To forecast the value of “Gold” for March-2012 guided By Mr.Vandit hEdau

Business Forecasting Techniques

INTERNATIONAL INSTITUTE OF PROFESSIONAL STUDIES

Gold has always been a very precious metal. It has lots of

significance for everyone and even in all the cultures. That can be broadly described under following 7 heads-

General Fascination. Literature, the Arts, and Entertainment. Monetary Unit. Gold Standard. Availability over Time. Present Relevance. Relationship to Silver.

Gold!!

There are various methods available to forecast the

value of any metal for a specific period.

But because of the trend and behavior of Gold, we would be using Holt’s method to predict its forecasted value for march 2012.

Methods to forecast

Holt’s Method- This is an extension of exponential smoothing to take into account a possible linear trend.

There are two smoothing constants α and β. The value of these constants lie between 0 to 1.

The equations of Holt’s method are:

 Lt = Yt + (1-)(Lt-1+bt-1) bt = β(Lt—Lt-1) + (1-β)bt-1

Ft + m = Lt + m* bt

 

Holt’s Method to forecast Gold

Here,

“Lt “ is (exponentially smoothed) estimate of the level of the series at time ‘t’.

“bt “ is (exponentially smoothed) estimate of the linear trend(slope) of the series at time ‘t’.

“F t+m “ is the linear forecast from t onwards.

And ”m” is the time interval for forecast.

Representation-

Before solving these equations, Initialization is required to be done( as we don’t have the initial values)

Thus, we require 2 estimates (Initial estimates are needed for L1 and b1 )

So we set-   L1 = Y1

(to get the 1st smoothed value of L1 )

b1 = Y2- Y1

(to get the 1st smoothed value of Y1 )

Initialization

Now, we need to take the value of alpha.

But we don’t have any such predetermined values for forecasting gold price.

So we put all possible values between 0 to 1, find the forecasted values, then find out the error, and then from error, we find the MSE- Mean square Error. ( or Mean Relative percentage error)

The alpha, for which MSE is min or nearest to 0 is then chosen.

Values of constants

In this particular case of forecasting value of gold, we don’t take two different values of alpha and beta.Instead we take –

alpha = beta = β

Thus, this method is equivalent to “Brown’s Double Exponential Smoothing method”.

0< = β>1

Values of constants

We have got the monthly data of gold prices from 1-31-

1979 to 8-31-2011.

That is we have a data of 392 observations.

We have chosen to take this many data, as more is the data, more is the accuracy of future prediction.

Here, the value of “m” would be 7 , March 2012- August 2011= 7 months

Calculations

But instead of this, to make the calculations easy, we take

m=1.

Find the forecasted value for September ( FS and also the value of LS and bS)

And then these value are taken as the actual value, we put m’=6, we calculate the forecasted value for march 2012 directly, putting-

F March 2012= L September 2011 + b September 2011 * m’

Calculations

Table- Alpha & M.S.E.Alpha M.S.E Alpha M.S.E0.1 216293.5 0.6278 39163.790.2 144082.1 0.6279 39163.810.3 94796.16 0.628 39163.84

0.4 65504.42 0.629 39164.76

0.5 47608.38 0.63 39166.82

0.56 41617.2 0.632 39174.4

0.59 39943 0.635 39194.45

0.6 39588.52 0.64 39251.280.62 39197.3 0.7 42425.160.625 39167.91 0.8 60630.32

0.627 39164.06 0.9 102171

0.6275 39163.8 0.99 172214.8

Graph- M.S.E &Alpha

0 0.2 0.4 0.6 0.8 1 1.20

50000

100000

150000

200000

250000

M.S.E

M.S.E

Alpha

M.S

.E.

Values

Alpha Beta

F September

2011

F March

2012ME MSE MRPE

0.6278

0.6278 30129.372 42698.1

97-

62.036

39163.8

-0.00403

9

0.124 0.124 25716.41 28394.04

0.0946

195706.3

-0.00541

0.999 0.999 33527.59 57954.31

-73.6

2181850

.4 -0.004

The forecasted valued of

Gold for March 2011 according to Holt’s Method is INR. 42698.1973, if we

consider mean square error to be minimum.

Forecasted value for March 2011

Anjali Patel- IM-2K8-05 Bhagyashree Gupta- IM-2K8-17

Thank You