Page 140 - Contributed Paper Session (CPS) - Volume 2

CPS1474 Jing R. et al.
estimation results have elastic and effectiveness, it can intuitively explain the
relationship between current period and lag period of the selected variables,
also through the sequence of time-varying coefficients can explain the degree
and directions of impact between them at each period. In this paper
observation equations and state equations are:
= + + , ~(0, ) Formula 1
2

2
= −1 + , ~(0, ) Formula 2

2
= −1 + , ~(0, ), t = 1, 2, …, T Formula 3

The state vector is " = ( , ) , where both components vary over time.
⊺

The full set of each variables is: " is the CCCI of each period; is the sub-

item at the same time, we analysis influences of each sub-item respectively;
indicates the influence for CCCI of other factors ; ′=( , , … , ) is
,
,0
,1

a vector of time-varying coefficients called state vector, not a “constant
,0
term” but as “local level”; error terms , and are, which are

independent identically distributed, corresponding variance are , and
2
2

.
2

Cross-Spectrum Analysis
A large number of studies have empirically pointed out the "average"
influence of consumer confidence on macro-economic trends. Nevertheless,
the evidence of causality is found in the frequency domain is much more
powerful than the time domain [7]. So, we attempt to explore if CCCI have a
leading effect to the macro-economy from a frequency domain perspective
by using cross-spectrum analysis. The time difference given by cross-spectrum
technique is relative to the whole fluctuation process of CCCI and macro-
economy indicators time series is relative to whole fluctuation process, rather
than determining leading and lagging relationship by only some points.
If the spectral density peak of two sequences appears at a similar
frequency, cross-spectrum technique is used to analyse the spectral
correlation of multivariable sequences. A simple definition of cross-spectrum
can be expressed as:
∞ 1
ℎ , () = ∑ , () −2 , || ≤
=−∞ 2
Obviously, the cross-spectrum is a Fourier series about the covariance of
and . For convenience, it is usually expressed in polar coordinates:
ℎ , () = |ℎ , ()| −2 , ()
In the above formula, , () express phase spectrum to reflect leading and
lagging relationship between CCCI and macro-economy indicators time
series. Furthermore, coherence spectrum can be calculated with cross-
spectrum to reflect the correlation degree of fluctuations among them：
129 | I S I W S C 2 0 1 9