Hi Spot9,
Firstly what I think of time. Time is a construct of man against which movement and frequency is given meaning within the constraints of our dimensional limitations.
So that sounds weird hey? Not meant to, essentially we measure everything by time, from the day of our inception to our departure. Not trying to ascribe any "weirdness" to this. It is what it is, we are constrained by it and consumed by it, hence we are so focused on it.
So is a lottery time series all non-stationary data? Can't answer for certain as I don't fully understand you definition of time series?
When I look at time attached to numbers that randomly drop or are picked or are plucked or maybe even harvested? Time in this setting is used to define one event from another, it can be without actual time but a definition of sequence, first ball is No. 3, followed by No. 17 etc.
Now if you remove time, either the actual millisecond or minute or hour or day or year from draws you are still left with a sequence of numbers drawn in a sequence. A list I guess without any reference back to dates.
Now if you remove the sequence? What do you have then? And how do you present that? A jumble of numbers which can be represented in my minds eye as Brownian motion within a constrained field (container of some type).
Brownian motion is normally attributed to fluids and the random movement of the particles that make up the fluid within a constrained environment. The initiator is generally derived from an outside influence such as heat which excites the fluid particles and starts the "random" movements. (very basic description).
In my universe everything is in motion, everything from macro size stars, black holes, spiral galaxies right through to the micro and down to the quantum.
I never see any data as potentially stationary or static, I always see things in dynamic, even if that dynamic is spread over a time frame far greater than my own.
But your question was about time... lotto time series to be precise.
"if a lottery time series was all non-stationary data?"
So having thought that through a little I would say my answer is Yes and No. A time series is never stationary
YES - If you only apply or extract a fixed sample of data from that time series. So if you are doing any analysis on historical outcomes you are working with a "static" set of numbers constrained by time.
NO - If you really want to see what is happening within a field of data you need to set aside static thinking and samples and review the data in it's entirety and dynamically. This is what I do, I find it immensely complex as I am not a mathematician, I can't even do calculus anymore :-(
So from my simplistic stance mathematical insights gleaned through statistics are simply that, insights. They give a point in time reference to a data series of past events, how does it then make any sense to use these "snapshots" to try to define a future outcome? I tried doing this for over 5 years like everyone else and found a pot of frustration at the end of that rainbow.
Now variable variance is a cool term, I'm guessing as a non establishment thinker that this relates to a variable that is in a constant state of flux or change, constantly evolving and changing with the data, which would make it essentially random? (sounds like my quantum and phantom bunnies).
To define this elusive beast one would first need to understand it's behaviour would they not? What makes up this variable variance? What factors weight in to define it's outcomes? What factors define those? And are they likewise variable variables?
Sorry long winded answer, I tend to ramble as I think things through on the fly.
It's all very large........