Signal Processing - May 2017 - 30
To identify market output characteristics, conventionally the
following first-order time-series model is used to test whether
the sales S t is evolving (a unit-root test with null hypothesis
H 0 : z = 1):
S t = n + zS t - 1 + e t .
When the sales S t is evolving, managers need to know the
role of the advertising investment A t in creating and supporting
sales evolution to budget advertising investment. The following
market input-output model is established given known A t:
S t = c + aS t -1 + bA t + e t .
S (t )/A (t )
S (t )/A (t )
S (t )/A (t )
S (t )/A (t )
Note that the sales St and advertising At are monetary value
time series. To examine whether the sales evolution is intrinsic
(i.e., a favorable market feature) or supported by advertising
(i.e., a less favorable market feature with which continuous
advertising needs to be budgeted), an intrinsic market evolution
(IME) test is proposed [10] to test null hypothesis H 0 : a = 1.
If H 0 is rejected, the market is intrinsically stationary; i.e.,
a short-term advertising investment has a short-term instantaneous effect on sales. Sales evolution needs to be supported by
1
0.5
0
0
2
4
6
(a) α = 0.8, γ = 0
8
10
A (t) = f (S (t - 1)) = c b S (t - 1).
1
0.5
0
0
2
4
6
(b) α = 0.8, γ = 0.1
8
10
0
2
4
6
(c) α = 0.8, γ = 0.2
8
10
0
2
4
6
(d) α = 0.8, γ = 0.3
8
10
1
0.5
0
1
0.5
0
S (t )
A (t )
FIGURE 10. The different sales effects of percentage advertising budget practices with different c b given a = 0.8, i.e., in an intrinsically
stationary market. (a) The sales die out without maintaining advertising.
(b) The sales still die out at a slower rate (along with the advertising) with
inadequate advertising percentage budget. (c) The continuous advertising
budget as a percentage of sales induces and supports the sales evolution.
(d) The continuous advertising budget as a larger percentage of sales
leads to increasing sales (and subsequent increasing advertising).
30
the persistent advertising spending. In SP language, the system
function has no poles on or outside the unit circle. The unit root
(pole) of the output S(Z) is indeed generated by the unit root of
input A(Z). In reality, when advertising of a product increases,
sales increase, but when advertising is withdrawn, sales revert
to the original level. Marketing managers need to evaluate the
investment return to maintain the most profitable sales level.
Conversely, if H0 is not rejected with the IME test, the market is inherently evolving. A short-term advertising investment
will have a long-term persistent effect on sales. In SP language,
the system function itself has poles on or outside the unit circle. The unit root (pole) of the output S(Z) is indeed generated
by the intrinsic market dynamic. Such a phenomenon is not
common in SP systems, and researchers may question why it
is important to identify intrinsically evolving markets. In the
economic and business world, an intrinsically evolving market indicates a more favorable business environment in which
a short-term advertising campaign drives sales up; when the
advertising is withdrawn, sales maintain their level or even
continue to grow. Such a phenomenon could be caused by the
intrinsically superior product characteristics that retain loyal
customers and attract new customers by word of mouth, or a
growing emerging market yearning for such products. Shortterm advertising only acts as ignition. When an intrinsically
evolving market is identified, managers can increase their
marketing campaign budgets to capture such opportunities in
time [12].
In addition to identifying the market nature, SP models
build budgeting strategy. For example, a simple percentage
budgeting model is
That is, the marketing budget is based on sales of the previous
period. By this budgeting model, the optimal budgeting
sequence can be quantified according to various constraints
and costs to support the sales evolution in an intrinsically stationary market. Figure 10 shows an example of various advertising budget effects with different c b given a = 0.8. More
detailed methodology, analysis, and applications are available
in [10]-[12].
Real-world marketing dynamics can be more sophisticated.
With possible lag effects of market inputs and outputs and multiple variables, multivariate [12] and higher-order models [11]
can be built based on these concepts. With more complexity in
data and model analysis, SP model-based econometric analysis
can certainly play an instrumental role in quantitative marketing and business research.
Time-varying risk models based on Kalman
filtering and Gaussian processes
Time-varying systematic risk analysis
based on Kalman filtering
In financial markets, the systematic risk is represented by the
market risk beta in the CAPM or the multifactor betas in the FF
IEEE Signal Processing Magazine
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May 2017
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Table of Contents for the Digital Edition of Signal Processing - May 2017
Signal Processing - May 2017 - Cover1
Signal Processing - May 2017 - Cover2
Signal Processing - May 2017 - 1
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Signal Processing - May 2017 - Cover3
Signal Processing - May 2017 - Cover4
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