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8/12/2019 Treasury Analytics INR VS US$
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To study Volatility between
INR and USD UsingHeteroskedastic Models
Submitted By:
Soumya Sreekumar12DM-145
Arifa Kazi12FN-024
Prakhar Saxena12DCP-080
Nikash Kumar12DCP-071
Tanuj Arora12DCP-117
Deepanshu Siddhanti12DCP-029
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Agenda
DataHistorical Exchange Rates for3 years (September 2010 -2013)
Tests for Stationarity If non stationary data exists, conversion to
stationary
Applying different ModelsARCH, GARCH, TARCH, E-GARCH and
PARCH
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Initial Approach
Exchange RatesTimeSeries Data
It can have VariableVariance andFar off Mean indicating
Non Stationarity
Thus, Cannot beModeled or Forecasted
as it is
Unit Root Testing inEviews determines Non
Stationarity
Conversion toStationarity by TakingLog Normal Returns
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Unit Root Tests
PhillipsPeron Test
Augmented Dickey-Fuller Test
P-value > 0.05means NullHypothesis cannot
be rejected.
Conclusion:Exchange Rate
data is non -stationary
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Conversion to Stationary Data
EviewsQuick TabGenerateSeries
Equation entered is:
usd_s = dlog(inr_usd) to giveContinuously Compounded Returns.
Applying Dickey Fuller Test
P-value < 0.05
means NullHypothesis can
be rejected
Conclusion:Exchange RateLog Return Data
is stationary
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ARMA Estimation Output
EviewsQuick TabEstimateEquation
Equation: Dlog(inr_usd) c ar(1) ma(1)
P-value < 0.05 meansNull Hypothesis can be
rejected
Conclusion:
Model is significant
ARYesterdays Pricedoes not have a
negative impact oncurrent price
MAYesterdaysVolatility has a positiveimpact on current price
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ARMA Graph
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Garch
AimForecast
variance based on
past information
All coefficients are
positive and
significant
Shocks to volatility
have a persistenteffecton the
conditional variance
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Tarch
AimTo check
asymmetric news
impact on the
volatility of
exchange rate
Gamma is negative
and significant
Bad news may not
increase volatility
Gamma 0 implies
asymmetric effect
of news is present
Dependent Variable: DLOG(INR_USD)Method: ML - ARCH (Marquardt) - Normal distributionDate: 09/11/13 Time: 20:48Sample (adjusted): 9/14/2010 9/10/2013Included observations: 763 after adjustmentsConvergence achieved after 15 iterationsMA Backcast: 9/13/2010Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*RESID(-1) 2*(RESID(-1)
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E-Garch
Variable Coefficient Std. Error z-Statistic Prob.
C 0.000177 0.000175 1.010816 0.3121AR(1) -0.596517 0.143221 -4.165017 0.0000MA(1) 0.711246 0.124667 5.705174 0.0000
Variance Equation
C(4) -0.617559 0.154017 -4.009679 0.0001C(5) 0.232701 0.041022 5.672543 0.0000C(6) 0.076575 0.019992 3.830366 0.0001C(7) 0.958289 0.012939 74.05972 0.0000
R-squared 0.012717 Mean dependent var 0.000423Adjusted R-squared 0.004881 S.D. dependent var 0.005930S.E. of regression 0.005916 Akaike info criterion -7.672488Sum squared resid 0.026456 Schwarz criterion -7.629944Log likelihood 2934.054 Hannan-Quinn criter. -7.656108F-statistic 1.622938 Durbin-Watson stat 2.006895Prob(F-statistic) 0.137822
Inverted AR Roots -.60Inverted MA Roots -.71
AimTo study the
leverage effect of
news on exchange
rate
All coefficients are
positive
Bad news may not
have a strongerimpact than good
news.
Last periods
forecast has great
impact
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P-Garch
Variable Coefficient Std. Error z-Statistic Prob.
C 0.000249 0.000189 1.316457 0.1880AR(1) -0.589688 0.142506 -4.137998 0.0000MA(1) 0.707184 0.123404 5.730659 0.0000
Variance Equation
C(4) 0.000156 0.000248 0.626489 0.5310C(5) 0.122865 0.024157 5.086068 0.0000C(6) -0.371455 0.087933 -4.224301 0.0000C(7) 0.863090 0.025924 33.29256 0.0000C(8) 1.073143 0.287283 3.735495 0.0002
R-squared 0.013432 Mean dependent var 0.000423Adjusted R-squared 0.004285 S.D. dependent var 0.005930S.E. of regression 0.005917 Akaike info criterion -7.671123Sum squared resid 0.026437 Schwarz criterion -7.622502Log likelihood 2934.534 Hannan-Quinn criter. -7.652403F-statistic 1.468497 Durbin-Watson stat 2.013825Prob(F-statistic) 0.175170
Inverted AR Roots -.59Inverted MA Roots -.71
AimTo study the
asymmetric impact
of news on the
volatility of
exchange rate
Gamma is negative
and significant
Bad news has a
stronger impact onvolatility of
exchange rate than
good news.
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Component Garch
All the coefficients
are positive.
and are not
significant.
This means if there
is any bad news
and the rupee
depreciates the
change would notbe significantly
higher than when a
good news comes.
MA Backcast: 9/13/2010Presample variance: backcast (parameter = 0.7)Q = C(4) + C(5)*(Q(-1) - C(4)) + C(6)*(RESID(-1)^2 - GARCH(-1))
GARCH = Q + C(7) * (RESID(-1)^2 - Q(-1)) + C(8)*(GARCH(-1) - Q(-1))
Variable Coefficient Std. Error z-Statistic Prob.
C 0.000148 0.000186 0.797620 0.4251AR(1) -0.557471 0.176975 -3.150003 0.0016MA(1) 0.665888 0.162626 4.094604 0.0000
Variance Equation
C(4) 0.000171 0.000226 0.757949 0.4485C(5) 0.999509 0.000652 1532.768 0.0000C(6) 0.008344 0.019350 0.431191 0.6663C(7) 0.102803 0.026665 3.855385 0.0001C(8) 0.872383 0.031717 27.50560 0.0000
R-squared 0.013533 Mean dependent var 0.000423Adjusted R-squared 0.004387 S.D. dependent var 0.005930S.E. of regression 0.005917 Akaike info criterion -7.658026Sum squared resid 0.026434 Schwarz criterion -7.609405Log likelihood 2929.537 Hannan-Quinn criter. -7.639307F-statistic 1.479687 Durbin-Watson stat 1.991976Prob(F-statistic) 0.171080
Inverted AR Roots -.56Inverted MA Roots -.67
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Conclusions
Recent news affects volatility to agreater extent
Exchange rate volatility shows highpersistence
Asymmetric Effects of news onvolatility are present
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Thank you