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^7` Exvhwwl/ I1 dqg D1F1 Kduyh| +5334,/ Whvwlqj iru wkh suhvhqfh ri d udqgrpzdon lq vhulhv zlwk vwuxfwxudo euhdnv1 Mrxuqdo ri Wlph Vhulhv Dqdo|vlv 55/

45:0831

^8` Exvhwwl/ I1 dqg D1F1 Kduyh| +5335,/ Ixuwkhu frpphqwv rq vwdwlrqdulw| whvwvlq vhulhv zlwk vwuxfwxudo euhdnv dw xqnqrzq srlqwv/ Mrxuqdo ri Wlph Vhulhv

Dqdo|vlv/ iruwkfrplqj1

^9` Exvhwwl/ I1 dqg D1P1U1 Wd|oru +5335,/ Whvwlqj djdlqvw vwrfkdvwlf wuhqg dqgvhdvrqdolw| lq wkh suhvhqfh ri xqdwwhqghg euhdnv dqg xqlw urrwv/ Xqlyhuvlw|ri Eluplqjkdp glvfxvvlrq sdshu/ 53350[[1

^:` Fdqhu/ P1 +4<<;,/ D orfdoo| rswlpdo vhdvrqdo xqlw urrw whvw/ Mrxuqdo ri Exvl0qhvv dqg Hfrqrplf Vwdwlvwlfv/ 49/ 67<0891

^;` Fdqryd/ I1 dqg E1H1 Kdqvhq +4<<8,/ Duh vhdvrqdo sdwwhuqv frqvwdqw ryhuwlphB D whvw iru vhdvrqdo vwdelolw|/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlv0

wlfv/ 5/ 5<5067<1

^<` Fdqryd/ I1 dqg H1 Jk|vhov +4<<8,/ Fkdqjhv lq vhdvrqdo sdwwhuqv1 Duh wkh|F|folfdoB/ Mrxuqdo ri Hfrqrplf G|qdplfv dqg Frqwuro/ 4;/ 4476044:41

^43` Fkdq/ Q1K1 dqg F1]1 Zhl +4<;;,/ Olplwlqj glvwulexwlrqv ri ohdvw vtxduhv hvwl0pdwhv ri xqvwdeoh dxwruhjuhvvlyh surfhvvhv/ Dqqdov ri Vwdwlvwlfv/ 49/ 69:07341

67

^44` Fohyhodqg/ Z1V1 dqg V1M Ghyolq +4<;3,/ Fdohqgdu h�hfwv lq prqwko| wlph vh0ulhv= ghwhfwlrq e| vshfwuxp dqg judsklfdo phwkrgv/ Mrxuqdo ri wkh Dphulfdq

Vwdwlvwlfdo Dvvrfldwlrq/ :8/ 7;:0<91

^45` gh Mrqj/ S1 dqg M1 Shq}hu +4<<;,/ Gldjqrvlqj vkrfnv lq wlph vhulhv/ Mrxuqdori wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ <6/ :<90;391

^46` Jk|vhov/ H1 +4<<3,/ Rq vhdvrqdo dv|pphwulhv dqg wkhlu lpsolfdwlrqv iruvwrfkdvwlf dqg ghwhuplqlvwlf prghov ri vhdvrqdolw|/ FUGH glvfxvvlrq sdshu/Xqlyhuvlw| ri Prqwuhdo1

^47` Kdplowrq/ M1G1 +4<<9,/ Wkh gdlo| pdunhw iru ihghudo ixqgv/ Mrxuqdo ri SrolwlfdoHfrqrp|/ 437/ 590891

^48` Kduyh|/ D1F1 +4<;<,/ Iruhfdvwlqj/ vwuxfwxudo wlph vhulhv prghov dqg wkh

Ndopdq �owhu/ Fdpeulgjh/ Fdpeulgjh Xqlyhuvlw| Suhvv1

^49` Kduyh|/ D1F1 +5334,/ Whvwlqj lq xqrevhuyhg frpsrqhqwv prghov1 Mrxuqdo riIruhfdvwlqj/ 53/ 404<1

^4:` Kduyh|/ D1F1 dqg P1 Vwuhleho +4<<:,/ Whvwlqj iru qrqvwdwlrqdu| xqrevhuyhgfrpsrqhqwv/ plphr1

^4;` Nlqj/ P1O1 dqg J1K1 Kloolhu +4<;8,/ Orfdoo| ehvw lqyduldqw whvwv ri wkh hu0uru fryduldqfh pdwul{ lq wkh olqhdu uhjuhvvlrq prgho/ Mrxuqdo ri wkh Ur|do

Vwdwlvwlfdo Vrflhw|/ Vhulhv E 7:/ <;04351

^4<` Nlwdjdzd/ J1/ dqg Z1 Jhuvfk +4<<9,/ Vprrwkqhvv sulruv dqdo|vlv ri wlph

vhulhv1 Ehuolq= Vsulqjhu0Yhuodj 1

^53` Nzldwnrzvnl/ G1/ Skloolsv/ S1F1E1/ Vfkplgw/ S1 dqg \1 Vklq +4<<5,/ Whvwlqjwkh qxoo k|srwkhvlv ri vwdwlrqdulw| djdlqvw wkh dowhuqdwlyh ri d xqlw urrw=krz vxuh duh zh wkdw hfrqrplf wlph vhulhv kdyh d xqlw urrwB/ Mrxuqdo riHfrqrphwulfv 77/ 48<04:;1

^54` Nrrspdq/ V1M1/ Q1 Vkhskdug dqg M1 Grruqln +4<<<,1 Vwdwlvwlfdo dojrulwkpviru prghov lq vwdwh vsdfh xvlqj VviSdfn 5151 Hfrqrphwulfv Mrxuqdo/ 5/ 4460991

^55` Nrrspdq/ V1M1/ D1F1 Kduyh|/ M1D1 Grruqln dqg Q1 Vkhskdug +5333,1 VWDPS

913 Vwuxfwxudo Wlph Vhulhv Dqdo|vlv Prghoohu dqg Suhglfwru/ Orqgrq= Wlp0ehuodnh Frqvxowdqwv1

68

^56` Oh|erxuqh/ V1M1 dqg E1S1P1 PfFdeh +4<<7,/ D frqvlvwhqw whvw iru d xqlw urrw/Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv 45/ 48:04991

^57` Q|eorp/ M1 +4<;<,/ Whvwlqj iru wkh frqvwdqf| ri sdudphwhuv ryhu wlph/ Mrxuqdori wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq ;7/ 55605631

^58` Slhufh/ G1D1 +4<:;,/ Vhdvrqdo dgmxvwphqw zkhq erwk ghwhuplqlvwlf dqgvwrfkdvwlf vhdvrqdolw| duh suhvhqw/ lq D1 ]hooqhu +hg1,/ Vhdvrqdo Dqdo|vlv ri

Hfrqrplf Wlph Vhulhv/ 57509</ Zdvklqjwrq GF= Exuhdx ri wkh Fhqvxv1

^59` Surlhwwl/ W1 +5333,/ Frpsdulqj vhdvrqdo frpsrqhqwv iru vwuxfwxudo wlph vhulhvprghov/ Lqwhuqdwlrqdo Mrxuqdo ri Iruhfdvwlqj/ 49/ 57:0931

^5:` Vdlnnrqhq/ S1 dqg U1 Oxxnnrqhq +4<<6,/ Whvwlqj iru d Prylqj Dyhudjh XqlwUrrw lq Dxwruhjuhvvlyh Lqwhjudwhg Prylqj Dyhudjh Prghov/ Mrxuqdo ri wkhDphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ ;;/ 8<909341

^5;` Vplwk/ U1M1 dqg D1P1U1 Wd|oru +4<<;,/ Dgglwlrqdo fulwlfdo ydoxhv dqg dv|ps0wrwlf uhsuhvhqwdwlrqv iru vhdvrqdo xqlw urrw whvwv/ Mrxuqdo ri Hfrqrphwulfv;8/ 59<05;;1

^5<` Vrxnxs/ U1M1 dqg G1I1 Ilqgoh| +5333,/ Rq wkh Vshfwuxp Gldjqrvwlfv xvhg e|[0450 DULPD wr Lqglfdwh wkh Suhvhqfh ri Wudglqj Gd| H�hfwv Diwhu Prgholqjru Dgmxvwphqw/ C 4<<< Surfhhglqjv ri wkh Exvlqhvv dqg Hfrqrplf VwdwlvwlfvVhfwlrq/ Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ 477047<1

^63` Vwrfn/ M1K1 +4<<7, Xqlw urrwv/ vwuxfwxudo euhdnv dqg wuhqgv/ lq U1I1 Hqjohdqg G1O1 PfIdgghq +hgv1,/ Kdqgerrn ri Hfrqrphwulfv 7/ Hovhylhu Vflhqfh/5:6<05;731

^64` Wd|oru/ D1P1U1 +5335d,/ Orfdoo| rswlpdo whvwv djdlqvw vhdvrqdo xqlw urrwv/iruwkfrplqj/ Mrxuqdo ri Wlph Vhulhv Dqdo|vlv1

^65` Wd|oru/ D1P1U1 +5335e,/ Urexvw vwdwlrqdulw| whvwv lq vhdvrqdo wlph vhulhvsurfhvvhv/ iruwkfrplqj/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv1

69

σ κ/σ

εIn

nov.

Sm

ooth

.In

nov.

Sm

ooth

.In

nov.

Sm

ooth

.m

=4

m=

8m

=4

m=

8m

=4

m=

8m

=4

m=

8

05.

104.

825.

635.

855.

565.

424.

294.

304.

754.

473.

843.

244.

163.

490.

010

8.52

8.10

9.36

9.97

9.23

9.90

7.31

7.23

7.77

7.31

6.32

5.49

6.74

5.61

0.02

526

.78

27.5

031

.52

33.4

731

.23

33.1

924

.75

23.9

325

.33

24.3

622

.52

20.2

423

.29

20.4

20.

050

60.3

764

.35

74.1

377

.96

74.0

777

.78

58.8

056

.68

58.7

856

.56

56.3

652

.43

56.4

452

.01

0.10

086

.27

92.6

195

.54

98.3

195

.40

98.1

586

.92

83.8

685

.95

83.2

785

.49

81.4

284

.54

80.4

50.

500

96.7

510

0.00

98.7

010

0.00

98.7

010

0.00

98.7

096

.71

97.7

295

.89

98.4

195

.50

97.2

194

.37

05.

134.

898.

588.

836.

926.

964.

534.

466.

465.

354.

534.

466.

465.

350.

010

10.0

19.

5314

.92

15.2

614

.67

15.0

48.

618.

3511

.24

9.71

8.61

8.35

11.2

49.

710.

025

30.4

430

.77

40.5

141

.64

40.3

341

.44

27.8

226

.54

31.4

928

.10

27.8

226

.54

31.4

928

.10

0.05

058

.05

60.7

174

.66

77.4

074

.28

77.0

454

.48

50.8

057

.46

52.4

754

.48

50.8

057

.46

52.4

70.

100

80.6

486

.91

91.2

596

.00

91.0

995

.79

76.7

369

.92

78.8

971

.23

76.7

369

.92

78.8

971

.23

0.50

094

.05

100.

0096

.43

100.

0096

.50

100.

0092

.12

83.2

093

.08

83.8

492

.12

83.2

093

.08

83.8

40

5.01

4.60

9.58

9.79

7.00

6.91

3.98

3.95

5.28

4.55

3.11

2.45

4.29

2.83

0.01

010

.32

10.2

415

.76

16.2

315

.59

16.0

58.

618.

1410

.63

9.28

7.13

5.27

8.93

6.02

0.02

540

.93

41.6

647

.25

48.1

846

.99

47.9

036

.71

34.6

140

.00

36.5

232

.84

26.8

035

.94

28.8

80.

050

81.3

182

.98

87.1

987

.78

86.8

687

.38

77.6

874

.84

79.2

775

.70

75.0

768

.70

76.9

469

.47

0.10

097

.76

98.7

799

.46

99.5

299

.29

99.3

496

.32

94.4

796

.63

94.6

395

.56

92.1

195

.85

92.2

50.

500

100.

0010

0.00

100.

0010

0.00

100.

0010

0.00

99.9

599

.53

99.9

399

.48

99.9

699

.13

99.9

399

.07

Tab

le 1

. Rej

ectio

n fr

eque

ncie

s fo

r a

rand

om w

alk

drift

plu

s no

ise

mod

el w

ith σ

η/σε=

0.1.

λ=π

-RLQW

CH

: lev

els

CH

: FD

Mod

el k

now

nB

SM

est

imat

edM

odel

est

imat

ed

λ=π/

2

Par

amet

ric te

sts

Non

para

met

ric te

sts

Spe

ctra

l: le

vels

Spe

ctra

l: F

D

σ κ/σ

εIn

nov.

Sm

ooth

.In

nov.

Sm

ooth

.In

nov.

Sm

ooth

.m

=4

m=

8m

=4

m=

8m

=4

m=

8m

=4

m=

8

05.

344.

905.

545.

985.

425.

711.

061.

924.

774.

630.

861.

244.

233.

420.

010

7.73

7.35

8.74

9.28

8.58

9.13

2.01

3.21

7.16

6.86

1.63

2.29

6.35

5.28

0.02

524

.57

24.9

628

.68

30.4

928

.50

30.2

010

.41

13.5

623

.13

22.0

38.

9810

.37

21.3

518

.63

0.05

057

.16

60.6

370

.62

74.2

570

.46

73.9

939

.18

43.4

355

.88

54.0

036

.51

38.3

053

.47

49.2

20.

100

84.4

690

.98

94.4

297

.66

94.3

797

.64

76.2

476

.88

84.4

181

.60

74.3

773

.24

82.8

178

.89

0.50

096

.58

100.

0098

.65

100.

0098

.63

100.

0098

.30

96.3

697

.67

95.7

797

.97

95.0

697

.20

94.3

10

5.18

4.93

9.26

9.42

8.28

8.47

1.47

2.40

6.13

5.18

1.47

2.40

6.13

5.18

0.01

09.

679.

3914

.91

15.1

814

.65

15.0

13.

394.

6010

.80

9.30

3.39

4.60

10.8

09.

300.

025

29.3

929

.62

38.9

740

.02

38.7

539

.76

16.2

619

.20

30.4

227

.26

16.2

619

.20

30.4

227

.26

0.05

056

.78

59.3

772

.99

75.2

772

.28

74.6

142

.75

44.2

556

.52

51.5

242

.75

44.2

556

.52

51.5

20.

100

80.1

585

.93

91.1

495

.19

90.9

195

.08

68.8

965

.94

77.9

170

.39

68.8

965

.94

77.9

170

.39

0.50

094

.41

99.9

996

.83

100.

0096

.72

100.

0091

.44

82.9

893

.01

83.7

791

.44

82.9

893

.01

83.7

70

5.19

4.60

9.27

9.51

8.57

8.73

0.80

1.42

5.31

4.59

0.55

0.68

4.29

2.79

0.01

09.

719.

4915

.49

15.8

815

.22

15.6

61.

983.

4410

.03

8.73

1.40

1.77

8.26

5.85

0.02

538

.25

38.5

844

.78

45.7

344

.38

45.3

115

.72

20.1

937

.40

33.7

312

.50

13.5

733

.64

26.2

70.

050

78.8

180

.40

84.6

585

.30

84.1

884

.81

57.7

061

.84

76.9

273

.18

53.3

053

.24

74.1

466

.60

0.10

097

.29

98.2

799

.26

99.2

999

.20

99.2

291

.16

90.6

195

.99

93.9

089

.07

87.1

395

.01

91.5

60.

500

100.

0010

0.00

100.

0010

0.00

100.

0010

0.00

99.9

399

.47

99.9

299

.49

99.8

798

.94

99.9

399

.00

Tab

le 2

. Rej

ectio

n fr

eque

ncie

s fo

r a

rand

om w

alk

drift

plu

s no

ise

mod

el w

ith σ

η/σε=

0.5.

λ=π

-RLQW

CH

: lev

els

CH

: FD

Mod

el k

now

nB

SM

est

imat

edM

odel

est

imat

ed

λ=π/

2

Par

amet

ric te

sts

Non

para

met

ric te

sts

Spe

ctra

l: le

vels

Spe

ctra

l: F

D

σ κ/σ

εIn

nov.

Sm

ooth

.In

nov.

Sm

ooth

.In

nov.

Sm

ooth

.m

=4

m=

8m

=4

m=

8m

=4

m=

8m

=4

m=

8

05.

334.

835.

335.

694.

995.

350.

160.

544.

904.

560.

100.

274.

173.

440.

010

7.08

6.60

7.46

7.94

7.07

7.61

0.30

1.02

6.61

6.50

0.24

0.61

5.64

4.64

0.02

519

.11

19.4

622

.73

24.3

822

.32

24.2

21.

984.

3518

.50

17.6

61.

562.

7616

.80

14.6

50.

050

49.2

552

.78

61.0

165

.18

61.6

765

.66

15.4

622

.57

48.3

746

.47

13.5

118

.16

46.3

541

.83

0.10

079

.83

86.3

591

.44

95.4

891

.64

95.4

352

.77

60.1

979

.78

77.1

550

.13

54.9

978

.28

73.9

70.

500

95.7

710

0.00

98.2

610

0.00

98.2

410

0.00

96.9

295

.14

97.5

295

.48

96.3

293

.81

96.9

494

.14

05.

044.

829.

799.

989.

459.

690.

350.

875.

834.

910.

350.

875.

834.

910.

010

9.20

8.90

14.6

514

.97

14.3

214

.55

0.91

1.77

9.66

8.60

0.91

1.77

9.66

8.60

0.02

526

.84

26.5

435

.90

36.8

235

.48

36.2

35.

929.

6027

.23

24.5

75.

929.

6027

.23

24.5

70.

050

53.9

255

.70

68.2

270

.61

68.2

970

.52

24.4

030

.80

53.0

448

.54

24.4

030

.80

53.0

448

.54

0.10

078

.30

83.2

389

.99

93.5

490

.54

93.5

153

.58

56.4

875

.69

68.5

053

.58

56.4

875

.69

68.5

00.

500

95.0

199

.98

96.9

510

0.00

97.0

499

.99

89.5

681

.93

92.8

983

.65

89.5

681

.93

92.8

983

.65

04.

934.

499.

689.

959.

279.

480.

100.

364.

994.

540.

030.

124.

082.

760.

010

8.61

8.22

14.4

214

.91

14.2

714

.61

0.19

0.69

8.96

7.72

0.09

0.23

7.13

4.76

0.02

532

.04

31.8

238

.92

39.9

138

.92

39.6

52.

936.

4131

.43

28.2

42.

003.

4527

.84

21.5

50.

050

72.2

773

.83

78.7

279

.39

78.9

379

.71

25.6

036

.60

70.2

666

.48

21.3

627

.01

67.2

259

.91

0.10

095

.79

97.1

098

.48

98.6

598

.16

98.3

372

.44

78.2

994

.22

91.6

768

.82

71.6

792

.94

88.9

60.

500

100.

0010

0.00

100.

0010

0.00

100.

0010

0.00

99.7

499

.25

99.9

299

.47

99.6

098

.58

99.8

998

.95

Tab

le 3

. Rej

ectio

n fr

eque

ncie

s fo

r a

rand

om w

alk

drift

plu

s no

ise

mod

el w

ith σ

η/σε=

1.

λ=π

-RLQW

CH

: lev

els

CH

: FD

Mod

el k

now

nB

SM

est

imat

edM

odel

est

imat

ed

λ=π/

2

Par

amet

ric te

sts

Non

para

met

ric te

sts

Spe

ctra

l: le

vels

Spe

ctra

l: F

D

σ κ/σ

εIn

nov.

Sm

ooth

.In

nov.

Sm

ooth

.In

nov.

Sm

ooth

.m

=4

m=

8m

=4

m=

8m

=4

m=

8m

=4

m=

8

05.

364.

775.

585.

866.

196.

434.

224.

222.

352.

963.

653.

291.

922.

220.

010

8.76

8.11

9.32

9.83

10.0

610

.57

7.15

7.05

4.20

5.13

6.17

5.18

3.39

3.71

0.02

527

.18

27.6

431

.82

33.6

233

.02

34.9

424

.11

23.8

618

.19

19.9

822

.35

19.5

915

.79

15.7

20.

050

60.5

664

.32

74.2

777

.68

75.1

878

.57

57.7

655

.99

50.7

351

.80

55.5

251

.45

47.9

546

.82

0.10

086

.37

92.5

095

.54

98.3

095

.59

98.3

685

.53

83.0

780

.76

79.9

384

.15

80.3

579

.06

76.9

30.

500

96.7

810

0.00

98.6

810

0.00

98.6

610

0.00

97.7

095

.91

95.4

394

.34

97.1

894

.36

94.6

192

.52

05.

134.

828.

668.

819.

289.

446.

165.

277.

415.

876.

165.

277.

415.

870.

010

9.99

9.43

14.8

315

.12

15.8

516

.16

10.8

59.

6012

.53

10.5

210

.85

9.60

12.5

310

.52

0.02

530

.59

30.8

240

.69

41.6

841

.78

42.7

830

.97

27.8

033

.17

29.0

730

.97

27.8

033

.17

29.0

70.

050

58.0

360

.74

74.3

877

.03

74.9

877

.95

57.1

552

.30

58.9

053

.12

57.1

552

.30

58.9

053

.12

0.10

080

.72

86.9

791

.31

95.7

391

.52

95.9

178

.63

71.0

279

.90

71.6

078

.63

71.0

279

.90

71.6

00.

500

94.0

610

0.00

96.3

210

0.00

96.3

810

0.00

93.0

883

.82

93.5

484

.05

93.0

883

.82

93.5

484

.05

05.

214.

569.

499.

6910

.23

10.5

34.

684.

193.

673.

513.

822.

642.

892.

140.

010

10.6

510

.06

15.6

616

.02

16.7

917

.22

9.82

8.85

8.26

7.81

8.18

5.78

6.91

4.85

0.02

541

.15

41.4

447

.45

48.2

548

.95

49.8

738

.70

35.7

735

.10

32.9

034

.31

27.9

831

.12

25.4

80.

050

81.0

482

.75

87.3

587

.88

87.8

788

.42

78.5

875

.29

75.9

173

.16

75.9

368

.87

72.8

266

.50

0.10

097

.82

98.7

799

.46

99.5

399

.46

99.5

496

.48

94.4

795

.72

93.8

695

.62

92.1

794

.70

91.1

50.

500

100.

0010

0.00

100.

0010

0.00

100.

0010

0.00

99.9

399

.48

99.9

199

.34

99.9

299

.06

99.8

198

.73

Tab

le 4

. Rej

ectio

n fr

eque

ncie

s fo

r a

smoo

th tr

end

plus

noi

se m

odel

with

σξ/σ

ε=0.

1.

-RLQW

CH

: FD

CH

: dou

ble

FD

Spe

ctra

l: do

uble

FD

Mod

el k

now

nB

SM

est

imat

edM

odel

est

imat

ed

λ=π/

2

Par

amet

ric te

sts

Non

para

met

ric te

sts

Spe

ctra

l: F

D

λ=π

σ κ/σ

εIn

nov.

Sm

ooth

.In

nov.

Sm

ooth

.In

nov.

Sm

ooth

.m

=4

m=

8m

=4

m=

8m

=4

m=

8m

=4

m=

8

05.

334.

695.

535.

845.

595.

900.

861.

482.

583.

150.

720.

962.

182.

190.

010

8.47

7.63

8.95

9.38

9.05

9.57

1.67

2.65

4.16

5.21

1.40

1.98

3.53

3.79

0.02

525

.64

25.7

830

.50

32.1

630

.74

32.5

29.

6212

.99

17.7

419

.08

8.24

9.65

15.4

615

.15

0.05

058

.43

61.8

971

.84

75.5

871

.94

75.8

837

.57

42.2

049

.42

50.4

634

.94

37.3

046

.87

45.5

90.

100

85.4

991

.48

94.7

997

.81

94.7

097

.84

73.4

675

.22

80.1

479

.29

71.7

771

.76

78.3

376

.27

0.50

096

.55

100.

0098

.50

100.

0098

.41

100.

0097

.30

95.5

395

.36

94.2

696

.76

93.9

694

.62

92.5

90

5.16

4.85

8.78

8.96

9.63

9.87

2.77

3.26

7.29

5.77

2.77

3.26

7.29

5.77

0.01

010

.06

9.51

15.0

715

.42

16.2

416

.51

5.98

6.58

12.3

610

.29

5.98

6.58

12.3

610

.29

0.02

530

.02

30.1

140

.20

41.3

041

.63

42.6

522

.20

22.9

232

.78

28.8

222

.20

22.9

232

.78

28.8

20.

050

57.8

860

.12

74.1

376

.49

74.7

877

.29

48.5

847

.34

58.5

152

.94

48.5

847

.34

58.5

152

.94

0.10

080

.89

86.5

791

.24

95.4

391

.61

95.6

672

.90

68.1

379

.73

71.4

772

.90

68.1

379

.73

71.4

70.

500

94.4

099

.99

96.6

610

0.00

96.8

810

0.00

92.6

983

.56

93.5

283

.99

92.6

983

.56

93.5

283

.99

05.

204.

229.

479.

8010

.10

10.3

71.

071.

423.

673.

500.

690.

733.

042.

090.

010

10.3

29.

4015

.88

16.2

816

.67

17.0

32.

543.

638.

247.

742.

032.

096.

734.

780.

025

39.6

139

.80

46.2

447

.09

47.2

048

.03

18.8

121

.88

34.1

032

.14

15.9

015

.37

30.3

624

.80

0.05

079

.96

81.5

186

.02

86.5

986

.47

87.0

659

.98

62.8

274

.86

72.2

555

.93

54.8

272

.02

65.5

00.

100

97.5

298

.50

99.3

699

.38

99.3

799

.40

91.1

590

.81

95.5

393

.34

89.1

187

.18

94.4

490

.94

0.50

010

0.00

100.

0010

0.00

100.

0010

0.00

100.

0099

.88

99.4

399

.91

99.3

499

.82

98.9

299

.82

98.7

1

Tab

le 5

. Rej

ectio

n fr

eque

ncie

s fo

r a

smoo

th tr

end

plus

noi

se m

odel

with

σξ/σ

ε=0.

5.

-RLQW

CH

: FD

CH

: dou

ble

FD

Spe

ctra

l: do

uble

FD

Mod

el k

now

nB

SM

est

imat

edM

odel

est

imat

ed

λ=π/

2

Par

amet

ric te

sts

Non

para

met

ric te

sts

Spe

ctra

l: F

D

λ=π

F'

=0

F'

=0.

5F'

=1.

0F'

=1.

5F'

=2.

0F'

=2.

5F'

=3.

0F'

=3.

5

)4.

907.

9818

.86

39.7

265

.21

85.5

295

.94

99.2

6

F6

=0

ω4.

907.

4616

.01

32.9

055

.85

77.3

791

.33

97.7

4

ω4.

894.

894.

894.

894.

894.

894.

894.

89

)9.

3412

.94

24.5

244

.17

66.3

684

.43

94.6

898

.75

F6

=1

ω10

.53

13.6

023

.03

39.0

858

.60

77.0

289

.81

96.6

0

ω6.

086.

086.

086.

086.

086.

086.

086.

08

)24

.52

28.1

938

.61

53.5

169

.58

83.0

292

.33

97.1

0

F6

=2

ω29

.07

31.8

339

.84

51.6

565

.16

77.8

587

.75

94.2

1

ω10

.32

10.3

210

.32

10.3

210

.32

10.3

210

.32

10.3

2

)45

.34

47.7

454

.35

63.9

474

.19

83.4

390

.61

95.3

4

F6

=3

ω51

.46

53.3

858

.28

64.9

272

.91

80.7

987

.45

92.6

6

ω18

.13

18.1

318

.13

18.1

318

.13

18.1

318

.13

18.1

3

)62

.72

63.9

767

.81

73.1

279

.32

85.2

690

.33

94.1

6

F6

=4

ω68

.83

69.7

072

.13

75.8

080

.10

84.6

988

.87

92.5

1

ω29

.22

29.2

229

.22

29.2

229

.22

29.2

229

.22

29.2

2

)74

.79

75.5

877

.52

80.6

384

.07

87.6

691

.06

93.9

6

F6

=5

ω80

.10

80.5

881

.76

83.5

685

.84

88.5

590

.97

93.1

6

ω41

.62

41.6

241

.62

41.6

241

.62

41.6

241

.62

41.6

2

)89

.59

89.8

290

.27

90.9

391

.87

93.0

194

.15

95.3

1

F6

=7.

5ω

92.7

992

.84

93.0

093

.46

94.0

294

.68

95.2

995

.97

ω68

.11

68.1

168

.11

68.1

168

.11

68.1

168

.11

68.1

1

)95

.09

95.2

195

.25

95.4

995

.70

96.0

596

.45

96.9

0

F6

=10

ω97

.03

97.0

597

.08

97.1

797

.27

97.4

497

.64

97.8

7

ω83

.73

83.7

383

.73

83.7

383

.73

83.7

383

.73

83.7

3

Tab

le 6

. Loc

al a

sym

ptot

ic p

ower

aga

inst

det

erm

inis

tic a

nd/o

r pu

re s

toch

astic

sea

sona

lity

of th

e )

, ω a

nd ω

test

s.