Mousavi R topics in Farsi

  

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  45 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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  43 . . . . . . . . . . . . . . . . . . . . . . . . .

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  56 `H= Qt

  Q=DioV}B R

  

W =Q= y x=Q |= @= QO w | t tR }= QO m v m } W Q t @ Q= i=s v |= @ t a Q W v

O x OvDU OD OD@ xv} u x | =U | =v w_v x R Q Q | wt =D w

  R

  " U= |R UxO B @ k u }=Q CQ Y @ m i o Q= k } R TQO @ } U QO w C = =} p = =o w x x C Q Q Q x C =

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} ] R= =Q L y |=x a w U= i o Q= k u= t k a xO U= OQ t x W o W v m UQ t v @

j Q Q}k s O C xD Q Q Ov x q =iD w O xDi xD w x O | Q_ x

  "O W t |Q= U U v R= H y R= m vO=O Q= k } N t w r OQ t vw r= B w | Ro =B =y = u}t x O Q V w C@L h] w l} QDm CU

  R

  

L t u= a } R L Q W v }= @ @ "sO i= O t @ X N L t R= |=xQ B D i @ x=Q t=O= QO x @

E =@ wv Q Q = =D w u Q =v =D O x = E =@ = x}y Qm x x Ov

  : : : R

  

"OO o t K t x @ l v= a @ L QO w Q t tR '| L }O t ' v tR | y| U v t QO x } w

Q | Q] Ov O C = O = u} O Q =k | = = Q Ov = S

  

@ L t }= w O W t } D i J QO u K W m OQ=O v tR | y| U @ X N= u t rw=

x E =@ u w | s Ok pY Ov Q x | = = Q x =YD EL@ u}

  

@ Z i m O W t u v ] N }= QO "O W Y L | D t W v D OO o t }= } w w @ } t t=O= Qw t

Q Q x w | =W Q = =Hv w p = Q Kkv xD w = Q |

  V Q O = | x Q

  R

  " U= xO v m =Q Q= i=s v @ rw= } W 'x } w L t D |= @ t= o x v= N m U= }= C wt ?U R Q = x} | =v S E =@ ?}ka Q | Q Ov w x C u

u < DQ= w K Y= |= @ |O B w v Q _= v o y R= x } v ' v N R= r N L x Hw , t

  =k q Q =yvW} Q_ =y x w Q OvU w CU} pr | = Q = R} =trU "O v y= N xO U= w p U= wt O w =iD =@kD

  Ww v| U t U U |v O w w O}a O}

  1391 } B u= D R} = Qy pw= pYi |v=tR |=y|QU

  |v=tR |QU

  1

  1

  

@ v= D t C= y t F a " m t D u tR QO m U= } y } i F R= DQ a v tR | y| U

x O w | O =W C@ pt Ovv | Q}}e = x C | = Ov Q C@ Ov =@ | = = Q

  

@ "OO o t m D |w t v tR Y= i @ o F |wQ }= QO "O } B s v= U B } w o CQ Y

= Q | O} = =U | = p w = xDUU C@ =Hv Q P =H xD w} = xDUU w

  1,2, ,n

  

@ C= y t a t w CQ Y @ v tR a t ' U t v tR T t w v tR <= t ? v=

x O =W x wtH w x | = x wtH ? =v | = =}k | = O@ =ND

  x x x fx : t =

  1 2 ng

  "O W t xO=O u v

  1 2 n } w t W

  w | =W = pm

  |rYi C= Q}}eD w OvwQ '|v=tR |QU s}UQD

  1

  1

  1 =y|QU s}UQD

  1

  1

  1

  1 AirP assengers R : : :

  

} i t O= D m O W t xO U= u= a } R O N QO } yxO=O } i R= w U D |= @

u Q =U Oa x w | =iD wv Q w | = p = s} Q Q

  1949-1960

  " U= x W F xQwO QO Q t }= " yO t u v =Q v Q= y L @ v y t r= @ C O C@ = u O | =W Qi R ?U Q x = = |rrt u}

  %p=Ft

  1391 '

  Q U R= |= x a wtH t

  Jan F eb Mar Apr Ma y Jun Jul Aug Sep Oct No v Dec 1950 115 126 141 135 125 149 170 170 158 133 114 140 1951 145

  @ u xH}D v x m

  Y x

  } R CQ w

  U= Q

  " C

  > x <{ AirP assengers > y <{ windo w(x, 1950, 1951)

  }

  Q } R l

  = tR |

  H w

  @ =Q | v

  C UO x

  @ " O yO

  =F

t

x

  D Q } R p

  H w

  " O}v m x

  W

  pm

  1

  " O}v m x

  D Q } R p

  =t

  } R CQ w

  }

  @ =

  =F t x

  D Q } R p

  H w

  " O}v m x

  Jan F eb Mar Apr Ma y Jun Jul Aug Sep Oct No v Dec 1950 115 126 141 135 125 149 170 170 158 133 114 140

  @ u xH}D v x m

  Y x

  U= Q

  =F t x

  " C

  > x <{ AirP assengers > y <{ windo w(x, 1950, c(1951,0))

  @ Q o =

  O} y= wN

  |rY i |wQ

  = U R=

  W=O p QDv m p

  = @ xD

  O} W

  @ x = t ,

qF

t '

  v %1

  }

  |v

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  D " C

  @ =

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  u =

  R

  @

  s = v x

  Hw

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  D | t x m OQ=O O w

  O v= w

  2 > AP <{ AirP assengers > plot(AP , ylab = "P assengers (1000's)")

  t

  w

  U

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  v|

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  100 200 300 400 500 600 u

  P assengers (1000’s) 1950 1952 1954 1956 1958 1960

  W Time

  L 1 1 pm

  > x <{ AirP assengers

  3 |v=tR |=y|QU 1 pYi

  Jan F eb Mar Apr Ma y Jun Jul Aug Sep Oct No v Dec 1950 126 141 135 125 149 170 170 158 133 114 140 1951 145 150 178

  "OQ= v } Q D m m H D } R | v y t v tR | U @ u m = O M = x O}v x w Q x = = | = Q x wv

  V1 V2

  V3 V4

  V5 V6

  V7 V8

  V9 V10 V11 V12

  1

  3.59

  2.20

  4.53

  7.01

  10.45

  43.86

  59.97

  92.29

  47.00

  19.16

  12.45

  8.84

  2

  9.60

  19.12

  21.93

  24.20

  25.22

  42.28

  37.32

  14.11

  6.75

  4.40

  2.62

  2.82

  3

  3.13

  3.97

  17.52

  11.77

  9.65

  18.26

  72.26

  32.45

  12.09

  5.12

  3.03

  2.46

  4

  2.76

  4.17

  6.71

  10.57

  9.87

  7.58

  15.45

  29.85

  4.25

  1.74

  1.12

  1.04

  5

  1.22

  2.81

  6.25

  9.07

  28.12

  20.00

  36.48

  45.32

  12.19

  2.98

  2.85

  2.19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  @ "O v UQ =Q yu U w xO=O Q= k y U B =Q |Q t | yp U } @ = @= v y t | yxO=O U D |= @ x wt s = TB Q s Q CW = = = O = OD x = = = s} Q Q

  " U= } R K W @ pw= CQ Y | y v= =Q Q m }= u= D t CQ Y wO )m "O=O s C Q Q x w = O =H = u w | w

  > < " _ "

  x { matrix(scan( F:/R les/data/ghar.txt ), ncol=12, byrow=T)

  > <

  y { t(x)

  > <

  y { matrix(y,ncol=1, byrow=T)

  >

  ts.plot(y) " U= } R K W @ swO CQ Y | y )m

  C Q Q x w = O

  > < " _ "

  x { read.table( F:/R les/data/ghar.txt )

  > <

  y { as.matrix(y)

  > <

  y { t(x)

  > <

  y { matrix(y, ncol=1, byrow=T)

  >

  ts.plot(y)

  |v=tR |QU OvJ

  2

  1

  1

  1 1990 1958

  r D } i p U D p U R= r= U= QO , t "O=O u v s-= D CQ Y @ =Q v tR | U J u= D t O} w p = = = = =} QD qF =W w w x | = Q Ov w |

  }= "OQ=O O Hw )D L @ C W w r u t L @ r=< t ' a U C=w m L @ j @ u w u ?U Q qm QD} w}r} ?U Q Q}aW = C = wr} ?U Q Q

  R online

  "O W t x v= N )m U D CQ Y @ | U U w | O w O \ w w x Q x

  > " // ~ "

  http: www.massey.ac.nz/ pscowper/ts/cbe.dat

  > <

  CBE { read.table(www, header = T) CBE 1:4, ]

  1391 ' Ww v| U t

  4

  |v O w w

  choc beer elec 1 1451 96.3 1497 2 2037 84.4 1463 3 2477 91.2 1648 4 2785 81.9 1595

  O O M = Qo =@ x OvDU = = O = = = w | x_ q x w =t

  |=Q=O w vQ= v } Q D }O CQ a @ " y x t w p U k i q @ | yxO=O O W t L t m Q ]u y

  Q wt p O@ | = Q x ts() ` = =iD = =} u O = u Q =v OvDU} | = Q =D =

  

|= @ "O v } D v tR | U @ @ D R= xO U= @ =Q < W= }= } @ }= @ @ " v v tR | U Q N U

  O}v x w Q = O x = u

  " m H D } R | y )m @ Q m }=

  > " // ~ "

  http: www.massey.ac.nz/ pscowper/ts/cbe.dat

  > <

  CBE { read.table(www, header = T)

  > <

  Elec.ts - ts(CBE , 3], start = 1958, freq = 12)

  > <

  Beer.ts - ts(CBE , 2], start = 1958, freq = 12)

  > <

  Choc.ts - ts(CBE , 1], start = 1958, freq = 12)

  >

  plot(cbind(Elec.ts, Beer.ts, Choc.ts))

  C = = O Q p = wt

  " U= q @ | y )m |= H= Y L 2 1 Q=O v cbind(Elec.ts, Beer.ts, Choc.ts)

  14000 10000 Elec.ts

  6000 2000 200

  .ts 150

  Beer 100 6000

  Choc.ts 2000

  1960 1965 1970 1975 1980 1985 1990 Time

  v tR | U J } v %2

  1 W

  | = Q Ov V =t pm

  5 v tR | y| U 1 i

  | = = Q pY

  |rYi C= Q}}eD w OvwQ

  3

  1

  1

  1

  3

  2

  1

  ,

v L= w C B }O t ' i C= D ' vwQ @ yO t UO @ =Q | U | r= D v v tR | U UQ

= =} Q Q =k |rY Q}}e O xmr O | C x Q wo =yv x | = Q s

' m r L QO w U= i C= D p U y QO r= Q= D q @ p t QO 'OR U t y _ v =Q N }O t

  

|r C = C |rY Q}}e = Q wo Qm = =F = | Q = R} =] Q =k

D |= @ p t } DxO U " } o vwQ ' v W v y _ @ w D CQ Y @ m v tR | U QO D U C= D

u}@ Q O u Q = Ov w O O w |t Q = | =v w x x | = Q l} =tDU} Q}}e

Q t D @ i C= D

F- D u= D t ' vwQ =w uOQw UO @ |= @ " U= N y m w }= i= ' vwQ

  = `}tH = |rY Q}}e Q} = w | O K C x Q C |] V =

  V R O

y }O t Y N "O W t s v= @ D R= xO U= @ QO Q m }= "O @ @ R= vq U Q t @ v y t

  

Q Q =k x q w | =H ` = =iD = = u Q u} x = = x x = =

aggregate() R

  

"OR U t t yxO=O R= } y |= @ =Q i @ D w O W t t @ D U D i

= | u}a = l Q Q pY ` = w |

  XNW ` = \ w pY cycle() boxplot()

  >

  data(AirPassengers)

  > <

  AP { AirPassengers

  >

  layout(1:2)

  >

  plot(aggregate(AP))

  > ~

  boxplot(AP cycle(AP)) " U= q @ | y )m |= H= Y L 3 1 Q=O v

  C = = O Q p = wt

  %p=Ft

  OO o t L t m Q ]u y "O W t x v= N )m U D CQ Y @ v y t |Q @ | yxO=O Q | x_ q x w =t w | O w O \ w w x x = = =m} =

  R online 5000 aggregate(AP) 2000

  1950 1952 1954 1956 1958 1960 Time 400 100

  1

  2

  3

  4

  5

  

6

  7

  8

  9

  10

  11

  12

  v b o xplot w x W D vq U | U } v %3

  1 W

  =y O `}tH x = Q V =t pm @ D R= v tR | U @ v } D |= @ w v v tR | U yxO=O }= " U= t s v

  ` = | = Q x =y p O@ Q OvDU} | = Q = u C Q}eD = ts() unemploy

  D @ D U D vq U U t "OO o t L t u QO ?w D xQwO w `w W t=Q B m 'O W t xO U=

`}tH ` = \ w x = \ wD Q | x_ q =v Q QD = x w | =iD

freq

  "O W t t D a w w | u}a s}Uk Qort

  > < " ~ "

  www { http://www.massey.ac.nz/ pscowper/ts/Maine.dat

  > <

  Maine.month { read.table(www, header = TRUE)

  1391 ' Ww v| U t

  6

  |v O w w

  > <

  Maine.month.ts { ts(unemploy, start = c(1996, 1), freq = 12)

  > <

  Maine.annual.ts { aggregate(Maine.month.ts)/12

  >

  layout(1:2)

  > " % "

  plot(Maine.month.ts, ylab = unemployed ( ) )

  > " % "

  plot(Maine.annual.ts, ylab = unemployed ( ) )

  C = = O Q p = wt

  " U= q @ | y )m |= H= Y L 4 1 Q=O v yed (%) 3456 unemplo

  1996 1998 2000 2002 2004 2006 Time yed (%)

  4.5

  3.5 unemplo

1996 1998 2000 2002 2004

Time

  v U t w |Q @ | U } v %4

  1 W

  =y \ wD =m} Q V =t pm

  |v=tR |=y|QU x} RHD

  2

  1 =ypOt

  1

  2

  1 = O u Q =v w | O =W |rY Q}}e = O = Q |r} O x_ q q@ x w =t

  

yp t }= @ @ "O W t x y t i C= D } w vwQ y| U R= N QO ' W L t , k m Q ]u y

  4 O = | Q w x x C |at O | = Q = x RH l OvDU | = xi w

  " W @ t } R CQ Y @ m ' U= H p t ' v tR | U xO U } D } " y } y t |=Q=O r-

  = + + t t t t

  

x m s z

  xi w C |rY Q}}e Ov =t O x =W xi w C O O =W Q = x

  t " U= i C= D x } v t w vwQ v v t t " U= x W x y t | U t w u tR u QO m r- r- s m x t

  O | =W =] R}

  " yO t u v =Q N v t z

  5 =W Q w x x C | Q O l ? =v O w Q = O l w x |rY Q}}e Q

  

u v } R CQ Y @ m ' U= @ p t } U t p t 'O W y _ vwQ } CQ Y @ i C= D o =

  w |

  "O W t xO=O

  = t t t t

  

x m :s :z

  7 v tR | y| U 1 i

  | = = Q pY "OO o t } D H p t @ @ p t ' N= @=Q R= } Q r i o @ O W t L t m Q ]u y

  Q | p O@ |at O x | Q O Q} x] sD =o uD Q = w | x_ q x w =t

  t t t t t

  

y = ln( x ) = ln( m ) + ln( s ) + ln( z )

  t t t

  = m s z + +

  R QO =yxir wt x} RHD

  2

  2

  1

  • o = " m t OQw @ l t v t VwQ R= xO U= @ =Q i C= D w vwQ @ D ' QO

  Q Ov | Q QLD u}o =} =iD = |rY Q}}e O ` = decompose() R

  

@ \ @ t xO=O p t |= @ "OO o t O }= Q=O v U @ W } x v 'O o Q= k @ D N=O j i @ D

x w Q =F Q Q | =H wt x = pm l =o Q} Q ` = p w ` =

plot()

  

| v= QO w O W t U D 5 1 W @ w H p t CQ Y @ } R | y )m QO ' q @ p t j @ r D

=yD w | s} Q pm | Q |at O w x Q = O = =F Q O} w

  

W OO o t L t } i C= D w vwQ Q=O v } |wQ x Nq @ w O W t p vO @ p t y

)m

pm Q | x_ q =Hm |rY Q}}e O wt l Q = w | =@ | Q O = O

  " 6 1 Decomposition of multiplicative time series

  14000 ved

  8000 obser

  2000 12000 trend

  6000 2000

  1.10

  1.00 seasonal

  0.90

  1.06

  1.00 random

  0.94 1960 1965 1970 1975 1980 1985 1990

  Time

  | U | y r t } v %5

  1 W

  • |oDU@ty

  Q = xi w V =t pm

  3

  1

  y J } @ v D w } D |= @ "O @ y= N y r= t | y t 'Cq L R= N QO |oDU@t u}v O = =y p}rL x RH Q w Ov w xDU@t | wD = Q}eD = |r}

| yxO=O } ] R= w O W t } D y @ D U D v tR | y| U QO y Q N U "OO o t

  

= j Q w | h Qa |oDU@t ` = \ w | = = Q |oDU@t =D = Q u}a

  1391 ' Ww v| U t

  8

  |v O w w 14000 10000 8000 6000 4000 2000

  1960 1965 1970 1975 1980 1985 1990 Time

  i C= D w vwQ } v %6

  1 W

  |rY Q}}e O V =t pm

  T = u}o =} h Qa

  v } Q=w w v t } D 1 3 1

  Q}eD u}o =} E (x) u Q =v C xa = u}o =} ` w | =W E Q = x | = O}

  t v t }= @ @ " U= t H v t k=w QO 'O W t xO=O u v h L @ m } Q t=

  2 x x C w = QL ` Q u}o =} E (x ; ) ] =@ w | V =t R} = x C x

  

@ m U= p L C i= v= @ t v t CQ a "O W t xO=O } v v @ m U=

  2 w | V =t R} = x w | xD =v x Q}eD T =

  "O W t xO=O } v v @ m O W t N W t v } Q=w

  |oDU@t T = w h Qa

  y w v } Q=w m } D 2 3 1

  C h Qa p = Q w x T = w = x | wyi O} = xD (x y ) Q}eD Q

  " U= } D @ k } R CQ Y @ v } Q=w m s v @ t t ' W @ W=O t wO o =

  (x y ) = E (x ; )(y ; )] x y n O x x wt l Q Q} | O (x y ) Q}eD u} |] =@ R} ` T = w

  

R= xR= v= @ |= v v } o = "O o t xR= v= =Q t wO @ N \ DQ= u= t k=w QO v } Q=w m

  C Q w x x] x wt Q x wt T = w w | O} = xD (x y )

  " U= } R CQ Y @ u @=Q m O v OQw @ =Q v v v } Q=w m u= D t W @ W=O i i

  X Co v (x y ) = (x ; x)(y ; y )=n i i

  • 1 u} ? Q u Ov | u}a Oa O w x (x y ) Q}eD u} =@ R} |oDU@t ? Q

  w @ } }= " m t t @ CQ Y @ =Q t wO @ \ DQ= u= t y } )@ uw

  O w (x y ) = Q}eD u} |] =@ x C |va u O O = Qi ? Q u Q Q +1

  "OQ= v O Hw | y t @ N \ DQ= m U= t } @ W @ Y } }= o = "OQ=O Q= k

  w | h Qa Q w x (x y ) = Q}eD u} |va xa = |oDU@t

  "O W t } D } R CQ Y @ | y t @ } t H y

  E (x ; )(y ; )] (x y ) x y (x y ) = =

  9 |v=tR |=y|QU 1 pYi

  "OO o t U t } R CQ Y @ v v y } Q | x@ =L Q w x x wt |oDU@t ? Q

  Co v (x y ) Cor(x y ) = sd (x) sd (y )

  |oDU@t w T = w w ` w h Qa

  yO N w v } Q= m D= @= D } D 3 3 1

CQ Y @ v tR | U } v t @ D "O W t N=O B v t @ = @= v tR | y| U y } D |= @

w x | = Q l u}o =} ` = w | xD Q u}o =} x OD | = = Q |oDU@t h Qa Q

  t

  " W @ t R= @ D w U= } R O = | |a = C Q

  (t) = E (x ) t

  

Q C =DU u}o =} | = Q =o O =@ = |a = |va O = C = u}o =} ` = Q

" U= } R CQ Y @ u |= v v

6 OQw @ w U= }= v t QO v tR | U x v ' W v u tR R= @ D } ' W @ @ F v t @ D o =

  C Q w x x wt

  n

  X x = x =n t i=1

  " W @ t } R CQ Y @ ' U= }= v t QO m v tR | U } v } Q=w @ D O = | Q w x C =DU u}o =} x | = Q l T = ` =

  2

  2 (t) = E (x ; ) ] t

  2

  2 (t)

  

CQ Y @ u |= v v OQw @ "OO o t @ F @ } D x v ' W @ }= v v } Q=w QO v tR | U o =

w x x wt Q Q | C = x p O@ =o O = =DU R} T = | = Q Q

  " U= } R C Q

  P

  2 (x ; x) t

  V ar(x) = n ;

  1

  y U= t y t t= " vO @ }= v } Q=w w v t QO m }O v L t =Q v tR | U u m D

xDU@t C umt = Q}eD = O w =DU T = u}o =} x O wt x_ q | = Q wv =

  @ v | ys o Cw D @ i y t @ y m U= swO D t | }= v tR | U " W @ v

|oDU =y = = =i x \k = Q}eD u} |oDU@t x C x@ Q =DU | = Q Ov = R}

  7

  " } o N- D =Q y t @ | ys o O= D " W @ W=O Ov w Q} = = Q}eD u} = = Oa O = xD

  9

  8

  

| U o = " t v B B y } w yO N =Q t | yu tR QO VO N @ t } y

Q Q Ov = | =} |oDU@t = |oDU@t w hrDN = = w = Q}eD l |oDU@t

  k (acvf ) k

  

CQ Y @ =Q U= R= @ D m } v } Q=w m D= @ D u= D t x v ' W @ swO D t | }= v tR

w x C |a = x |va T = w w ` = w | =o O = x@ Q =DU | =

  "O v u @ } R wt =} Q

  = E (x ; )(x ; )] k t t+k E (x ) = E (x ) = t t+k k

  

@ D " U= } ' v u tR @ @=w v t = } R OQ= v u tR @ @ @ D

` = C |va CU} = x xDU u}o =} Q O = x |oDU ` =

  k (acf )

  "O W t } D } R CQ Y @ N- D @ yO N w | h Qa Q w x Q} = = |oDU@t w

  k = k

  2

  2 = =

  1

  " W @ t = } R ' U= m i o v u= D t q @ } D R= xO U= @ O = | Q C x C Q xH}D w | = h Qa =iD =

  1391 '|vWwOv|wUwt

  10 |oDU@tyOwN x@U=Lt

  1

  3

  3

  1 O =W Ci n ; 1 w | O = xDUU | = Q l x x x O =W n O}v Q wv

  x y t H u= D t " W @ o v tR | U }

  1 2 n x y t m Z i u m = |va

  }

  (x x ) (x x ) (x x )

  1

  2

  2 3 n;1 n Q Q}eD wv x O =W u} Q}eD wv x Q O =W u} Q C =

  

Z i swO t u= a @ =Q x y t twO w pw= t u= a @ GwR y QO =Q x y t rw= o = " N U =Q

  C Q w x |oDU@t ? Q O}v

  " U= } R CQ Y @ y } ' m

  n;1 ; ;

  P x ; x x ; x t (1) t+1 (2) t=1 s r =

  1 n;1 n;1 P ; P ;

  2

  2 x ; x x ; x t (1) t+1 (2) t=1 t=1 n n;1

  P P

  1

  1 Ov = O =W u} |oDU@t w ? Q C x = x x = x x

  " t v C= y t @ yO N } =Q u w U=

  2 t w 1 t u QO m n;1 n;1 t=2 t=1

  C hrDN = = x Q}eD u} |oDU@t ` x

  " U= t | yu tR QO t @ y k=w QO m

  w | =iD Q w Q r O = R | = O x n Q

  "O W t xO U= } R p t i R=

  1 W @ nQ @ i m xR= v= @ o = n;1 P

  (x ; x) (x ; x) t t+1 t=1 r =

  1 n P

  2 (x ; x) t t=1 n

  P

  1 wt x@ =L k Q} = = |oDU@t w ? Q w | j Q u}t x C x = x x

  "O v U t N- D @ =Q yO N } u= D t } ] y @ " U= t u QO m

  n t=1 n;k

  P (x ; x ) (x ; x ) t t+k t=1 r = k =

  1

  2 k n

  P

  2 (x ; x ) t t=1 n

  | = Q = q |r} w u Q Q x@ =L = r O =@ k > Q =k Q wta k

  

R= =Q v tR | U C a ]= R= N CQ Y }= QO = } R "O m U t =Q y } v }O t |= @ ,q t

  4 O} | C

  " yO t UO

  2 p w | xD Q Q_ Ok 5% w |va K] = r xr = Q Q

  "O W t i o v QO Q= t uO @ Q=O t U @ k |= Y i OQw @ |= @

  n

  10 Q=ov|oDU@ty

  2

  3

  3

  1 w | =iD = w wL k ?U Q = Q wL r wt | = = Q Q}Ui Q}@a Q k

  

"O W t xO U= yp ] Q t L @ yZ a Q t Q=O v R= ' v tR | y| U D w D |= @

  wL C Oa O Q |oDU@t w Q =k x = Q wL Ov = =o |oDU@t wt u

  

Q t " U= @ OQ=O Q= k |wQ yO N }O t m yZ a Q t " t v Q v y =Q Q=O v }=

)@ uw

C@U

  Q @ " 7 1 pm

  J =

  D Q =y

  N- =

  U Q D Q}

  | t s}

  W OO Q o

  ) |=

  | = yxO=O '

  "

  red

  "

  lag.plot(LakeHuron, lag=4, labels=F, do.lines=F, diag.col =

  >

  Q @

  D LakeHuron

  C U= lag=4 u w

  = D s}

  D |

  pm

  1

  v %7

  

wt

  yQ=O

  =

  N

  J 'q =

  576 577 578 579 580 581 582 Q}

  Lak eHuron 576 577 578 579 580 581 582

  Lak eHuron lag 4

  576 577 578 579 580 581 582 lag 2 Lak eHuron lag 3

  Lak eHuron 576 577 578 579 580 581 582

  @ p =F t QO lag 1

  U Q D |=

  Q} N-

  11

  U

  =

tR

xr

  | v

  "OQ=O | Q} o x v wt v

  i

  pY

  1

  Q

  @ |oDU

  y|

  =

  tR |

  =

  v

  |

  Y = i x

  @ O yO

  = y

  W | t xO

  v hrDN t |

  @

  = D R= s y x

  ` @

  R QO lag.plot()

  =iD U=

  @ "O w

  | t u

  ] p =F t u= wv a x

  = yp w

  = D x m

  Q} N-

  = y

  =W v =Q

  W

  • =

  U= Q

  =y v x

  W |t v

s

  UQ x O W xDi o Q=O wt v '

  O W =

  @ FALSE u

  = t w oQ u

  }= Q o = R=

  @ |

  Q }O

  U QD UO |=

  Q @ w OO

  Q o

  | t x

  Q} NP acf(x)

  $

  

acf

CQ w

  =k t w O w

  @ acf

  @ |Q=O Q

  V} B |=Q=O

  | t s

  UQ Q =o v

  |oDU@t y Q=O wt v CQ w

  Y u

  }= QO w C

  

U=

TRUE Z Q i

  |k]v t u

  = D |=R= x

  = t w oQ u

  }= % plot

  "O w

  W | t A

  = J

  = y

  Q} N-

  Y x

  @ QO Q

  V} B "OO

  C U= l

  Q @

  T }

  O v= u= wv a x

  @ Q}

  N- =

  D u = tR "

  } Q

  W | t xO

  @= Q

  @ acf

  $

  acf 1] Q=

  Ok t '

  O W =

  @

  =iD U= Q=O

  @ "O w

  }O =k t u

  Q o = "

  }= x m

  O} W

  = @ xD

  W=O x

  H w

  D k=0

  C U= acf

  @ =v

  $

  acf k+1] CQ w

  Y x

  @ q =

  @ Q=O Q

  @ u

  

}=

Q

  Q o

  }= Z Q i

  } R CQ w

  C U=

  "

  ,

  "

  partial

  "

  ), plot=TRUE) u QO x m "

  = yxO=O Q=O

  "

  Q @ % x

  | x]

  @=Q R= x m

  C U= Z

  Q i

  V} B |=Q=O

  R 'OO

  covariance

  

,

  P L u

  = D R=

  Y x