Table 6 Open in new tab Tests for...

	Frequency	${LM}_{T}^{HAC}$	p-value	${LM}_{T, Adj}^{HAC}$	p-value	S	T
USD/EUR:	Hourly	123.7	0.0000	109.6	0.0000	24	518
	30-minute	187.2	0.0000	176.9	0.0000	48	518
	15-minute	218.5	0.0000	218.5	0.0000	96	518
	5-minute(*)	236.2	0.0000	236.2	0.0000	96	518
	5-minute	252.4	0.9303	252.4	0.9303	288	518
	1-minute(*)	241.0	0.0004	241.0	0.0004	173	518
USD/JPY:	Hourly	112.6	0.0000	99.8	0.0000	24	518
	30-minute	148.1	0.0000	140.0	0.0000	48	518
	15-minute	193.6	0.0000	193.6	0.0000	96	518
	5-minute(*)	218.8	0.0000	218.8	0.0000	96	518
	5-minute	250.5	0.9414	250.5	0.9414	288	518
	1-minute(*)	236.2	0.0008	236.2	0.0008	173	518
GBP/USD:	Hourly	134.3	0.0000	119.0	0.0000	24	518
	30-minute	180.7	0.0000	170.8	0.0000	48	518
	15-minute	211.5	0.0000	211.5	0.0000	96	518
	5-minute(*)	235.5	0.0000	235.5	0.0000	96	518
	5-minute	250.3	0.9423	250.3	0.9423	288	518
	1-minute(*)	244.4	0.0002	244.4	0.0002	173	518
USD/CAD:	Hourly	128.1	0.0000	113.5	0.0000	24	518
	30-minute	172.3	0.0000	162.9	0.0000	48	518
	15-minute	211.7	0.0000	211.7	0.0000	96	518
	5-minute(*)	232.2	0.0000	232.2	0.0000	96	518
	5-minute	251.4	0.9365	251.4	0.9365	288	518
	1-minute(*)	237.6	0.0007	237.6	0.0007	173	518
AUD/USD:	Hourly	137.9	0.0000	122.2	0.0000	24	518
	30-minute	166.2	0.0000	157.1	0.0000	48	518
	15-minute	207.4	0.0000	207.4	0.0000	96	518
	5-minute(*)	227.6	0.0000	227.6	0.0000	96	518
	5-minute	252.0	0.9330	252.0	0.9330	288	518
	1-minute(*)	236.3	0.0008	236.3	0.0008	173	518
USD/CHF:	Hourly	139.4	0.0000	123.5	0.0000	24	518
	30-minute	184.1	0.0000	174.0	0.0000	48	518
	15-minute	218.0	0.0000	218.0	0.0000	96	518
	5-minute(*)	240.0	0.0000	240.0	0.0000	96	518
	5-minute	253.4	0.9239	253.4	0.9239	288	518
	1-minute(*)	241.8	0.0004	241.8	0.0004	173	518

Frequency

{LM}_{T}^{HAC}

p-value

{LM}_{T, Adj}^{HAC}

p-value

USD/EUR:

Hourly

123.7

0.0000

109.6

0.0000

518

30-minute

187.2

0.0000

176.9

0.0000

518

15-minute

218.5

0.0000

218.5

0.0000

518

5-minute(*)

236.2

0.0000

236.2

0.0000

518

5-minute

252.4

0.9303

252.4

0.9303

288

518

1-minute(*)

241.0

0.0004

241.0

0.0004

173

518

USD/JPY:

Hourly

112.6

0.0000

99.8

0.0000

518

30-minute

148.1

0.0000

140.0

0.0000

518

15-minute

193.6

0.0000

193.6

0.0000

518

5-minute(*)

218.8

0.0000

218.8

0.0000

518

5-minute

250.5

0.9414

250.5

0.9414

288

518

1-minute(*)

236.2

0.0008

236.2

0.0008

173

518

GBP/USD:

Hourly

134.3

0.0000

119.0

0.0000

518

30-minute

180.7

0.0000

170.8

0.0000

518

15-minute

211.5

0.0000

211.5

0.0000

518

5-minute(*)

235.5

0.0000

235.5

0.0000

518

5-minute

250.3

0.9423

250.3

0.9423

288

518

1-minute(*)

244.4

0.0002

244.4

0.0002

173

518

USD/CAD:

Hourly

128.1

0.0000

113.5

0.0000

518

30-minute

172.3

0.0000

162.9

0.0000

518

15-minute

211.7

0.0000

211.7

0.0000

518

5-minute(*)

232.2

0.0000

232.2

0.0000

518

5-minute

251.4

0.9365

251.4

0.9365

288

518

1-minute(*)

237.6

0.0007

237.6

0.0007

173

518

AUD/USD:

Hourly

137.9

0.0000

122.2

0.0000

518

30-minute

166.2

0.0000

157.1

0.0000

518

15-minute

207.4

0.0000

207.4

0.0000

518

5-minute(*)

227.6

0.0000

227.6

0.0000

518

5-minute

252.0

0.9330

252.0

0.9330

288

518

1-minute(*)

236.3

0.0008

236.3

0.0008

173

518

USD/CHF:

Hourly

139.4

0.0000

123.5

0.0000

518

30-minute

184.1

0.0000

174.0

0.0000

518

15-minute

218.0

0.0000

218.0

0.0000

518

5-minute(*)

240.0

0.0000

240.0

0.0000

518

5-minute

253.4

0.9239

253.4

0.9239

288

518

1-minute(*)

241.8

0.0004

241.8

0.0004

173

518

	Frequency	${LM}_{T}^{HAC}$	p-value	${LM}_{T, Adj}^{HAC}$	p-value	S	T
USD/EUR:	Hourly	123.7	0.0000	109.6	0.0000	24	518
	30-minute	187.2	0.0000	176.9	0.0000	48	518
	15-minute	218.5	0.0000	218.5	0.0000	96	518
	5-minute(*)	236.2	0.0000	236.2	0.0000	96	518
	5-minute	252.4	0.9303	252.4	0.9303	288	518
	1-minute(*)	241.0	0.0004	241.0	0.0004	173	518
USD/JPY:	Hourly	112.6	0.0000	99.8	0.0000	24	518
	30-minute	148.1	0.0000	140.0	0.0000	48	518
	15-minute	193.6	0.0000	193.6	0.0000	96	518
	5-minute(*)	218.8	0.0000	218.8	0.0000	96	518
	5-minute	250.5	0.9414	250.5	0.9414	288	518
	1-minute(*)	236.2	0.0008	236.2	0.0008	173	518
GBP/USD:	Hourly	134.3	0.0000	119.0	0.0000	24	518
	30-minute	180.7	0.0000	170.8	0.0000	48	518
	15-minute	211.5	0.0000	211.5	0.0000	96	518
	5-minute(*)	235.5	0.0000	235.5	0.0000	96	518
	5-minute	250.3	0.9423	250.3	0.9423	288	518
	1-minute(*)	244.4	0.0002	244.4	0.0002	173	518
USD/CAD:	Hourly	128.1	0.0000	113.5	0.0000	24	518
	30-minute	172.3	0.0000	162.9	0.0000	48	518
	15-minute	211.7	0.0000	211.7	0.0000	96	518
	5-minute(*)	232.2	0.0000	232.2	0.0000	96	518
	5-minute	251.4	0.9365	251.4	0.9365	288	518
	1-minute(*)	237.6	0.0007	237.6	0.0007	173	518
AUD/USD:	Hourly	137.9	0.0000	122.2	0.0000	24	518
	30-minute	166.2	0.0000	157.1	0.0000	48	518
	15-minute	207.4	0.0000	207.4	0.0000	96	518
	5-minute(*)	227.6	0.0000	227.6	0.0000	96	518
	5-minute	252.0	0.9330	252.0	0.9330	288	518
	1-minute(*)	236.3	0.0008	236.3	0.0008	173	518
USD/CHF:	Hourly	139.4	0.0000	123.5	0.0000	24	518
	30-minute	184.1	0.0000	174.0	0.0000	48	518
	15-minute	218.0	0.0000	218.0	0.0000	96	518
	5-minute(*)	240.0	0.0000	240.0	0.0000	96	518
	5-minute	253.4	0.9239	253.4	0.9239	288	518
	1-minute(*)	241.8	0.0004	241.8	0.0004	173	518

Table 6

Open in new tab

Tests for non-stationary periodicity in the zero-process of intraday exchange rate returns: All trading hours, that is, from 00:00 CET to 24:00 CET (see Section 3.1)

	Frequency	${LM}_{T}^{HAC}$	p-value	${LM}_{T, Adj}^{HAC}$	p-value	S	T
USD/EUR:	Hourly	123.7	0.0000	109.6	0.0000	24	518
	30-minute	187.2	0.0000	176.9	0.0000	48	518
	15-minute	218.5	0.0000	218.5	0.0000	96	518
	5-minute(*)	236.2	0.0000	236.2	0.0000	96	518
	5-minute	252.4	0.9303	252.4	0.9303	288	518
	1-minute(*)	241.0	0.0004	241.0	0.0004	173	518
USD/JPY:	Hourly	112.6	0.0000	99.8	0.0000	24	518
	30-minute	148.1	0.0000	140.0	0.0000	48	518
	15-minute	193.6	0.0000	193.6	0.0000	96	518
	5-minute(*)	218.8	0.0000	218.8	0.0000	96	518
	5-minute	250.5	0.9414	250.5	0.9414	288	518
	1-minute(*)	236.2	0.0008	236.2	0.0008	173	518
GBP/USD:	Hourly	134.3	0.0000	119.0	0.0000	24	518
	30-minute	180.7	0.0000	170.8	0.0000	48	518
	15-minute	211.5	0.0000	211.5	0.0000	96	518
	5-minute(*)	235.5	0.0000	235.5	0.0000	96	518
	5-minute	250.3	0.9423	250.3	0.9423	288	518
	1-minute(*)	244.4	0.0002	244.4	0.0002	173	518
USD/CAD:	Hourly	128.1	0.0000	113.5	0.0000	24	518
	30-minute	172.3	0.0000	162.9	0.0000	48	518
	15-minute	211.7	0.0000	211.7	0.0000	96	518
	5-minute(*)	232.2	0.0000	232.2	0.0000	96	518
	5-minute	251.4	0.9365	251.4	0.9365	288	518
	1-minute(*)	237.6	0.0007	237.6	0.0007	173	518
AUD/USD:	Hourly	137.9	0.0000	122.2	0.0000	24	518
	30-minute	166.2	0.0000	157.1	0.0000	48	518
	15-minute	207.4	0.0000	207.4	0.0000	96	518
	5-minute(*)	227.6	0.0000	227.6	0.0000	96	518
	5-minute	252.0	0.9330	252.0	0.9330	288	518
	1-minute(*)	236.3	0.0008	236.3	0.0008	173	518
USD/CHF:	Hourly	139.4	0.0000	123.5	0.0000	24	518
	30-minute	184.1	0.0000	174.0	0.0000	48	518
	15-minute	218.0	0.0000	218.0	0.0000	96	518
	5-minute(*)	240.0	0.0000	240.0	0.0000	96	518
	5-minute	253.4	0.9239	253.4	0.9239	288	518
	1-minute(*)	241.8	0.0004	241.8	0.0004	173	518

	Frequency	${LM}_{T}^{HAC}$	p-value	${LM}_{T, Adj}^{HAC}$	p-value	S	T
USD/EUR:	Hourly	123.7	0.0000	109.6	0.0000	24	518
	30-minute	187.2	0.0000	176.9	0.0000	48	518
	15-minute	218.5	0.0000	218.5	0.0000	96	518
	5-minute(*)	236.2	0.0000	236.2	0.0000	96	518
	5-minute	252.4	0.9303	252.4	0.9303	288	518
	1-minute(*)	241.0	0.0004	241.0	0.0004	173	518
USD/JPY:	Hourly	112.6	0.0000	99.8	0.0000	24	518
	30-minute	148.1	0.0000	140.0	0.0000	48	518
	15-minute	193.6	0.0000	193.6	0.0000	96	518
	5-minute(*)	218.8	0.0000	218.8	0.0000	96	518
	5-minute	250.5	0.9414	250.5	0.9414	288	518
	1-minute(*)	236.2	0.0008	236.2	0.0008	173	518
GBP/USD:	Hourly	134.3	0.0000	119.0	0.0000	24	518
	30-minute	180.7	0.0000	170.8	0.0000	48	518
	15-minute	211.5	0.0000	211.5	0.0000	96	518
	5-minute(*)	235.5	0.0000	235.5	0.0000	96	518
	5-minute	250.3	0.9423	250.3	0.9423	288	518
	1-minute(*)	244.4	0.0002	244.4	0.0002	173	518
USD/CAD:	Hourly	128.1	0.0000	113.5	0.0000	24	518
	30-minute	172.3	0.0000	162.9	0.0000	48	518
	15-minute	211.7	0.0000	211.7	0.0000	96	518
	5-minute(*)	232.2	0.0000	232.2	0.0000	96	518
	5-minute	251.4	0.9365	251.4	0.9365	288	518
	1-minute(*)	237.6	0.0007	237.6	0.0007	173	518
AUD/USD:	Hourly	137.9	0.0000	122.2	0.0000	24	518
	30-minute	166.2	0.0000	157.1	0.0000	48	518
	15-minute	207.4	0.0000	207.4	0.0000	96	518
	5-minute(*)	227.6	0.0000	227.6	0.0000	96	518
	5-minute	252.0	0.9330	252.0	0.9330	288	518
	1-minute(*)	236.3	0.0008	236.3	0.0008	173	518
USD/CHF:	Hourly	139.4	0.0000	123.5	0.0000	24	518
	30-minute	184.1	0.0000	174.0	0.0000	48	518
	15-minute	218.0	0.0000	218.0	0.0000	96	518
	5-minute(*)	240.0	0.0000	240.0	0.0000	96	518
	5-minute	253.4	0.9239	253.4	0.9239	288	518
	1-minute(*)	241.8	0.0004	241.8	0.0004	173	518

${LM}_{T}^{HAC}$ and ${LM}_{T, Adj}^{HAC}$ ⁠, the LM statistics in Equations (2.15) and (3.7), respectively, see Section 2. p-value, $P (χ^{2} (S - 1) > x)$ where x is the value on the statistic in question. (*), only every third period included in the vector of seasons representation (after removal of columns to ensure nonsingularity). S, number of intraday periods included in test. T, number of days. All computations in R.

This Feature Is Available To Subscribers Only