Random Flow Theory and FOREX - page 69
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I was breaking it up into intervals of 3 cents, I can't remember now, maybe because of this, I got inconsistency around zero. The point is that the frequencies tend to the HP.
AlexEro, I wrote about it here already.
Ease of calculation is not a criterion for stationarity.
The coin example (1,-1) is the cumulative sum: if a series of one flip, the variance of the cumulative sum is 1; if two flips, it is 2, if three flips, it is almost 4, and so on. That is, the variance depends on the length of the series.
Now, compare it with the process of tossing a coin: as many times as you toss it, the variance is 1, i.e. it does not depend on the length of the series.
In the previous reply: by considering a series of variable lengths you are considering a new series, which is unconditionally non-stationary.
The example with a coin (1,-1) is a cumulative sum: if a series of one flip, the variance of the cumulative sum is 1; if two flips, it is 2, If three throws, it's almost 4., and so on.
It's obvious, Timbo, that you have never counted anything with your hands (and head). In which primer did you read this marvellous result? Another Timbovian miracle?
In the previous reply: by considering a series of variable lengths you are considering a new series, which is unconditionally non-stationary.
I'm considering a random walk, which, oh wonder!!!, is a non-stationary process after all. Any slices of the same length - would be noise, which is where we started.
There are still two of the toughest professionals out there who firmly believe that random walk is a stationary process. But they're already tired of "sorting it out" and are unlikely to admit that they've said something stupid.
It's obvious, Timbo, that you have never counted anything with your hands (and head). In which primer did you read this marvellous result? Another Timbovian miracle?
Come on, come on, come on, come on... How's "your" random walk, still stationary or not so stationary anymore? How about "semi-stationary"? Kinda like you haven't exactly been rambling on for a dozen pages in a row, save face, but also get closer to the real thing at the same time.
It's obvious, Timbo, that you have never counted anything with your hands (and head). In which primer did you read this marvellous result? Another Timbo miracle?
I propose a deal: I'll reduce the variance to "almost 3" and you admit that the random wandering "almost" is NOT stationary.
It all depends on which series to consider. A cumulative sum of indefinite length is not a series, a series is some discretisation of the original one. It is this discretization that can make the new series non-stationary. Or vice versa, it can turn a stationary series into non-stationary one. But the original series is stationary.
Experience 25... How is it not a series? So the price of oil or any stock is not a series? I mean they can be represented as a series of daily increments. Tell me you're overreacting...
Let's not get fancy and look at the definitions:
A time series is a time-ordered sequence of values of some arbitrary variable. Each individual value of a given variable is called a time series count.
How does a cumulative total not conform to this definition?
The cumulative series is stationary. Dispersion=1 for each term of the series. If it is split into series of variable length, the new series is not stationary. What you probably mean is that if you calculate MO and variance for a series of the entire length of the series (14 values), then if you then continue the series and calculate variance for more values (100 for example), it will be larger and will increase with the number of members in the series. I don't argue with that and wrote about series of variable length. Such series will be non-stationary. In short, everything depends on the partitioning of the initial series, but the initial series is stationary.
We are talking about the transient probability. The ACF shows it well. The smaller the sample, the greater the spread of the ACF and vice versa.
The graphs show a discrete simulation of -1;1 with a probability of 0.5. And the ACF of 10000 trials with a sliding window of 100 and 1000 outcomes.
Experience 25... How is it not a series? So the price of oil or any stock is not a series? I mean they can be represented as a series of daily increments. Tell me you're overreacting...
Let's not get fancy and turn to definitions:
Where does a cumulative amount not fit that definition?
Of course, a series of daily increments is a series. A discretisation step is defined here. If you formulate the same for the cumulative sum of a coin, you get a series too and it is stationary.
Just in the definition of stationarity invariance in time or invariance is not that "by increasing the length of the series the variance will be unchanged". >> well, I'm repeating myself.