110
Haugh-Pierce Test
The Haugh-Pierce test for instantaneous and unidirectional causal
ity utilized quarterly data filtered by appropriate ARIMA models. The
ARIMA filter models necessary to transform the original quarterly price
data for the 31-40 size class into approximate white noise processes are
given in terms of the backshift operator B as
(1 B)(1 .161B3 + .409B6)E. e. B-P xfo-l^OS and cr -.305
(.147) (.155)
(1-B)(1 165B + .344B6)W w,. B-P xL-13.01 and cr -.279
(.143) (.150) C C w
(1-B)(1 -.417B)R r. B-P x?q13.00 and a-.341
(.125) C
where Et and Wt, and Rfc are ex-vessel, wholesale, and retail prices,
respectively, et, wt, and rt are the corresponding white noise resi
duals, B-P refers to the Box-Pierce chi-square statistic, a is the
standard deviation associated with each white noise residual series, and
the values in parentheses are standard errors of the estimates. The
ARIMA filter models necessary to transform the original quarterly price
data for the 21-25 size class into approximate white noise processes are
given in terms of the backshift operator as
(1B)( 1 .169B2 + .203B4 + ,425B6)E. e. B-P x?7-12.72 and o-.349
(.151) (.161) (.169) C C *
(1-B)(1 + .259B4 + .334B6)W w B-P x?a=8.34 and a -.385
(.161) (.166) C C 10 w
(1-B)(1 .460B + .154B5)R r.. B-P X?q=,8.24 and a -.322
(.127) (.130)