Civil Engineering Reference
In-Depth Information
Tabl e 2
Bandwidths using local-linear least-square estimation
Tw i ce t he
STDEV
Varible
Bandwidth
The monthly average crude oil price
5.84
45.89
Consumer price index
2.10
5.83
Retail price index
0.61
5.97
Producer price index
1.92
10.98
Benchmark one-year deposit rate
0.30
1.36
4
Further Empirical Results
In Sect.
3
, the coefficients in model (1),
are time-varying; they are
functions on
t
, but their analytic expressions are unknown, so that they have been
approximated by linear functions, as shown in (3). In order for convenience in
empirical study,
t
0
is constant. In the previous section,
t
0
is the median of the sample
period. The problem is that the more the point is far away from
t
0
, the greater the
error. As a mend, we let
t
0
change with the time of sample point, such that the one-
degree term in (3) is always zero and constant and
a
1
and
b
1
are different along
with
t
0
. According to the results in Sect.
3
, there are four linear variables—two
lagged dependent variables, consumer price index, and producer price index—and
four control variables: time, the monthly average crude oil price, retail price index,
and benchmark one-year deposit rate, that is, time path and additional variable path.
To compare the nonparametric path design method with parametric one, we
employ them to forecast the textile price index in June and July 2012 with the
observations from January 2008 to May 2012. The textile price is the independent
variable; two of its lagged variables and the initial 14 variables are the regressors.
Adjusted R-squared
a
(
t
i
)
,
and
b
(
t
i
)
0.97. The Pearson correlation coefficients between one-,
two-, and three-lagged-independent terms and the residual series of the regression
equation are 0.029, 0.074, and
=
010, respectively. It means that the random
disturbance has no relation to the random independent variables, and the estimators
of the coefficients are unbiased and consistent. We use the equation to forecast the
index in June and July 2012. The result is shown in Table
3
. Then we forecast
the index in June and July 2012 by the nonparametric path design model. With the
estimation of the coefficients of May 2012 to estimate those in August 2012 and 53,
the estimation is (
7
).
−
0
.
y
t
=
0
.
646048
y
t
−
1
−
0
.
931149
y
t
−
2
+
0
.
955555
z
t
5
+
0
.
179460
z
t
7
+
g
(
Z
t
,
T
)
(7)
T
Z
t
=(
z
t
2
,
z
t
6
,
z
t
8
)
,
t
,
T
=
1
,
2
,...,
53
.
The two forecasting results are presented in Table
3
. We can find that nonpara-
metric path design model's forecasting is more accurate than that of the parametric
model.
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