + Y t-1 + βt + ε t )
Another example is a non-stationary process that combines a random walk with a drift component (α) and a deterministic trend (βt). It specifies the value at time "t" by the last period's value, a drift, a trend, and a stochastic component.
Yes, in the simplest case, it does.Not disparaging your work. You have done a good job, but more logical ways of identifying trends have been devised for the financial markets. They're still valid today. They accurately characterise a trend. There's a sketched example in my thread.
If everything is already made up and it is more logical, please mark up this chart and draw conclusions about its characteristics.
Random Walk with Drift and Deterministic Trend (Y t = α + Y t-1 + βt + ε t )
Another example is a non-stationary process that combines a random walk with a drift component (α) and a deterministic trend (βt). It specifies the value at time "t" by the last period's value, a drift, a trend, and a stochastic component.
yes, in the simplest case it is.IMHO intraday:
in our cases, the drift can be neglected, it just doesn't exist.
and the trend component, that is beta, can take strictly defined values, 5-7, including 0. There are only a few of them, it's a la quantised.
and the question always arises - knowing this, how can we determine the beta chosen by the market earlier?
at beta=0 we have a clear and beautiful RandomWalk (in a "liquid" market it is directly visible, and on Mondays/rarely Fridays without warming up with news).
IMHO intraday:
in our cases drift can be neglected, it just isn't there
and the trend component, that is beta, can take strictly defined values, 5-7 of them, including 0. There are only a few of them, it's a la quantised
and the question always arises - knowing this, how can we determine the beta chosen by the market earlier?
at beta=0 we have a clear and beautiful RandomWalk (in a "liquid" market it is directly visible, and on Mondays/rarely Fridays without warming up with news).
I think it's a ph for the whole series, not for "intraday" only :) And there is a drift there