2. Gold!!
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.
3. Methods to forecast
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.
4. Holt‘s Method to forecast
Gold
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
5. Representation-
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.
6. Initialization
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 )
7. Values of constants
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.
8. 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
9. Calculations
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
10. 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’
13. Values
Alpha Beta F September 2011 F March 2012 ME MSE MRPE
0.6278 0.6278 30129.372 42698.197 -62.036 39163.8 -0.004039
0.124 0.124 25716.41 28394.04 0.0946 195706.3 -0.00541
0.999 0.999 33527.59 57954.31 -73.62 181850.4 -0.004
14. Forecasted value for
March 2011
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.
