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AFTBA Assignment 3Forecasting the Rupee per Dollar Value
2013
Naba Kumar Medhi
Group 6
Ilica Chauhan(16)Naba Kumar Medhi (24)Pankaj Malhotra (27)Tanmoy Mondal(40)
Keerthi Hari(56)
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The monthly time series of Rupee per Dollar value is used as the data set. The
range of value is from 1st January 2005 to 1st July 2013. The objective is to forecast
the Rupee Dollar value on 1st August 2013. Eviews software is used for testing the
model and forecasting.
GRAPH
The graph for the data set is as follows:
Looking at the graph we can see that there are traces of cyclic behaviour by thedata set. We will use the use the Correlogram to see if it is AR or MA or ARMA
behaviour.
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Correlogram of V
From the Correlogram we can see that AC is dying down, and PAC is cut-off after 1
lag. This is an Auto-Regressive behaviour.
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Now,
We have to test if the series is stationary or non-stationary.
Looking at the AC we can see that the series is dying down slowly. Thus the series
could be non-stationary.
Confirmation through Dickey Fuller test1. D(V) = V(-1), Random walk
Dependent Variable: D(V)
Method: Least Squares
Date: 09/08/13 Time: 01:19
Sample (adjusted): 2005M02 2013M07
Included observations: 102 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
V(-1) 0.003488 0.002149 1.622859 0.1077
R-squared 0.001717 Mean dependent var 0.157459
Adjusted R-squared 0.001717 S.D. dependent var 1.014796S.E. of regression 1.013924 Akaike info criterion 2.875289
Sum squared resid 103.8323 Schwarz criterion 2.901024
Log likelihood -145.6398 Hannan-Quinn criter. 2.885710
Durbin-Watson stat 1.270075
Coefficient of V(-1) is +ve. Thus >1, non-stationary
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2. D(V) = C + V(-1),Random walk with drift
Dependent Variable: D(V)
Method: Least Squares
Date: 09/08/13 Time: 01:13
Sample (adjusted): 2005M02 2013M07
Included observations: 102 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.534702 1.070083 -0.499683 0.6184
V(-1) 0.014885 0.022910 0.649716 0.5174
R-squared 0.004204 Mean dependent var 0.157459
Adjusted R-squared -0.005754 S.D. dependent var 1.014796
S.E. of regression 1.017712 Akaike info criterion 2.892404
Sum squared resid 103.5737 Schwarz criterion 2.943874
Log likelihood -145.5126 Hannan-Quinn criter. 2.913246
F-statistic 0.422131 Durbin-Watson stat 1.287735
Prob(F-statistic) 0.517365
Coefficient of V(-1) is +ve. Thus >1, non-stationary
2. D(V) = C + V(-1) + T ,Random walk with drift and trend
Dependent Variable: D(V)
Method: Least Squares
Date: 09/08/13 Time: 01:21
Sample (adjusted): 2005M02 2013M07
Included observations: 102 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -205.5544 114.6783 -1.792444 0.0761
T 0.000282 0.000158 1.787858 0.0769
V(-1) -0.025882 0.032149 -0.805076 0.4227
R-squared 0.035349 Mean dependent var 0.157459
Adjusted R-squared 0.015862 S.D. dependent var 1.014796
S.E. of regression 1.006716 Akaike info criterion 2.880234
Sum squared resid 100.3342 Schwarz criterion 2.957440
Log likelihood -143.8920 Hannan-Quinn criter. 2.911497
F-statistic 1.813919 Durbin-Watson stat 1.276865
Prob(F-statistic) 0.168390
Coefficient of V(-1) is -ve. Thus
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ARIMA(1,1,0)
The stats are as follows
Dependent Variable: D(V)
Method: Least Squares
Date: 09/08/13 Time: 02:12
Sample (adjusted): 3 103
Included observations: 101 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(V(-1)) 0.381364 0.093299 4.087547 0.0001
R-squared 0.122011 Mean dependent var 0.159406
Adjusted R-squared 0.122011 S.D. dependent var 1.019666
S.E. of regression 0.955438 Akaike info criterion 2.756558
Sum squared resid 91.28618 Schwarz criterion 2.782450
Log likelihood -138.2062 Hannan-Quinn criter. 2.767040Durbin-Watson stat 1.858944
The t-Statistic is greater than 2 and Probability is greater than .05. Thus the model
has a predictive value. The DW stat is 1.85 (very close to 2), which means the
residual (errors) has very less serial correlation and cannot be forecasted further.
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Correlogram of the residuals
Prob > 0.05, thus we cannot reject the null hypothesis. This implies there is no
correlation in the residuals (they are no patterns in them). Thus our forecasting
model hold good.
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Model Verification
Actual value of 103rd observation = 59.6758
Forecasted value of 103rd observation = 59.67976
Difference in value = 0.007% (very accurate)
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Forecasting 104th value
According to the model the forecasted value of IND/USD should be 60.17410. This
is the forecasted INR/USD value for month of August 2013.
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