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S tatistical models for time series prediction

S tatistical models for time series prediction. Autoregressive model(AR(1)). y t =f(y t-1 ) y t = a1 *y t-1. y t = a0+a1 *y t-1 y t-1 = a0+a1 *y t-2 y t-2 = a0+a1 *y t-3 y t = a0 +a1 (a0 + a1(a0+a1*y t-3 )). y t-1. y t-2. Give expectation. White noise.

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S tatistical models for time series prediction

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  1. Statistical models fortime series prediction

  2. Autoregressive model(AR(1)) • y t=f(yt-1 ) • yt = a1 *yt-1

  3. y t = a0+a1 *yt-1 • yt-1 = a0+a1 *yt-2 • yt-2 = a0+a1 *yt-3 • y t= a0 +a1 (a0 + a1(a0+a1*yt-3))

  4. yt-1 yt-2

  5. Give expectation

  6. White noise

  7. ARMA(p,q) model • AR(p) • AR(1) • AR(2)

  8. MA(q) model

  9. ARMA(p,q)

  10. Stationary condition

  11. ACF and PACF • AR(1) Give expectation

  12. Stationary.

  13. Variance of yt Variance of constant = 0

  14. Because of WN,

  15. ACF

  16. ACF of AR(2)

  17. ACF of MA • MA(1)

  18. When , • ACF of MA(1)

  19. PACF of ARMA

  20. PACF

  21. ARIMA • Example , , roots B = Not stationary

  22. Given

  23. One-order differential • Two-order differential • d-order differential

  24. Given is not stationary get “d” is ARMA(p,q) is ARIMA(p,d,q)

  25. Initial value

  26. 1.Determine the ACF and PACF of series • 2.If ACF or PACF do not match the ARMA rule of recognition , it is not stationary. • 3.Do difference , using ARIMA

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