What is not understood and taken into account when discussing the random walk model (RBS)
Usually discussing the original premise:
But they don't consider the continuation of the text at all:
Here's the main thing that all the debaters fail to consider:
SB is a discrete random process with independent STATIONARY increments.
Stationary increments are random variables with ZERO MOTION.
And their DISPERSION is LIMITED.
That is why SB will always be similar to price movements of currency pairs and in general to price movements of ALL financial assets and can always be used scientifically as a model of price movements of any financial akitv, including currency pair quotes on forex.
The variance of financial series increments is not a constant.
In addition, the cumulative sum of prices of financial assets under normal conditions cannot be a negative value, and for SB there is no such restriction.
The variance of the increments of a financial series is not a constant
Have you calculated it yourself? Can you now present the results of your calculations?
Have you worked it out for yourself?
Of course I have.
What is the problem with taking the first price increments of any TF and calculating the variance at different parts of the series?
Sure.
What's the problem with taking the first price increments of any TF and calculating the variance at different parts of the series?
Have you already done it? Show me the results of your calculations.
Have you done the maths yet? Show me the results of your calculations.
They already write and do not even think about the fact that there is a Theory of Probability and there is a Limit Theorem of Probability Theory, which states:
The variance of the sum of random processes = the sum of the variances of random processes.
What does it mean?
It makes sense to think first before writing all sorts of refutations.
Have you done the maths yet? Show me your calculation results.
What, Nikolaev 2?
EURJPY series, open H1, increments from 02.01.2018 to 06.09.2019, 2614 observations.
The MO of the increments is non-zero -0.0067.
The variance of the first half is0.047153, the variance of the second half is 0.030413.
What, Nikolaev 2?
EURJPY series, open H1, increments from 02.01.2018 to 06.09.2019, 2614 observations.
The MO of the increments is non-zero -0.0067.
First half variance0.047153, second half variance 0.030413
And what is the difference between MO and zero?
In Probability Theory, there is no absolute certainty about the values of the MO and the variance.
The MO is zero (MO=0) only in the transition when the number of experiments or measurements of random variables tends to infinity.
You plot the increments and post them here and then it will be clear to everyone that the process is stationary.
The variance of financial series increments is not a constant.
Also, the cumulative sum of financial asset prices cannot be negative under normal conditions, and there is no such limitation for SB.
I wrote that"their DISPERSION is LIMITED", but I did not write that the Dispersion is a constant.
Further, what makes you think that just the sum of the increments, which you call "cumulative sum" for some reason, must necessarily become negative?
All financial assets have a finite variance that varies within well-specified limits and that keeps the present values of the sum of the increments in the price of the financial asset in the positive area.
In random processes, there are sometimes 'outliers', where individual values of the sum of the increments are much larger than all the others.
But this does not change the overall picture.
I wrote that"their DISPERSION is LIMITED", but I did not write that the Dispersion is a constant.
Further, what makes you think that just the sum of increments, which you call "cumulative sum" for some reason, must necessarily become negative?
All financial assets have a finite variance that varies within well-specified limits and that keeps the present values of the sum of the increments in the price of the financial asset in the positive area.
In random processes, there are sometimes 'outliers', where individual values of the sum of the increments are much larger than all the others.
This does not change the overall picture.
1. There is no concept of "variance bounded" in TV. Limited by what? From minus infinity to plus infinity? Or from minus a million to plus a million? The variance of a stationary process must be a constant.
2. There are no outliers in one-dimensional discrete random walk - look at the increments. What kind of outliers if the increments can only be plus or minus 1?
3. Nowhere did I write "necessarily be negative". The sum of SB increments can be negative, the sum of the increments of a range of market prices cannot be negative under normal conditions.
You plot the increments and post them here and then it will be clear to everyone that the process is stationary.
Nothing will be clear to anyone - stationarity is not determined by eye.
It is the variance and the MO of the sections of the series that are compared.
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It is common to discuss the original premise:
But they don't consider the continuation of the text at all:
Here's the main thing that all the debaters fail to consider:
SB is a discrete random process with independent STATIONARY increments.
Stationary increments are random variables with ZERO MOTION.
And their DISPERSION is LIMITED.
That is why SB will always be similar to price movements of currency pairs and in general to price movements of ALL financial assets and can always be used scientifically as a model of price movements of any financial akitv, including currency pair quotes on forex.
At present, the most adequate model of price movement can be considered a NON-STATIONARY random process with STATIONARY random increments.