In this report we will focus on analysing four different time series that include sales data. In the first section we will withhold the last 12 observations of the data and we will a 12 months forecast using 11 different methods. Then to evaluate the results and to make predictions about the accuracy of our analysis we will test all eleven forecast methods with at least three different error measures. At the end of the section the best method for each time series will be selected. In the second part of the report instead of withholding the last 12 observation, the last 18 will be withhold. Then a 12 month forecast will be produced for each of the time series. At the end a comparison between the results received will be performed to see if there are any differences and if yes what are they and by what are they caused. In the third section a combination between the three best forecast methods for each time series is performed. Then the results will be evaluated and discussed. In the last two sections a single optimal method for all time series will be chosen and based on this decision a further twelve months forecast for each time series will be produced.
In this paper four different sets of data will be analysed for twelve months ahead through different forecasting methods such as Naïve, Naïve Season, Moving Average, exponential smoothing etc. Then all the methods will be tested using three different error measures, which will allow our team to make a decision and to choose the best possible forecasting method for each data series. In the second part will expand the forecasting period to 18 months. However in this section we will just use the three best forecasting methods found by us in the first part. In the third part we will combine all three different forecasting methods and we will provide further analysis on the accuracy of our projections. In the fourth section our goal would be to choose the best forecasting method that fits optimal all data series analysed by us so far.
Main Section
Section 1
In this section we will provide analysis and forecasts for the four time series we have. To do that we will use 11 different forecasting methods. Below in Table 1 you can find the last 12 observations for MNM65 using all the required forecasting methods. At least different 3 error measures are required in order to forecasting accuracy of the methods. Error measurement plays an essential role in finding which forecasting method performs best. Some common errors, such as MSE, RMSE and MAE, are included in the scale dependent which can be used to compare different methods on the same time series. Other common errors, for instance MAPE and SMAPE, are scale independent that allows to compare and contrast between time series.
Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), Symmetric Mean Absolute Error (sMAPE) and Geometric Mean Relative Absolute Error (GMRAE) maybe considered contrasting different methods on the MNM65 time series in this section. The large errors are calculated by using RMSE on this time series. Therefore, the MAPE, sMAPE and GMRAE error measures are chosen. Using each error measure evaluates the results of different forecasting methods, which is shown in the following paragraph.
1.1 MNM65
Firstly, there is not appearing that MAPE becomes infinite. Only the method of Arithmetic Mean has the maximum error which is 61.72%. Secondly, sMAPE is the same as MAPE. Each method has the lower error. The large value is 22.35% on the method of Arithmetic Mean. The minimum error is 1.83%. Lastly, GMRAE is the relative error measures. There are six methods that the
