![](bg6.png)
The computation was conducted on the Intel(R)
Core(R) CPU i7-7820HQ @ 2.9GHz with 16GB
RAM. The task consisted of the following steps: (1)
200 AAPL share prices were encrypted, (2) MACD
analysis was performed, (3) encrypted trading deci-
sions were generated and (4) the decisions were de-
crypted. The time required to produce the MACD
signal as well as the trading decision for a single day
were measured and summarised in table 3. The trad-
ing indicator implemented with SEAL can also run on
1-second candles and HEAAN implementation can be
applied to 15-seconds candles. The total time con-
sumed per data unit is 0.99 and 12.34 seconds for
SEAL and HEAAN implementations respectively.
Table 2: Performance of MACD and decision analysis.
Method Computation Time
MACD-SEAL 0.73 sec
MACD-HEAAN 7.085 sec
Decision-SEAL 0.26 sec
Decision-HEAAN 5.255 sec
Total-SEAL 0.99 sec
Total-HEAAN 12.34 sec
At this point, there are two significant limitations
in our implementation. Firstly, the lack of recursion
reduces the decision accuracy as the multiplicative
depth is constrained by the HE parameters. Although,
HEAAN supports bootstrapping, it introduces sub-
stantial noise and is also computationally intensive
(Acar et al., 2018). Therefore, we did not implement
bootstrapping in our approach. Secondly, operation
of bootstrapping is slow, due to the absence of logi-
cal and relational operators in the state-of-the-art HE
libraries. Only approximate decisions can be imple-
mented. However, the presented algorithm accurately
implements the MACD indicator and could be applied
in the real world applications.
6 CONCLUSIONS
We have implemented the MACD indicator on a stock
price time-series. To the best of our knowledge, this
is the first time HE methods are applied to finan-
cial time-series analysis. The algorithm implemented
with SEAL is able to produce the trading indicator in
less than a second and could be applied to 1-second
candle data as well as to lower resolution data. For
the future work we plan to implement linear systems
and corresponding recessive AR and MA based fil-
ters, including exponential moving average.
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