man - - PowerPoint PPT Presentation

SLIDE 1

• man

SLIDE 2

SLIDE 3

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

SLIDE 5

• 25

50 75 100 −1.0 −0.5 0.0 0.5 1.0 soi recruitment

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

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

SLIDE 8 −0.6 −0.4 −0.2 0.0 0.2 −20 −10 10 20 Lag CCF Series: soi & recruitment

• O

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

SLIDE 10

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

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

SLIDE 13

SLIDE 14

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

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

SLIDE 17

SLIDE 18

SLIDE 19

• ii d

Ut n NCO , of )

SLIDE 20 5 10 25 50 75 100 t y Linear trend

SLIDE 21

• =

St Pt t we It

• Ye
• Yt

. I = (

ft

Htt

ve )

• (ft

DH

• 1)

t ut . I ) = Vt

• Wf

. , t D ⇒ is

stationary

SLIDE 22 −1 1 2 25 50 75 100 t resid Detrended −2 2 25 50 75 100 t y_diff Differenced

SLIDE 23 3 6 25 50 75 100 t y Quadratic trend

SLIDE 24

• −2.5

0.0 2.5 5.0 25 50 75 100 t resid Detrended − Linear −2 −1 1 2 3 25 50 75 100 t resid Detrended − Quadratic

SLIDE 25

• d !

= d ' e

• d 's

. , = ( Yt

• Yet )
• I Yt
• i
• Yet

. z ) = ( ( St Ptt 8 t 't Vet

• (

ft

B ( t

• I )

t Ht

• is

't

• 1¥

#

t rft

• it

't ut . . ) t B t Ht

• 4 't

ut . D ) = Vt

• wt

. i t we . z t

8ft

• 28

(

tf

• ft
• 11 )

t 8 (

tf

• 4ft
• 14 )

= Vf

• wt

. I t WE

• L

t 28

SLIDE 26

• −2

2 25 50 75 100 t y_diff 1st Difference −6 −3 3 6 25 50 75 100 t y_diff 2nd Difference

SLIDE 27 0.00 0.25 0.50 0.75 5 10 15 20 Lag ACF Series: y 0.00 0.25 0.50 0.75 5 10 15 20 Lag PACF Series: y −0.4 −0.2 0.0 0.2 5 10 15 Lag ACF Series: diff(y) −0.4 −0.2 0.0 0.2 5 10 15 Lag PACF Series: diff(y) −0.50 −0.25 0.00 0.25 5 10 15 Lag ACF Series: diff(y, differences = 2) −0.50 −0.25 0.00 5 10 15 Lag PACF Series: diff(y, differences = 2)

SLIDE 28

SLIDE 29

SLIDE 30 AR(1) w/ phi = 0.9 AR(1) w/ phi = 1 AR(1) w/ phi = 1.01 100 200 300 400 500 −4 4 8 20 40 60 500 1000 1500 2000 2500 t y

• I

X

g 1.05

SLIDE 31 AR(1) w/ phi = −0.9 AR(1) w/ phi = −1 AR(1) w/ phi = −1.01 50 100 150 200 −4 4 −10 −5 5 10 −10000 −5000 5000 t y

• ft

x

SLIDE 32

• Yt

= 8 t d Yt

• i

t Vt = 8 t ¢ ( St 01 Yt . z t Vt . i ) t Vt = St lost ¢ ' Yt . a t ut t love . , = S t d s t

• l

' ( s

• 144¥

,

• 1

hit

• a )

t htt duh , = St as t ¢ 's t d ' Yt . 3 t we t d 4-

• i

t Ol ' ut . z =

! dis

t ! .

• live

. i

SLIDE 33

• ①

E Ht ) = e ( I . . dis ) t E ( I.

• oiu

= 8 t d St 4 ' Std 's t . .

• .

= 8

(

It to t

• l 't
• l 't

. . .

)

= { s to149 c I es

• therwise

SLIDE 34

• TO

Var Ht ) = Var ( I s ) t Var ( I.

• l

'

ut

. i ) =

I.

, var

( olive

. i ) =

!

. do " var I ve .

i

) = oof E

• u

'

( I

t

• l

' t

• l

" t 46 t lost . . .) =

{

Elite )

it 42 c , as

• ther

nice

SLIDE 35

• 8 ( h )

= Cov l Yt , Yt

• h)

Ho ) = Co . Ht , Yt ) = Va . la . ) =

Ya

= OI l I

• 1017/0

" to 't . . .) 84 ) = E ( I Ye

• E Htt

) I Yt

• I
• E

Itt

. ,)) ) =

486 )

= E ( ( I. di " i )

( ! olive

. e . i ) ) r

• elf

' "

:

"

it :

= E ( ¢ vi. , t 4 '

via

+

45

vi. , t . . . ) =

• f
• f

t do ' OI +05 oft .

• .

=

• ld (

Itd

't

¢ " t

loft

. . . )

SLIDE 36

• r

(2)

= E (

(

ut t lout . , + 4 ' ut

• 2

t d ' ut . z t

• .

)

(

Vt . 2 t ¢ ut . , t 102 ve

• qtr
• =

E ( ¢ ' we . a t Ol " we

• 3

t 46 ut

• y

t . . . ) = ¢ ' a t

• l

" oi + 46 of +

4%

' e . . . µ =

• f
• ? (

It

• l

'

• 1
• l

" -146

• c

. . .

)

=

• f

' 86 )

SLIDE 37

• END

=

¥¢

Var I Yet = , a = No ) Hh ) =

• f

" ' no )

Plh )

• 3¥

= a " '

SLIDE 38

• Assume

Stationary

• E

( Yt ) = E I St ¢ Yt . , t Ve ) E I Yt ) =

Stole

C Ye . i ) µ =

Stam

µ

• 4M

= S µ =

I

I

• d

SLIDE 39 phi=−0.5 phi=−0.9 phi= 0.5 phi= 0.9 25 50 75 100 25 50 75 100 −5.0 −2.5 0.0 2.5 5.0 −5.0 −2.5 0.0 2.5 5.0 t vals

SLIDE 40 −0.25 0.00 0.25 0.50 5 10 15 20 Lag ACF Series: phi= 0.5 0.0 0.3 0.6 5 10 15 20 Lag ACF Series: phi= 0.9 −0.4 −0.2 0.0 0.2 5 10 15 20 Lag ACF Series: phi=−0.5 −0.5 0.0 0.5 5 10 15 20 Lag ACF Series: phi=−0.9

SLIDE 41 −0.2 0.0 0.2 0.4 0.6 5 10 15 20 Lag PACF Series: phi= 0.5 0.0 0.3 0.6 5 10 15 20 Lag PACF Series: phi= 0.9 −0.4 −0.2 0.0 0.2 5 10 15 20 Lag PACF Series: phi=−0.5 −0.9 −0.6 −0.3 0.0 5 10 15 20 Lag PACF Series: phi=−0.9