* Differencing Model . . ARCD aimed - - PowerPoint PPT Presentation

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* Differencing Model . . ARCD aimed - - PowerPoint PPT Presentation

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* Differencing Model . . ARCD aimed

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SLIDE 1
  • *
. Differencing . ARCD Model aimed
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SLIDE 2
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SLIDE 3
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SLIDE 4 soi recruitment 1950 1960 1970 1980 25 50 75 100 −1.0 −0.5 0.0 0.5 1.0 date Variables recruitment soi
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SLIDE 5
  • 25
50 75 100 −1.0 −0.5 0.0 0.5 1.0 soi recruitment
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SLIDE 6 −1.0 −0.5 0.0 0.5 1.0 100 200 300 400 fish$soi −0.4 −0.2 0.0 0.2 0.4 0.6 5 10 15 20 25 30 35 Lag ACF −0.4 −0.2 0.0 0.2 0.4 0.6 5 10 15 20 25 30 35 Lag PACF
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SLIDE 7
  • 25
50 75 100 100 200 300 400 fish$recruitment −0.5 0.0 0.5 5 10 15 20 25 30 35 Lag ACF −0.5 0.0 0.5 5 10 15 20 25 30 35 Lag PACF
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SLIDE 8 −0.6 −0.4 −0.2 0.0 0.2 −20 −10 10 20 Lag CCF Series: soi & recruitment
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SLIDE 9 0.025 −0.299 −0.565 0.011 −0.53 −0.481 −0.042 −0.602 −0.374 −0.146 −0.602 −0.27 lag 8 lag 9 lag 10 lag 11 lag 4 lag 5 lag 6 lag 7 lag 0 lag 1 lag 2 lag 3 −1.0 −0.5 0.0 0.5 1.0−1.0 −0.5 0.0 0.5 1.0−1.0 −0.5 0.0 0.5 1.0−1.0 −0.5 0.0 0.5 1.0 30 60 90 120 30 60 90 120 30 60 90 120 soi recruitment
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SLIDE 10
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SLIDE 11
  • Model 3 − soi lags 5,6,7,8 (RMSE: 18.8)
Model 2 − soi lags 6,7 (RMSE: 20.8) Model 1 − soi lag 6 (RMSE: 22.4) 1950 1960 1970 1980 25 50 75 100 125 25 50 75 100 125 25 50 75 100 125 date recruitment
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SLIDE 12 −75 −50 −25 25 50 100 200 300 400 residuals(model3) −0.3 0.0 0.3 0.6 0.9 5 10 15 20 25 Lag ACF −0.3 0.0 0.3 0.6 0.9 5 10 15 20 25 Lag PACF
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SLIDE 13
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SLIDE 14
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SLIDE 15
  • Model 5 − AR(2); soi lags 5,6 (RMSE: 7.03)
Model 4 − AR(2); soi lags 5,6,7,8 (RMSE: 6.99) Model 3 − soi lags 5,6,7,8 (RMSE: 18.82) 1950 1960 1970 1980 25 50 75 100 125 25 50 75 100 125 25 50 75 100 125 date recruitment
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SLIDE 16
  • −40
−20 20 100 200 300 400 residuals(model5) −0.1 0.0 0.1 5 10 15 20 25 Lag ACF −0.1 0.0 0.1 5 10 15 20 25 Lag PACF
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SLIDE 17
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SLIDE 18
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SLIDE 19
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SLIDE 20 3 6 9 12 25 50 75 100 t y Linear trend
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SLIDE 21
  • de
= Yt
  • Yet
= 1 S + Ptt 14 )
  • ( S
t B It
  • 1 )
t Ye . i ) = p + Yt
  • Kt
  • i
  • stationary
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SLIDE 22 −3 −2 −1 1 2 3 25 50 75 100 t resid Detrended −2 2 25 50 75 100 t y_diff Differenced
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SLIDE 23 0.0 2.5 5.0 7.5 25 50 75 100 t y Quadratic trend
  • v
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SLIDE 24
  • −4
−2 2 4 25 50 75 100 t resid Detrended − Linear −2 −1 1 2 25 50 75 100 t resid Detrended − Quadratic
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SLIDE 25
  • Yc
. = St Bt + 2 at Xt dt
  • dt
. , = ( Yt . Yt . i )
  • ( Ye
. ,
  • Yet

:÷I¥I¥¥i*III¥"I!:tI.;""*O

= j

tXt-2Xt_X

stationary
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SLIDE 26
  • −2
2 4 25 50 75 100 t y_diff 1st Difference −4 4 25 50 75 100 t y_diff 2nd Difference
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SLIDE 27 0.00 0.25 0.50 0.75 5 10 15 20 Lag ACF Series: qt$y −0.25 0.00 0.25 0.50 0.75 5 10 15 20 Lag PACF Series: qt$y −0.50 −0.25 0.00 0.25 5 10 15 Lag ACF Series: diff(qt$y) −0.4 −0.2 0.0 0.2 0.4 5 10 15 Lag PACF Series: diff(qt$y) −0.75 −0.50 −0.25 0.00 0.25 5 10 15 Lag ACF Series: diff(qt$y, differences = 2) −0.75 −0.50 −0.25 0.00 5 10 15 Lag PACF Series: diff(qt$y, differences = 2)
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SLIDE 28
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SLIDE 29
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SLIDE 30 AR(1) w/ phi = 0.9 AR(1) w/ phi = 1 AR(1) w/ phi = 1.01 100 200 300 400 500 −5.0 −2.5 0.0 2.5 5.0 7.5 −10 10 500 1000 1500 t y
  • Hatio€
non.stationfnon-stati.no#
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SLIDE 31 AR(1) w/ phi = 0.9 AR(1) w/ phi = −1 AR(1) w/ phi = −1.01 100 200 300 400 500 −5.0 −2.5 0.0 2.5 5.0 −50 −25 25 50 −1000 −500 500 1000 t y
  • |Stationary
p \non.stat.on# No a Station a , y
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SLIDE 32
  • It
→ as ) Yt = S t 4 Yet + Ee = 8 + ¢ ( St ¢ Yt . it E ← , ) t E ← = s + ¢ s + 4Th . . it Ee + ¢ Et . , = g + 48 + 4 ' ( St 01 Yt . 3t ft . z ) t to +

¢E←

, = St lost ¢ 's t 43k . , + Et t # . ,

then

= S ( 1 + ¢ to 't 014 . . . ) t ( tit ¢ tt.it 44£ . it Pet . ,
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SLIDE 33
  • l
.

Elyi✓<

as

EHt✓s

2 , E He

)fµ

va.tl/=o'Yt=S(H4+o2t...)g.ym..g..y,.,y....y=c_)

+ , ↳ + ¢gµ , ¢ , g. + ... y E ( Yt )= S 11+4+444 't . . . ) to =

I

, if # ( 1 Var ( Yt )=Va , ( tttott . , to ' tent . . . ) a E =
  • f
442kt 44 It Poet . . . ± 03 =
  • f
( 1+4404+4 't . . .) = For
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SLIDE 34
  • j ( h )
= ( a I Yt , Yt
  • h )
y ( o ) = Va , ( yt ) = I 1- 42 8 ( i) = Co. ( Yt , Yet I = E ( l 'H
  • M ) ( Yt
. I

D)

=e l '

* Yt¥tiYY¥I

.IE#IYii.a+...g

= ¢ E ( te , ' ) + 43 Etty t FE Kai) + .
  • .
= ¢
  • f
t ¢3 of + ¢5oi t . . . = ¢ OI lit 4 't a " + It . . . ) = ¢ 84 )
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SLIDE 35
  • y ( 2)
= 02819 8 (3) = ¢3r(o ,

part

Yoga

01h

;( h )

= ¢hr(

gentle

#

"
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SLIDE 36 phi=−0.5 phi=−0.9 phi= 0.5 phi= 0.9 25 50 75 100 25 50 75 100 −3 3 −3 3 t vals
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SLIDE 37 −0.2 0.2 Lag ACF Series sims$‘phi= 0.5‘ 5 10 15 20 −0.2 0.4 Lag ACF Series sims$‘phi= 0.9‘ 5 10 15 20 −0.3 0.0 0.3 Lag ACF Series sims$‘phi=−0.5‘ 5 10 15 20 −0.5 0.5 Lag ACF Series sims$‘phi=−0.9‘ 5 10 15 20