Download - MFEFM 2nd Assignment.pdf
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Problem Statement : Forecast the value of Sensex for first week of September
based on previous six months values.
Graph of Sensex
The above graph shows that the data chosen for the study is continuous and that
there is no gap/break in the data.
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Correlogram of Sensex
From the correlogram, we can see that the autocorrelation demonstrates an
exponentially decaying pattern. This is an indication of the presence ofseasonality.
From the partial correlation graph we can see the presence of AR(1) and possibly
SAR(7). However, we shall conduct the unit root test before going for regression.
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ADF Unit Root Test on Sensex
From the unit root test we can say that, there is 28.76% probability that the series
has a unit root.
Unit root tests in isolation are inconclusive, but along with the correlogram, they
give an insight into the presence of trend in the data being studied. Here, both
the unit root test and the correlogram suggest that trend is present in the data
being studied.
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ADF Unit Root Test on Sensex first Difference
This validates our claim of white noise being achieved directly.
So, instead of de-trending first lets go for de-seasonalizing and check the results.
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Correlogram of Deseasonalized Sensex
We can see the presence of various variables here from this correlogram. Lets
prepare a model through which we can run the regression and check the results.
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First regression after Deseasonalizing
We will need to remove insignificant variables from this which is MA(2).
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FINAL REGRESSION RESULTS
Now, we have prepared a model in which we have accounted for all the relevant
variables for Sensex. Before going for forecasting let’s have a look at the
correlogram to check whether white noise has been achieved or not.
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CORRELOGRAM OF DESEASONALIZED SENSEX
As can be seen from the above correlogram we have been able to achieve the
White Noise process. So now we can go for forecasting.
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STATIC FORECAST RESULTS
As we can see that the Mean Absolute Percent Error for our model is pretty low
i.e. 0.78%. It shows that our model captures the Sensex value with enough
precision. Lets have a look at the graph to see the pattern.
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GRAPHS FOR STATIC FORECAST
In our original dataset we had left blank the values of Sensex from 01/09/2015 to
10/09/2015. Lets have a look at the values our model has given for the following
dates.
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DYNAMIC FORECAST RESULTS