Statistics / Stat.CO

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Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package

์ด ๋…ผ๋ฌธ์€ ํ”„๋ž™ํƒˆ ์˜ค๋ฅด๋„ค์ŠคํŠธ ์šธํ—จ๋ฐฑ(fOU) ๊ณผ์ •์˜ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์— ๋Œ€ํ•ด ์‹ฌ๋„ ์žˆ๋Š” ๋ถ„์„์„ ์ œ๊ณตํ•˜๋ฉฐ, ํŠนํžˆ ๋””์Šคํฌ๋ฆฌํŠธ ๊ด€์ฐฐ ๋ฐ์ดํ„ฐ์—์„œ ํ—ˆ์ŠคํŠธ ์ง€์ˆ˜(H), ํ™•์‚ฐ ๊ณ„์ˆ˜(ฯƒ), ๊ทธ๋ฆฌ๊ณ  ๋“œ๋ฆฌํ”„ํŠธ ๋งค๊ฐœ๋ณ€์ˆ˜(ฮป)๋ฅผ ๋™์‹œ์— ์ถ”์ •ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์‹œํ•ฉ๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๊ธฐ์กด์˜ ์—ฐ๊ตฌ์™€ ๋‹ฌ๋ฆฌ ๋ชจ๋“  ๋งค๊ฐœ๋ณ€์ˆ˜๊ฐ€ ์•Œ๋ ค์ง€์ง€ ์•Š์€ ์ƒํƒœ์—์„œ๋„ ํšจ๊ณผ์ ์ธ ์ถ”์ •์ด ๊ฐ€๋Šฅํ•˜๋„๋ก ์„ค๊ณ„๋˜์—ˆ์Šต๋‹ˆ๋‹ค. 1์žฅ: ์„œ๋ก  ์„œ๋ก ์—์„œ๋Š” ํ”„๋ž™ํƒˆ ์˜ค๋ฅด๋„ค์ŠคํŠธ ์šธํ—จ๋ฐฑ(fOU) ๊ณผ์ •์— ๋Œ€ํ•œ ๋ฐฐ๊ฒฝ๊ณผ ์ด์ „ ์—ฐ๊ตฌ๋“ค์˜ ๊ฒฐ๊ณผ๋ฅผ ๊ฐ„๋žตํžˆ ์„ค๋ช…ํ•ฉ๋‹ˆ๋‹ค. ํŠนํžˆ, fOU๋Š” dYt ฮปYt dt + ฯƒdWHt๋กœ ์ •์˜๋˜๋ฉฐ, ์—ฌ

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