From theory to practice. Part 2 - page 81
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1. What does this have to do with "time cycles of working periods" anyway? What are these cycles - daily changes in volatility?
2. Break the price series into chunks, determine the variance of each chunk. You compare - if it is different - it depends on time.
You haven't answered the question. And for SB, different chunks will randomly have different variance too, especially the shorter ones. And they are assumed to have no time dependence. Although this is a strange statement in general, if the function varies over time, then it has a time dependence)
The question is why you think the variance of the CD is time dependent.
This is exactly the case.
If in SB the first differences are strictly stationary process, and the integrated series is stationary with equal samples or sets of realisations with finite sampling,
the price series does not have these properties.
Therefore, the price BP is much more complicated. There is nothing to argue about here.
Here's the inarticulate....
In SB, the first differences are a SLOWLY stationary process, because the autocovariance function is ZERO (the variables are NOT CORRELATED WITHIN).
The same is true for the price series
You haven't answered the question. And in SB, different sections will randomly have different variance too, especially the short ones. And they are assumed to have no time dependence. Although this is a strange statement in general, if the function varies over time, then it has time dependence)
Question why you think the variance of the CD is time dependent.
1. RETURN: You take a price series, break it into chunks, determine the variance - it's different. So the variance of the price series is time dependent.
2. What is highlighted is not understood at all - of course SB has variance as a function of time. That's why SB is a non-stationary process, just like a price series
1. I repeat: you take the price series, break it up into chunks, determine the variance - it is different. So the variance of the price series depends on time.
2. What's highlighted is not understood at all - of course SB has variance as a function of time. That's why SB is a non-stationary process, just like a price series
Apparently we had different maths teachers. I disagree. If a function varies over time, that doesn't mean there is any dependence on time at all. We can describe it over time, but the dependence / correlation on time may be zero. This is just about SB.
A school problem, can 1,000 women walk across a bridge at once. Logically the same number of men and women walk at different times, and it is not a function of time, but of external circumstances. The answer is that it can if a women's regiment is stationed nearby. If the circumstances are time-dependent, only then can it be argued that morning and evening as time affects the number of men on the bridge.
I look at the crowd of physicists and smile. They argue about who is smarter and who has a cooler degree.) And not at a leisurely pace how to profit from the market.
They look at the sine wave and think how to ride it. And it is a bouncy filly, physicists and mathematicians do not give any profit, only losses and destruction of nerves.
The market is the security of small transactions that lead to a definite trend. Physics plays a small role here. Only the psychology of the crowd pushes the price.
Who hasn't shown the diploma Daddy bought yet????)))))))))
Apparently we had different maths teachers. I disagree. If a function changes over time, it doesn't mean there is any dependence on time at all. We can describe it in time, but the dependence / correlation on time may be zero. This is just about SB.
A school problem, can 1,000 women walk across a bridge at once. Logically the same number of men and women walk at different times, and it is not a function of time, but of external circumstances. The answer is that it can if a women's regiment is stationed nearby. That's if circumstances are time-dependent, then only then can it be argued that morning and evening as time affects the number of men on the bridge.
Let's go over it again for the very young.
For a stationary process, variance and MO are constants. For a non-stationary process, variance and MO are time dependent (let's not take the more complex measures).
Time dependence means that the MO and variance change over time. Dependence is not necessarily functional dependence, nor is it correlation.
Don't take the complicated one for granted
So on a random process, can you make money? Or can you earn by chance, but not all the time?
On random wandering you can, but randomly. You can win at the oracle, but you can't win all the time
Naturally, SB is a non-stationary process, but it is a process with stationary (synonymous with homogeneous) increments. The term DS-row is used in econometrics.
Roughly speaking, if there is an algorithm by which a non-stationary series is constructed from a stationary series (for example, it is summation for SB), then this non-stationarity can (for our problems) be declared "simple" or "irrelevant", because for such series the problem of possibility (impossibility) to earn on them is solved strictly mathematically.
In my opinion, price series are non-stationary very "essentially" and extremely "not easily")
Naturally, SB is a non-stationary process, but it is a process with stationary (synonymous with homogeneous) increments. The term DS-row is used in econometrics.
Roughly speaking, if there is an algorithm by which a non-stationary series is constructed from a stationary series (for example, it is summation for SB), then this non-stationarity can (for our problems) be declared "simple" or "insignificant", because for such series the problem of possibility (impossibility) to earn on them is solved strictly mathematically.
In my opinion, price series are non-stationary very "essentially" and extremely "not easy")
How are the first differences of the SB different from the first differences of the price series?