lag

LL

LR

df

p

FPE

AIC

HQIC

SBIC

0

−169.705

-

-

-

0.011371

12.5504

12.6376

12.8358^*

1

−140.239

58.932

36

0.009

0.019347

13.0171

13.628

15.0154

2

−107.153

66.172

36

0.002

0.035425

13.2252

14.3597

16.9364

3

−15.8226

182.66^*

36

0.000

0.00253

9.27304^*

10.9312^*

14.697

4

-

-

36

-

−2.0e−50*

-

-

-

‘^*’

An appears next to the LR statistic indicating the optimal lag

LL

log likelihood

LR

likelihood ratio(sequential modified LR test statistic (each test at 5% level))

FPE

final prediction error

AIC

Akaike’s information criterion

HQIC

Hannan and Quinn information criterion

SBIC

Schwarz’s Bayesian information criterion