The document presents research on analyzing long memory and volatility in foreign exchange markets using Hurst exponent analysis. It includes sections on objectives, methodology, data analysis, findings, and limitations. The data analysis finds a Hurst exponent value of 0.028 for USD, indicating mean reversion behavior. It suggests Hurst exponent can provide insights on predictability. Limitations include difficulties in estimation and lack of data. The conclusion states fractal analysis is becoming popular in finance research areas like econophysics.

1. Presented by-
Roll No - MBA/14/04

2. • Introduction
• Objectives
• Hurst exponent
• Research methodology
• Data analysis and interpretation
• Findings and suggestion
• Limitation of the study
• Conclusion

3. Introduction
Foreign exchange is the exchange of one currency for another or the
conversion of one currency into another currency.
Foreign exchange also refers to the global market where currencies
are traded virtually around the clock. The largest trading centers are
London, New York, Singapore and Tokyo. The term foreign exchange
is usually abbreviated as "forex“.
The global foreign exchange market is the largest financial market in
the world, with average daily volumes in the trillions of dollars.
The U.S. dollar is the most actively traded currency.
Long memory means systems are characterized by their ability to
remember events in the lag history of time series data and their ability
to make decision on the basis of such memories.

4. • 1- To determine currency convertibility and
liquidity in foreign exchange market.
• 2- To determine currency volatility
• 3- To determine the long memory in the
foreign exchange market

5. TOP 10 CURRENCY TRADER- % IN OVERALL VOLUME, MAY
2015
Rank Name Market share
1 Citi 16.11%
2 Deutsche Bank 14.54%
3 Barclays Investment Bank 8.11%
4 JPMorgan 7.65%
5 UBS AG 7.30%
6
Bank of America Merrill
Lynch
6.22%
7 HSBC 5.40%
8 BNP Paribas 3.65%
9 Goldman Sachs 3.40%
10 Royal Bank of Scotland 3.38%

6. • Originally invented for the field of hydrology by Harold Edwin Hurst,
the technique was developed to predict Nile River flooding in advance
of the construction of the Aswan High Dam. The dam needed to fulfill
multiple and divergent purposes, including serving as both a store of
water to protect against drought for farmers down river, and as flood
protection for those same farmers during typical annual flooding.
Rainfall levels in Central Africa were seemingly random each year,
yet the Nile River flows seemed to show autocorrelation. That is,
rainfall in one time period seemed to influence rainfall in subsequent
periods. Hurst needed to be able to see if there was a hidden long-term
trend — statistically known as a long-memory process — in the Nile
River data that might guide him in building a better dam for Egypt.

7. • Rescaled range analysis is a statistical technique designed to assess
the nature and magnitude of variability in data over time. In investing
rescaled range analysis has been used to detect and evaluate the
amount of persistence, randomness, or mean reversion in financial
markets time series data.

8. ” A Hurst exponent ranges between 0 and 1, and measures three types
of trends in a time series: persistence, randomness, or mean reversion.
• If a time series is persistent with H ≥ 0.5, then a future data point is
likely to be like a data point preceding it. So an equity with H of 0.77
that has been up for the past week is more likely to be up next week
as well, because its Hurst exponent is greater than 0.5.
• If the Hurst exponent of a time series is H < 0.5, then it is likely to
reverse trend over the time frame considered. Thus, an equity
with H = 0.26 that was up last month is more likely than chance to be
down next month.
• Time series that have Hurst exponents near to 0.5 display a random
(i.e., a stochastic) process, in which knowing one data point does not
provide insight into predicting future data points in the series.

9. Data analysis and interpretation
TABLE-1
Data (USD) RESULT
Start Date 29/2/2012
End Date 29/3/2016
R 1894.59
Volatility 0.0043
Log(R/s) 12.97
Hurst 0.028

10. 0
20
40
60
80
100
120
140
160
Price
Vol. in K
BACK

11. 9.6
9.6
9.7
9.7
9.8
9.8
9.9
9.9 0
20
40
60
80
100
120
R/s
k
BACK

12. Finding and suggestion
Findings - Hurst > 0.5, persistence — and positive price appreciation
would be attractive to a growth manager wanting future capital appreciation.
SUGGESTION:
Hurst exponent for each time series is computed as the slope of the linear fit
of the log-log graph of the standard deviation (volatility) of the log-returns
series versus the time delay.
Volatility refers to the amount of uncertainty or risk involved with the size
of changes in a currency exchange rate.
 The higher the volatility, the riskier the trading of the currency pair of.
Volatility is usually considered a negative as it represents uncertainty and
risk. However, higher volatility can make FOREX trading more attractive to
the market player.

13. Limitation of study
• i- Adequate information is not available
• ii- Testing software to estimate the Hurst exponent is
difficult.
• iii- It is not so much calculation as estimated. Accuracy
of the estimation can be complicate issue.
• iv- it is time consuming in searching and collecting the
data

14. conclusion
Computing of Hurst exponent of a time series gives valuable
information on the predictability in the process that generated it.
Recently, the fractal analysis has become popular in the finance
research, particularly in the context of Econophysics , a relatively new
area of study, developed by cooperation between economists,
mathematicians and physicists.
 It applies ideas, methods and models of statistical physics and
complexity theory to analyze data from economical phenomena.
The normality tests on the daily exchange rate returns for the last four
year or so indicate the need to explore the application of non-linear
modeling techniques while understanding exchange rate behavior. But
we come to see that the results from the persistence tests are split.

15. Data of USD
Date Price Open High Low Vol. in K Change Returns vol/1000 #
row
r(k) x(k) y(k) n log(n) log(R/s) R/s
29-Mar-16 95.2 95.94 96.23 95.08 0 0 -0.80% 0.00% 1 8 -0.004 -1.8016 -1.802 505 6.225 12.974 431140
28-Mar-16 96 96.38 96.42 95.84 0 -0.85% -0.40% 0.00% 2 9 0.0008 -1.7968 -3.598 510 6.234 12.974 431109
24-Mar-16 96.2 96.09 96.39 96.06 0 -0.19% 0.08% 0.00% 3 10 0.0044 -1.7932 -5.392 515 6.244 12.974 430899
23-Mar-16 96.1 95.64 96.24 95.63 14.47 0.11% 0.44% 1.45% 4 11 0.0021 -1.7955 -7.187 520 6.254 12.974 430897
22-Mar-16 95.6 95.44 95.75 95.28 20.35 0.44% 0.21% 2.04% 5 12 0.0021 -1.7955 -8.983 525 6.263 12.973 430728
21-Mar-16 95.3 95.1 95.41 95.02 12.49 0.36% 0.21% 1.25% 6 13 0.0034 -1.7942 -10.78 530 6.273 12.973 430559
18-Mar-16 95.1 94.8 95.19 94.61 20.39 0.19% 0.34% 2.04% 7 14 -0.01 -1.8078 -12.58 535 6.282 12.973 430469
17-Mar-16 94.8 95.78 95.86 94.67 30.54 0.34% -1.02% 3.05% 8 15 -0.008 -1.8052 -14.39 540 6.292 12.973 430469
16-Mar-16 95.9 96.66 97.09 95.56 30.94 -1.17% -0.77% 3.09% 9 16 0.0002 -1.7974 -16.19 545 6.301 12.976 431888
15-Mar-16 96.7 96.65 96.91 96.49 12.48 0.78% 0.02% -0.27% 10 17 0.0023 -1.7953 -17.98 550 6.31 12.975 431669
14-Mar-16 96.5 96.3 96.5 96.17 1.29 0.16% 0.23% 0.13% 11 18 0 -1.7976 -19.78 555 6.319 12.975 431507
11-Mar-16 96.2 96.17 96.7 95.94 16.88 0.36% 0.00% 1.69% 12 19 -0.013 -1.8103 -21.59 560 6.328 12.975 431288
10-Mar-16 96.1 97.3 98.43 95.94 52.91 0.11% -1.27% 5.29% 13 20 -0.001 -1.7986 -23.39 565 6.337 12.978 432936
9-Mar-16 97.2 97.26 97.58 96.94 27.94 -1.13% -0.10% 2.79% 14 21 0.0014 -1.7961 -25.19 570 6.346 12.978 432729
8-Mar-16 97.2 97.07 97.28 96.89 16.22 -0.05% 0.14% 1.62% 15 22 -0.003 -1.8002 -26.99 575 6.354 12.977 432530
7-Mar-16 97.1 97.33 97.7 97.05 14.49 0.13% -0.26% 1.45% 16 23 -0.003 -1.8007 -28.79 580 6.363 12.977 432388
4-Mar-16 97.3 97.64 98.05 97.03 33.76 -0.27% -0.31% 3.38% 17 24 -0.006 -1.804 -30.59 585 6.372 12.977 432278
3-Mar-16 97.6 98.23 98.36 97.46 22.22 -0.27% -0.64% 2.22% 18 25 -0.001 -1.7987 -32.39 590 6.38 12.977 432538
2-Mar-16 98.2 98.33 98.59 98.15 14.51 -0.63% -0.11% 1.45% 19 26 0.0016 -1.796 -34.18 595 6.389 12.977 432332
1-Mar-16 98.4 98.2 98.58 98.11 19.34 -0.14% 0.16% 1.93% 20 27 0.0004 -1.7972 -35.98 600 6.397 12.977 432139
29-Feb-16 98.2 98.18 98.39 97.83 19.93 0.14% 0.04% 1.99% 21 28 0.0085 -1.7891 -37.77 605 6.405 12.976 431919
26-Feb-16 98.2 97.34 98.28 97.11 26.71 -0.43% 0.85% 2.67% 22 29 -0.003 -1.8003 -39.57 610 6.413 12.977 432529
25-Feb-16 97.3 97.54 97.73 97.22 15.81 -0.48% -0.27% 1.58% 23 30 -2E-04 -1.7978 -41.37 615 6.422 12.977 432391
24-Feb-16 97.5 97.48 97.92 97.24 27.97 -0.54% -0.02% 2.80% 24 31 0.0013 -1.7963 -43.17 620 6.43 12.977 432169
23-Feb-16 97.5 97.35 97.58 97.15 14.12 -0.59% 0.13% 1.41% 25 32 0.0066 -1.791 -44.96 625 6.438 12.976 431966
22-Feb-16 97.4 96.75 97.61 96.72 15.6 -0.65% 0.66% 1.56% 26 33 -0.002 -1.7991 -46.76 630 6.446 12.977 432245
19-Feb-16 96.6 96.75 97.26 96.58 17.97 -0.70% -0.16% 1.80% 27 34 0.0013 -1.7962 -48.55 635 6.454 12.976 432050
BACK

16. •Thank you