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7/31/2019 Flies Time Series
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arXiv:0811
.1561v2
[stat.AP]
16Nov2008
, ,
Z
Z
1
{x(t) | t N} x(t)
x(t + n) a1x(t + n 1) anx(t) = 0
a1, . . . , an R
x(t) = x (t) + (t)
x (t) 2
(t)
x(t + n) a1x(t + n 1) anx(t) = (t)
(t) = (t + n) a1(t + n 1) an(t)1
2
http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2http://arxiv.org/abs/0811.1561v2
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7/31/2019 Flies Time Series
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(t) 0
limN+
(0) + (1) + + (N)
N+ 1= 0
t N
,N(t) =(t) + (t + 1) + + (t + N)
N+ 1
0 N(t)
3
4
5
3
4
5
Z X x
z
n
[X x(0) x(1)z1
x(n 1)z(n1)
] an1z[X x(0)] anX = 0
Xx z X R(z)
X=P(z)
Q(z)
P(z) = b0zn1 + b1z
n2 + + bn1 R[z]Q(z) = zn an1z an R[z]
x(t) t 0X
P Qx(0), . . . , x(n 1)
x(t + n) a1x(t + n 1) anx(t)
=
(t)t +
(t) sin(t + )
(t), (t) R[t] ,, R ZX R(z) x(t)
x(t) t 0
K= Q (a1, . . . , an, b0, . . . , bn1)
Qa1, . . . , an, b0, . . . , bn1
K K
X K(z)X K K(z)
ddz
K
M 2n+ 1th 0 2n
d
dzznX, . . . ,
d
dzX,
d
dzzn1, . . . ,
d
dz1
M 2nx
n
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7/31/2019 Flies Time Series
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xn
a1, . . . , an, b0, . . . , bn16
a1, . . . , an (n+ 1) (n+ 1)N th 0 n + 1
dn+
dzn+znX, . . . ,
dn+
dzn+X
Xn+ 1
b0, . . . , bn1 N n
a1, . . . , an
Pb0, . . . , bn1 n
b0, . . . , bn1
xx
7
24008
5
3
6
a1, . . . , an, b0, . . . , bn12n
d
dzX d
dzzm 0 m n 1
7
8
0 500 1000 1500 2000 2500
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Samples
5
0 500 1000 1500 2000 2500
3
2
1
0
1
2
3
Samples
a1 . a2 a3 5
(t),N(t) ,N(t)
N = 100
,N(t)
x(t)
,N(t) =
N
=0((t + ) ,N(tN+ ))2
N+ 1
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7/31/2019 Flies Time Series
4/6
1050 1100 1150 1200 1250 1300 1350 1400 1450
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
Samples
0 500 1000 1500 2000 2500
0.03
0.02
0.01
0.00
0.01
0.02
0.03
Samples
5
50 65.6%
100 88.3%
200 62.3%
300 67.1%
,N(t)x(t) 5
N = 1009
9
3 3 99% 98.7%
2 2 95% 92.2%
68% 64.4%
5
0 500 1000 1500 2000 2500
0.20
0.15
0.10
0.05
0.00
0.05
0.10
0.15
0.20
Samples
95% 5
10
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7/31/2019 Flies Time Series
5/6
1050 1100 1150 1200 1250 1300 1350 1400 14501.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
Samples
0 500 1000 1500 2000 2500
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Samples
10
10
10
0 500 1000 1500 2000 2500
0.03
0.02
0.01
0.00
0.01
0.02
0.03
Samples
10
11
12
13
11
12
13
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7/31/2019 Flies Time Series
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0 500 1000 1500 2000 2500
0.20
0.15
0.10
0.05
0.00
0.05
0.10
0.15
0.20
Samples
95% 10
e
rd
e
th
z
rd
th
rd
nd
