์นดํ…Œ๊ณ ๋ฆฌ ๋ณด๊ด€๋ฌผ: stats

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Granger ์ธ๊ณผ์„ฑ ํ…Œ์ŠคํŠธ ๊ฒฐ๊ณผ ํ•ด์„ ์œ ์šฉํ•œ ๋„๊ตฌ ์ธ Bivariate Granger Causality-Free Statistics

Granger Causality์— ๋Œ€ํ•ด ์Šค์Šค๋กœ ๊ต์œกํ•˜๋ ค๊ณ ํ•ฉ๋‹ˆ๋‹ค. ์ด ์‚ฌ์ดํŠธ์˜ ๊ฒŒ์‹œ๋ฌผ๊ณผ ๋ช‡ ๊ฐ€์ง€ ์ข‹์€ ๊ธฐ์‚ฌ๋ฅผ ์˜จ๋ผ์ธ์—์„œ ์ฝ์—ˆ์Šต๋‹ˆ๋‹ค. ๋˜ํ•œ ์‹œ๊ณ„์—ด์„ ์ž…๋ ฅํ•˜๊ณ  Granger Stats๋ฅผ ๊ณ„์‚ฐํ•  ์ˆ˜ ์žˆ๋Š” ๋งค์šฐ ์œ ์šฉํ•œ ๋„๊ตฌ ์ธ Bivariate Granger Causality-Free Statistics Calculator ๋ฅผ ๋ฐœ๊ฒฌํ–ˆ์Šต๋‹ˆ๋‹ค. ์•„๋ž˜๋Š” ์‚ฌ์ดํŠธ์— ํฌํ•จ ๋œ ์ƒ˜ํ”Œ ๋ฐ์ดํ„ฐ์˜ ์ถœ๋ ฅ์ž…๋‹ˆ๋‹ค. ๋˜ํ•œ ๊ฒฐ๊ณผ๋ฅผ ํ•ด์„ํ•˜๋Š” ๋ฐ ์–ด๋ ค์›€์„ ๊ฒช์—ˆ์Šต๋‹ˆ๋‹ค.

๋‚ด ์งˆ๋ฌธ :

  • ๋‚ด ํ•ด์„์ด ๋ฐฉํ–ฅ์ด ๋งž์Šต๋‹ˆ๊นŒ?
  • ์–ด๋–ค ์ฃผ์š” ํ†ต์ฐฐ๋ ฅ์„ ๊ฐ„๊ณผ ํ–ˆ์Šต๋‹ˆ๊นŒ?
  • ๋˜ํ•œ CCF ์ฐจํŠธ์˜ ์˜๋ฏธ์™€ ํ•ด์„์€ ๋ฌด์—‡์ž…๋‹ˆ๊นŒ? (CCF๊ฐ€ ์ƒํ˜ธ ์ƒ๊ด€์ด๋ผ๊ณ  ๊ฐ€์ •ํ•ฉ๋‹ˆ๋‹ค.)

๋‹ค์Œ์€ ๋‚ด๊ฐ€ ํ•ด์„ ํ•œ ๊ฒฐ๊ณผ์™€ ๋„ํ‘œ์ž…๋‹ˆ๋‹ค.

Summary of computational transaction
Raw Input   view raw input (R code)
Raw Output  view raw output of R engine
Computing time  2 seconds
R Server    'Herman Ole Andreas Wold' @ wold.wessa.net

Granger Causality Test: Y = f(X)
Model   Res.DF  Diff. DF    F   p-value
Complete model  356
Reduced model   357 -1  17.9144959720894    2.94360540545316e-05

Granger Causality Test: X = f(Y)
Model   Res.DF  Diff. DF    F   p-value
Complete model  356
Reduced model   357 -1  0.0929541667364279  0.760632773377753

์—ฌ๊ธฐ์— ์ด๋ฏธ์ง€ ์„ค๋ช…์„ ์ž…๋ ฅํ•˜์‹ญ์‹œ์˜ค

๋‚ด ํ•ด์„ :

  • ํ…Œ์ŠคํŠธ๋Š” 357 ๊ฐœ์˜ ๋ฐ์ดํ„ฐ ํฌ์ธํŠธ๋ฅผ ๊ธฐ๋ฐ˜์œผ๋กœํ•˜๋ฉฐ 1์˜ ์ง€์—ฐ ๊ฐ’์œผ๋กœ ์ˆ˜ํ–‰๋˜์—ˆ์Šต๋‹ˆ๋‹ค.
  • p- ๊ฐ’ 0.0000294๋Š” x๊ฐ€ Y = f (x)์— ๋Œ€ํ•ด y๋ฅผ ์œ ๋ฐœํ•˜์ง€ ์•Š๋Š”๋‹ค๋Š” ๊ท€๋ฌด ๊ฐ€์„ค์„ ๊ธฐ๊ฐ ํ•  ์ˆ˜ ์žˆ์Œ์„ ์˜๋ฏธํ•ฉ๋‹ˆ๋‹ค.
  • p- ๊ฐ’์ด .76์ด๋ฉด X = f (Y)์— ๋Œ€ํ•ด null์„ ํ—ˆ์šฉ ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
  • ์ฒซ ๋ฒˆ์งธ ๊ฐ€์„ค์ด ๊ธฐ๊ฐ๋˜๊ณ  ๋‘ ๋ฒˆ์งธ ๊ฐ€์„ค์ด ์ธ์ •๋œ๋‹ค๋Š” ์‚ฌ์‹ค์€ ์ข‹์€ ๊ฒƒ์ž…๋‹ˆ๋‹ค
  • ๋‚˜๋Š” F- ๊ฒ€์ •์— ์กฐ๊ธˆ ๋…น์Šฌ ์—ˆ์œผ๋ฏ€๋กœ ์ง€๊ธˆ์€ ์ด๊ฒƒ์— ๋Œ€ํ•ด ํ•  ๋ง์ด ์—†์Šต๋‹ˆ๋‹ค.
  • CCF ๊ทธ๋ž˜ํ”„๋ฅผ ํ•ด์„ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ž˜ ๋ชจ๋ฅด๊ฒ ์Šต๋‹ˆ๋‹ค.

Granger-causality์— ์ •ํ†ตํ•œ ์—ฌ๋Ÿฌ๋ถ„ ์ค‘ ๋ˆ„๊ตฌ๋ผ๋„ ๋‚ด๊ฐ€ ์˜ฌ๋ฐ”๋ฅด๊ฒŒ ์ธํ„ฐํŽ˜์ด์‹ฑํ•˜๊ณ  ์žˆ๋Š”์ง€ ์—ฌ๋ถ€๋ฅผ ์•Œ๋ ค ์ฃผ์‹œ๋ฉด ๊ฐ์‚ฌํ•˜๊ฒ ์Šต๋‹ˆ๋‹ค.

๋‹น์‹ ์˜ ๋„์›€์„ ์ฃผ์…”์„œ ๊ฐ์‚ฌํ•ฉ๋‹ˆ๋‹ค.



๋‹ต๋ณ€

์ฃผ์˜ ์‚ฌํ•ญ : ๋‚˜๋Š” Granger ์ธ๊ณผ ๊ด€๊ณ„์— ํŠนํžˆ ์ •ํ†ตํ•˜์ง€๋Š” ์•Š์ง€๋งŒ ์ผ๋ฐ˜์ ์œผ๋กœ ํ†ต๊ณ„์ ์œผ๋กœ ์œ ๋Šฅํ•˜๋ฉฐ Judea Pearl โ€˜s Causality๋ฅผ ์ฝ๊ณ  ์ดํ•ด ํ–ˆ์œผ๋ฉฐ ๋” ๋งŽ์€ ์ •๋ณด๋ฅผ ๊ถŒ์žฅํ•ฉ๋‹ˆ๋‹ค.

๋‚ด ์ธํ„ฐ ๋Ÿฝ ํ…Œ์ด์…˜ ๋ฐฉํ–ฅ์ด ์ •ํ™•ํ•ฉ๋‹ˆ๊นŒ?

X

Y

๋‚ด๊ฐ€ ๊ฐ„๊ณผ ํ•œ ์ฃผ์š” ํ†ต์ฐฐ

Z

X

Y

Y

X

Z

Y

X

p- ๊ฐ’์ด .76์ด๋ฉด X = f (Y)์— ๋Œ€ํ•ด null์„ ํ—ˆ์šฉ ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.

X=f(Y)

๋‚˜๋Š” F ํ…Œ์ŠคํŠธ์—์„œ ์กฐ๊ธˆ ๋…น์Šฌ ์—ˆ์Šต๋‹ˆ๋‹ค.

X

Y

Y

X1

X2

X2

X1

X1

X2

CCF ๊ทธ๋ž˜ํ”„๋ฅผ ํ•ด์„ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ž˜ ๋ชจ๋ฅด๊ฒ ์Šต๋‹ˆ๋‹ค.

Y

X

์•ฝ 120 ์‹œ๊ฐ„ ๊ฐ„๊ฒฉ์˜ ํ”ผํฌ ํˆฌ ํ”ผํฌ์ฃผ๊ธฐ๋ฅผ ๊ฐ–๋Š” ๋ฐœ์ง„์„ ๊ฐ–๋Š”๋‹ค (์•ฝ 60 ์‹œ๊ฐ„ ๊ฐ„๊ฒฉ์œผ๋กœ ์ž์ฒด์ ์œผ๋กœ ์Œ์˜ ์ƒ๊ด€ ๊ด€๊ณ„๊ฐ€ ์žˆ๊ธฐ ๋•Œ๋ฌธ).


๋‹ต๋ณ€