95
distributed lag model that relates the two price series once the causal
relationship has been identified. This specification ability is not
provided by the Granger or Sims approach and is necessary to specify a
complete econometric model of price dependent demands.
The Haugh-Pierce procedure requires that each price series for both
size classes be reduced to a white noise process. The estimated time
series ARIMA filter models that were necessary to transform the price
series for the 31-40 size class into approximately white noise processes
were found to be
(1B)(1 -.390B + ,135B3)E. e.
(.072) (.073) c c
, B-P Xjg17.44 and <^-.149
(1-B)(1 .466B + .093B2)W w
(.078) (.079)
(1-B)(1 .352B .276B8 + ,235B9)R r
(.075) (.069) (.079)
, B-P x?o20.69 and a -.199
* 18 r
where Et, Wfc, and Rt are ex-vessel, wholesale, and retail price, respec
tively, et, wt, and rt are the corresponding white noise residuals, B-P
refers to the Box-Pierce chi-square statistic, a is the standard devia
tion associated with each white noise residual series, and the values in
parentheses are standard errors of the estimates. The ARIMA models that
were necessary to transform the price series for the 21-25 size class
into approximately white noise processes were found to be
(1-B)(1 .239B + .098B3 + .115B5)E e
(.076) (.080) (.089)
, B-P x?-,*14*27 and a -.205
17 e
(1-B)(1 .281B + .113B3)W w
(.076) (.077) C C
B-P x?o*14.40 and a -.217
lo w
(1-B)(1 .1944B)R r
(.077) C C
I