#autoregressive

[isomorphismes]

"You can keep blaming your parents for your life in your 20's, but by the time you're 30 it's your own fault."

--having a difficult time getting an original source on this quote

This is like unknotting an autoregressive term in a time series. Even if the past only has a hold on the present back to 5 years ago, your upbringing still influences you when you're 70.

Because

who you were at 15 influences who you were at 20 ρ¹,

which in turn influences who you were at 25 ρ²,

and so on until 9 half-decades later there's a ρ¹¹ echo of your 15-year-old self

whose apprehension at the way she looked (or rather didn't look) rumbles faintly, faintly, faintly, faintly, faintly, faintly, faintly, faintly, faintly, faintly, faintly through time--the decisions then affected the next decisions which altered the next decisions ... on and on to the present.

If the initial spike was −1<ρ<1, then the rumble of the thunder diminishes geometrically over time. So a ρ=½ only shivers .00049 eleven knots into the future, and even a ρ=.9 recedes to a .314 by the time it's so deep past. 

  Maybe I can spot a corollary to the new parents' dilemma as well. If the present choices are always framed by the habits formed in the past, then ε perturbations in the baby's care echo forward, and forward, and forward...and can they really be undone?

[isomorphismes]

Autocorrelation

A "truly" random, uniform random, completely random sequence might look like

◯◯⨯◯⨯⨯⨯⨯◯◯⨯◯◯⨯⨯◯⨯◯◯⨯⨯◯⨯⨯◯⨯◯◯⨯◯ R code: > xooooo = sample( c("◯", "⨯") , 30, rep = T) 

like the flips of a fair coin. But there are other "random"s as well.

Biased

For example, biased random, like an unfair coin with 4/5 bias, might generate a sequence that looks like this:

◯◯◯◯⨯◯◯⨯◯◯⨯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯

R code: > xooooo = sample( c("◯","◯","◯","◯", "⨯") , 30, rep = T)  

Self-Correlated

But there's also autocorrelated, or serially correlated, randomness.

◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯◯⨯⨯⨯◯◯◯◯◯◯◯

For example you feel fine ◯ 80% of the time and 20% you're sick ⨯ -- and of course the sick days are more likely to come one after another. Or 80% of the time you don't smoke ◯ but then you buy a pack and all of a sudden you smoke ⨯⨯⨯ three days in a row. Once you've broken your resolve, you're more likely to smoke again the next day.  

Equation-wise, autocorrelation amounts to adding a self-lag term to the other explanatory variables (plus unexplained residual). Besides habit and viral invasion, autocorrelation brings many things under the penumbra of randomness:

income. The strong gets more, while the weak ones fade. If you made a lot of money at your previous job, your next employer will pay you more either to steal you away or simply because salary history determines compensation in HR's formula.

unemployment. Jobless today, jobless tomorrow. Those who are unemployed for more than six months are even more likely to be unemployed for the long term. Also people who take care of their own kids as their job are likely to still be doing so next week and next year rather than working for a company.

likelihood of cancer. Back to the subject of smoking, your likelihood of getting cancer accumulates faster and faster the more you smoke. I've seen claims that there is a kink in the cumulative propensity to cancer rate above one pack / day.

stock prices. Stocks don't just jump around in a Cauchy distribution, although maybe the daily change in stock price does. Daily change is a lag term  so that's serial correlation.

Serial correlation or autocorrelation refers to things that bunch together. When it rains, it pours.