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A small sample correction of the test for cointegrating rank in the vector autoregressive model

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(181) 2 o ' 2.d|oi@K  ,c6  6, _,n6n __ _K K@ jo n S 3  6n ' 2.d|oi@K  6  6K_ Eu  __ _K K@ jo S f 3 n ' 2|oi  6  6.dK_ Eu 6n __ _K o.dK@@K ojc n ehfdxvh K_ lv dv|pswrwlfdoo| lqghshqghqw ri K@ @K c vhh Ohppd 9 Zh wkhuh0 iruh hydoxdwh S 3 3 .dK_ Eu 6n __ _K o ' | .d| _| Eu 6n __ _| | o S   6n 3 ' | _| Eu  __ _| U?K ' |oiEu 6n jU?K ' ?_ U?K c. vlqfh |oiu6j ' ?_ 1 Zh wkhq qg f. .dg

(182) o ' 2?_ .d|oi

(183)   jo. +83,. Ne .dge o ' 2A 3 |oi@+ +K EKK_  A U?K K@ j Wklv whup kdv wkh vdph vwrfkdvwlf frpsrqhqwv dv g c dqg lv ri orzhu rughu ri pdjqlwxgh/ vxfk wkdw f. .dge o ' f. +84,. Froohfwlqj whupv zh qg iurp +7;,/ +7<,/ dqg +83,/ +84, wkh h{suhvvlrq iru .dg o N5 Zh kdyh 3 .dg2 o ' .d|oi@KEK+_ ++_ +K_ K@ joc f. f. 3 3 dqg vlqfh K+_ ++_ +K_ ' K+ ++ +K ' A 3 K+ +K c zh jhw f. f. .dg2 o ' |oi.dK@ @K o.dK+ +K oj ' ?+ 6 c 67.

(184) vhh Ohppd 81 N6 qg. Djdlq zh fdq gurs wkh frqglwlrqlqj rq _| dqg uhsodfh ++ e| A U?+ dqg f. .dg

(185) o ' |oi.d@KK@ @+ +@ojc zklfk e| +6;, fdq eh zulwwhq dv f. n  n n  n .dg

(186) o ' |oi.d@KK@ E@ w n @K  Ew@ n K@ oj   n n ' |oiw wj|oi.d@K K@ oj n |oi.d K@ @K K@ @K oj ' |oi.d oj|oiw wj n .d|oie   jo ' |oi.d ojw n .d|oie   jo. N7 Zh gurs wkh frqglwlrqlqj rq _| dqg uhsodfh ++ e| A U?+ dqg qg iurp Ohppd 8 f. .dge o ' A 3 |oi.d@+ +K K+ +@ oj f n n  n n  ' A 3 |oi.dEw@ n K@ E@ w n @K  o.d+K K+ oj   ' ?K E?@ |oiww j n .d|oiS  jo ' ?K E?@ w n .d|oiS   jo Wklv frqfoxghv wkh surri ri Wkhruhp 41. 68.

(187)

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