How to forecast using ARIMA

7/29/2019 How to forecast using ARIMA

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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

-0.2

0

0.2

0.4

0.6

0.8

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


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2. D(V) = C + V(-1),Random walk with drift



Date: 09/08/13 Time: 01:13




C -0.534702 1.070083 -0.499683 0.6184

V(-1) 0.014885 0.022910 0.649716 0.5174


Adjusted R-squared -0.005754 S.D. dependent var 1.014796

S.E. of regression 1.017712 Akaike info criterion 2.892404



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



Date: 09/08/13 Time: 01:21




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


Adjusted R-squared 0.015862 S.D. dependent var 1.014796




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



Date: 09/08/13 Time: 02:12

Sample (adjusted): 3 103



D(V(-1)) 0.381364 0.093299 4.087547 0.0001


Adjusted R-squared 0.122011 S.D. dependent var 1.019666



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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