5-42 The following tables gives the average monthly exchange rate between the U.

Question

5-42

The following tables gives the average monthly exchange rate between the U.S. dollar and the euro for 2009. It shows that 1 euro was equivalent to 1.289 U.S. dollars in Janurary 2009. Develop a trend line that could be used to predict the exchange rate for 2010. Use this model to predict the exchange rate for January 2010 and Feb 2010.

5-43

For the data in problems 5-42, develop an exponential smoothing model with a smoothing constant of 0.30. Using MSE, compare this with the model in Problems 5-42.

Discussion:

Which of the models (from 5-42 and 5-43) would be best to determine the forecast for January and February, 2010? Explain.

month exchange rate January 1.289 February 1.324 March 1.321 April 1.317 May 1.28 June 1.254 July 1.23 August 1.24 September 1.287 October 1.298 November 1.283 December 1.311

Explanation / Answer

Solutions

5-42.

Using Excel, the trend equation is = 1.299– 0.002X

.For January of 2010, X = 13; = 1.299 – 0.002(13) = 1.273.

For February of 2010, X = 14; = 1.299 – 0.002(14)= 1.271.

The MSE = 0.00084

5-43.

The forecast for January 2010 would be 1.288.

The MSE with the trend equation is 0.00084.

The MSE (with time period 1 included) with this exponential smoothing model is 0.00096.

If time period 1 is omitted, this is 0.00105.

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