방학의 후유증이 가시지 않은 개강 첫날, 재미있는 글 하나 올려봅니다.
여기 나오는 그녀의 멍멍이 "올리버"는 부르면 잘 오는데, 저희 집 멍멍이는
부르면 더더욱 멀리 달아난다는..
(이런 글 올려서 죄송합니다. 교수님 ㅠ.ㅠ)
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<The Tale of the Drunk and Her Dog> Michael P. Murray
....
The drunk is NOT the only creature whose behavior follows a random walk.
Puppies, too, wander aimlessly when unleashed. Each new scent that crosses
the puppy's nose dictates a direction for the pup's next step, with the last
scent forgotten as soon as the new one arrives. (중략) One key trait of random
walks is that the most recently observed value of the variable is the best
forcaster of future values. If I come out of a bar with a friend who asks me,
"Where is that puppy we saw out here earlier?", I am likely to answer, "Well,
he was right over there when I went in." We might have the same exchange about
a drunk we saw earlier as well.
A second key trait of random walks is that the longer we have been in the bar,
the more likely it is that the puppy or the drunk has wandered far from where
we last saw them. If my friend and I had been in the bar a long while, I'd say
about either the dog or the drunk, "But heaven only knows where they've got to
by now." This growing variance in location characterizes the "nonstationarity"
of random walks.
But what if the dog belongs to the drunk? The drunk sets out from the bar, about
to wander aimlessly in random walk fashion. But periodically she intones "Oliver,
where are you?", and Oliver interrupts his aimless wandering to bark. He hears her;
she hears him. He thinks, "Oh, I can't let her get too far off; she'll lock me out."
She thinks, "Oh, I can't let him get too far off; he'll wake me up in the middle
of the night with his barking." Each assesses how far away the other is and moves
to partially close that gap.
Now neither drunk nor dog follows a random walk; each has added what we formally call
an 'error-correction mechanism' to her or his steps. But if one were to follow either
the drunk or her dog, one would still find them wandering seemingly aimlessly in
the night; as time goes on, the chance that either will have wandered far from the bar
grows. The path of the drunk and the dog are still nonstationary.
Significantly, despite the nonstationarity of the paths, one might still say, "If you
find her, the dog is unlikely to be very far away." If this is right, then the distance
between the two paths is stationary, and the walks of the woman and her dog are said
to be 'cointegrated of order zero'. ......
"A Drunk and Her Dog: An Illustration of Cointegration and Error Correction", The
American Statistician, February 1994, Vol. 48, No.1
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여기 나오는 그녀의 멍멍이 "올리버"는 부르면 잘 오는데, 저희 집 멍멍이는
부르면 더더욱 멀리 달아난다는..
(이런 글 올려서 죄송합니다. 교수님 ㅠ.ㅠ)
======================================================================
<The Tale of the Drunk and Her Dog> Michael P. Murray
....
The drunk is NOT the only creature whose behavior follows a random walk.
Puppies, too, wander aimlessly when unleashed. Each new scent that crosses
the puppy's nose dictates a direction for the pup's next step, with the last
scent forgotten as soon as the new one arrives. (중략) One key trait of random
walks is that the most recently observed value of the variable is the best
forcaster of future values. If I come out of a bar with a friend who asks me,
"Where is that puppy we saw out here earlier?", I am likely to answer, "Well,
he was right over there when I went in." We might have the same exchange about
a drunk we saw earlier as well.
A second key trait of random walks is that the longer we have been in the bar,
the more likely it is that the puppy or the drunk has wandered far from where
we last saw them. If my friend and I had been in the bar a long while, I'd say
about either the dog or the drunk, "But heaven only knows where they've got to
by now." This growing variance in location characterizes the "nonstationarity"
of random walks.
But what if the dog belongs to the drunk? The drunk sets out from the bar, about
to wander aimlessly in random walk fashion. But periodically she intones "Oliver,
where are you?", and Oliver interrupts his aimless wandering to bark. He hears her;
she hears him. He thinks, "Oh, I can't let her get too far off; she'll lock me out."
She thinks, "Oh, I can't let him get too far off; he'll wake me up in the middle
of the night with his barking." Each assesses how far away the other is and moves
to partially close that gap.
Now neither drunk nor dog follows a random walk; each has added what we formally call
an 'error-correction mechanism' to her or his steps. But if one were to follow either
the drunk or her dog, one would still find them wandering seemingly aimlessly in
the night; as time goes on, the chance that either will have wandered far from the bar
grows. The path of the drunk and the dog are still nonstationary.
Significantly, despite the nonstationarity of the paths, one might still say, "If you
find her, the dog is unlikely to be very far away." If this is right, then the distance
between the two paths is stationary, and the walks of the woman and her dog are said
to be 'cointegrated of order zero'. ......
"A Drunk and Her Dog: An Illustration of Cointegration and Error Correction", The
American Statistician, February 1994, Vol. 48, No.1
===============================================================================