Signal Processing - May 2017 - 32
superior volatility prediction performance with both simulated
and empirical financial data compared with alternative GARCH
and SV models. The previous examples show that SP can contribute to investigating time-varying characteristics of finance
and economic systems.
Up Patterns
1.06
1.05
1.04
Price
1.03
1.02
Big data analysis of financial data based on SP
1.01
Returning to stock returns, we present some empirical statistical facts to illustrate the potential information that can be
sifted from financial big data.
1
0.99
0.98
0.97
0.96
Does the path matter in momentum patterns?
1
2
Pattern 1
Pattern 4
3
Pattern 2
Pattern 5
Pattern 3
Down Patterns
1.04
1.03
1.02
Price
1.01
1
0.99
0.98
0.97
0.96
0.95
0.94
1
2
Pattern 6
Pattern 9
3
Pattern 7
Pattern 10
Pattern 8
FIGURE 12. The ten preset three-point patterns: five with up direction with
different paths and five with down direction with different paths.
Table 1. The statistical analysis of historical stock
returns conditional on ten three-point patterns.
KS Test
t-Test
Pattern
Matches
Mean
Std
H
p
H
p
All
2,855,470
0.000
0.996
0
1
0
1.000
1
189,760
−0.016*
0.969
1
0
1
0.000
2
333,443
0.003
0.937
1
0
0
0.067
3
445,424
0.004*
0.916
1
0
1
0.021
4
362,097
0.010*
0.937
1
0
1
0.000
5
170,181
0.007*
0.938
1
0
1
0.002
6
168,005
−0.001
0.975
1
0
0
0.598
7
337,782
0.011*
1.051
1
0
1
0.000
8
435,628
0.012*
1.106
1
0
1
0.000
9
306,364
−0.032*
1.076
1
0
1
0.000
10
163,672
−0.034*
1.012
1
0
1
0.000
Null hypothesis H0: the mean return is not significantly different from zero. The null
hypothesis is rejected in eight of ten patterns (significant values are marked by an
asterisk under a = 0.05 ).
32
Stock price momentum is a well-known phenomenon in
which the stock return continues its direction in the short run.
The momentum factor is included in the Carhart four-factor
model [25]. From an SP perspective, the momentum is a simple two-point pattern. A natural question is, would multiple
point patterns (paths) predict the stock return behavior?
The data set is CRSP monthly price data from 1965 to
2012. The CRSP data set is the gold standard in historical
stock return research. To compare stock returns of different
stocks, all stock returns are normalized using the methodology in [6]. Ten preset three-point price patterns are constructed. Specifically, ten groups of three-point price patterns in the
data set are created according to their correlation with each of
the ten preset patterns, as shown in Figure 12. The correlation
similarity threshold is 0.95. The subsequent one-month stock
returns conditional on each of the ten three-point patterns
are analyzed. The null hypothesis H 0 is that the mean conditional return of the subsequent month is zero, i.e., the same
as unconditional returns. Both a nonparametric Kolmogorov-
Smirnov (KS) test and parametric t-test are conducted. Table 1
summarizes the results.
There are more than 2.8 million three-point patterns. The
means of all stock returns are normalized to zero. As can be
seen, eight of ten conditional returns have statistically significant
means with different directions. The p-values are reliable given
the large number of samples. This statistical fact shows that in
historical stock return data, 1) the three-point patterns contain
information about future returns and 2) the path does matter in
addition to the two-point momentum pattern.
That said, the results do not necessarily mean that one can
profit from these patterns because potential constraints, such
as liquidity and transaction costs, exist to prevent trading profit, and the results are just a summary of historical data. Rather,
these results along with the results presented in [6] show that
fine structures exist in stock returns and markets (more than
traditional economic research indicates) and that SP can provide powerful analytical tools.
Can the past inform about the future?
All theories and models are based on historical data with the
assumption that the past can represent the future. In SP,
researchers do not often ask the question of whether the past
can inform about the future because they are confident about
natural physical laws. However, in financial markets, people
IEEE Signal Processing Magazine
|
May 2017
|
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