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Business Forecasting Techniques To forecast the value of “Gold” for March-2012 guided By Mr.Vandit hEdau
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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.
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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.
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Holt‘s Method to forecast GoldHolt’s Method- This is an extension of exponential smoothing to takeinto account a possible linear trend. There are two smoothing constants α and β. The value of theseconstants 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
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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.
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Initialization Before solving these equations, Initialization is required to bedone( 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 )
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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.
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Values of constants In this particular case of forecasting value of gold, we don‘t taketwo different values of alpha and beta.Instead we take – alpha = beta =βThus, this method is equivalent to “Brown’s Double ExponentialSmoothing method”. 0< = β>1
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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
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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’
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Values Alpha Beta F September 2011 F March 2012 ME MSE MRPE0.6278 0.6278 30129.372 42698.197 -62.036 39163.8 -0.0040390.124 0.124 25716.41 28394.04 0.0946 195706.3 -0.005410.999 0.999 33527.59 57954.31 -73.62 181850.4 -0.004
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Forecasted value for March 2011 The forecasted valued of Gold for March 2011 according to Holt’sMethod is INR. 42698.1973, if weconsider mean square error to be minimum.
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