Problem 2.1 (35 marks): Forecasting monthly sales at the restaurant "Au Canard Truff"

The restaurant "Au Canard Truff" opened over seven years ago in Sarlat, a town in the Prigord region in the South West of France. The restaurant has become one of the best in the area. Management has concluded that in order to plan better the growth of the restaurant in the future, it is necessary to develop a system that will enable them to forecast food and beverages sales by month for up to 6 months in advance. They have available data on the total food and beverage sales that have been realised since they opened on 1 February 2014. These data (sales in thousand pounds) are provided on (https://drive.google.com/file/d/1UXjvwbYq5hTC_5oM2K9yKLVi8KWbV1CJ/view?usp=sharing). Assume we are now at the beginning of May 2021.

a) Plot the data as a time series

b) Analyse the data for seasonality. Include the seasonal indices for each month, and comment on the high seasonal and low seasonal sales months. Do the seasonal indices make intuitive sense? Discuss.

c) Forecast sales for May 2021 to October 2021 using decomposition method (de-seasonalising first) with trend projection. In order to compare the results obtained with those of other methods, compute the mean error (bias), the mean absolute deviation (MAD), the mean square error (MSE), and the mean absolute percentage error (MAPE) of the forecasts.

d) Forecast sales for May 2021 to October 2021 using the decomposition method combined with Holt's method [you must determine the smoothing constants and that minimise the MAD].

e) Briefly describe another method that would be appropriate here and apply it. Compute again the mean error (bias), the mean absolute deviation (MAD), the mean square error (MSE), and the mean absolute percentage error (MAPE) of the forecasts.

f) Plot the errors for each method as time series. Comment on these graphs, and on randomness and autocorrelations of errors.

g) Summarise your results in a table and make recommendations as to which forecasting system/method should be used. Justify your answer.

h) We are now in November 2021. The observed monthly sales for May-October 2021 have been 313, 374, 413, 405, 355, and 266. What method has actually performed better?