The Air Finance Division is one of several divisions within United Parcel Service Financial Corporation, a wholly-owned subsidiary of United Parcel Service (UPS). The Air Finance Division has the responsibility of providing financial services to the company as a whole with respect to all jet aircraft acquisitions. In addition, this division provides financing to independent outside entities for aviation purchases as a separate and distinct operation. Historically, the non-UPS financing segment of the Air Finance Division has provided a higher rate of return and greater fee income than the UPS segment; however it is more costly to pursue. Funding forecasts for the non-UPS market segment of the Air Finance Division have been highly subjective and not as reliable as the forecasts for other segments. The table below lists 10 years of monthly funding requirements for the non-UPS Air Finance Division segment. These data were collected from management reports during the period from January 1989 through December 1998 and of the month end figures in millions of dollars. YEAR 1989 1990 Jan 16.2 20.1 Apr 18.8 21.9 1991 20.0 21.6 1992 1993 1994 1995 1996 1997 1998 20.2 21.0 21.2 21.8 20.7 22.9 25.6 Feb 16.7 21.6 20.4 21.1 21.7 22.5 21.9 22.0 23.8 26.5 Mar 18.7 21.6 20.9 21.5 22.2 22.7 23.1 22.5 24.8 27.2 22.2 23.1 23.6 23.2 23.6 25.4 27.9 May 20.6 23.4 23.2 23.4 24.8 25.1 24.2 25.2 27.0 29.4 Jun 22.5 25.9 25.6 25.7 26.6 27.6 27.2 27.6 29.9 31.8 Jul 23.3 26.0 26.6 26.3 27.4 28.2 28.0 28.2 31.2 32.7 Aug 23.8 26.2 26.3 26.2 27.1 27.7 27.6 28.0 30.7 32.4 Sep 22.3 24.7 23.7 23.6 25.3 25.7 25.2 26.3 28.9 30.4 Oct 22.3 23.5 22.2 22.8 23.6 24.3 24.1 25.9 28.3 29.5 Nov 22.1 23.4 22.7 22.8 23.5 23.7 23.6 25.9 28.0 29.3 Dec 23.6 23.9 23.6 23.3 24.7 24.9 24.1 27.1 29.1 30.3 The objective is to develop a time series forecasting model. The year 1998 data is to be reserved as a test set. The forecasting model is to be developed based on the years 1989 to 1997. You are to answer the questions by performing the appropriate analyses using Excel and/or Minitab. The data will be found in the Excel file UPS Data. You can copy and paste the data from Excel into Minitab. In the course of the assignment you will construct two different forecasting models, one based on multiplicative decomposition and the other using the Box-Jenkins ARIMA methodology. You will then test both models using measures of forecast error to determine which model is best. Finally, you will use the best model to forecast funding for the year 1998. In this assignment, you will gain experience in constructing forecasting models using the first 9 years of data (1989-1997), and then you will use the models to forecast funding for 1998 To accomplish this, first create two new data sets, one consisting of the observations for years 1989 to 1997, inclusive, and the other (called the test set) consisting of the 12 observations for the years 1998. Task 1 Using the data from 1989 - 1997, draw a time series plot of the data and comment on the time series components that you observe. What can you say about seasonality in the data? Task 2 Use the Trend Analysis feature of Minitab to obtain a linear trend for funding. Comment on the average annual increase in funding. Task 3 Use the Decomposition module in the Time Series menu to obtain Seasonal Indices for the data. Specify the worst and best months for funding, explaining the meaning of the corresponding indexes. Using the multiplicative decomposition model obtain trend-seasonal (TS) forecasts for 1998. Task 4 Take a first difference of the time series data and construct an autocorrelation plot of the differenced data with 60 lags. Do you think the data is stationary? Explain you answer. Task 5 Now take a difference of Lag 12 and draw the autocorrelation and partial autocorrelation plots. Task 6 Based on the plots obtained in Task 5, use the ARIMA feature in Minitab to obtain two potential seasonal ARIMA models, one based on the autoregressive components and the other on the moving average components. Write out the autoregressive equations for the two models. Obtain monthly forecasts for 1998 for these two models. Task 7 Using MAPE as a measure of forecast accuracy compare your time series decomposition forecasts for 1998 with your ARIMA forecasts based on the two ARIMA models. Based on these results specify your recommended forecasting model. Hint: For this part of the assignment, it is easiest to use Excel. The Air Finance Division is one of several divisions within United Parcel Service Financial Corporation, a wholly-owned subsidiary of United Parcel Service (UPS). The Air Finance Division has the responsibility of providing financial services to the company as a whole with respect to all jet aircraft acquisitions. In addition, this division provides financing to independent outside entities for aviation purchases as a separate and distinct operation. Historically, the non-UPS financing segment of the Air Finance Division has provided a higher rate of return and greater fee income than the UPS segment; however it is more costly to pursue. Funding forecasts for the non-UPS market segment of the Air Finance Division have been highly subjective and not as reliable as the forecasts for other segments. The table below lists 10 years of monthly funding requirements for the non-UPS Air Finance Division segment. These data were collected from management reports during the period from January 1989 through December 1998 and of the month end figures in millions of dollars. YEAR 1989 1990 Jan 16.2 20.1 Apr 18.8 21.9 1991 20.0 21.6 1992 1993 1994 1995 1996 1997 1998 20.2 21.0 21.2 21.8 20.7 22.9 25.6 Feb 16.7 21.6 20.4 21.1 21.7 22.5 21.9 22.0 23.8 26.5 Mar 18.7 21.6 20.9 21.5 22.2 22.7 23.1 22.5 24.8 27.2 22.2 23.1 23.6 23.2 23.6 25.4 27.9 May 20.6 23.4 23.2 23.4 24.8 25.1 24.2 25.2 27.0 29.4 Jun 22.5 25.9 25.6 25.7 26.6 27.6 27.2 27.6 29.9 31.8 Jul 23.3 26.0 26.6 26.3 27.4 28.2 28.0 28.2 31.2 32.7 Aug 23.8 26.2 26.3 26.2 27.1 27.7 27.6 28.0 30.7 32.4 Sep 22.3 24.7 23.7 23.6 25.3 25.7 25.2 26.3 28.9 30.4 Oct 22.3 23.5 22.2 22.8 23.6 24.3 24.1 25.9 28.3 29.5 Nov 22.1 23.4 22.7 22.8 23.5 23.7 23.6 25.9 28.0 29.3 Dec 23.6 23.9 23.6 23.3 24.7 24.9 24.1 27.1 29.1 30.3 The objective is to develop a time series forecasting model. The year 1998 data is to be reserved as a test set. The forecasting model is to be developed based on the years 1989 to 1997. You are to answer the questions by performing the appropriate analyses using Excel and/or Minitab. The data will be found in the Excel file UPS Data. You can copy and paste the data from Excel into Minitab. In the course of the assignment you will construct two different forecasting models, one based on multiplicative decomposition and the other using the Box-Jenkins ARIMA methodology. You will then test both models using measures of forecast error to determine which model is best. Finally, you will use the best model to forecast funding for the year 1998. In this assignment, you will gain experience in constructing forecasting models using the first 9 years of data (1989-1997), and then you will use the models to forecast funding for 1998 To accomplish this, first create two new data sets, one consisting of the observations for years 1989 to 1997, inclusive, and the other (called the test set) consisting of the 12 observations for the years 1998. Task 1 Using the data from 1989 - 1997, draw a time series plot of the data and comment on the time series components that you observe. What can you say about seasonality in the data? Task 2 Use the Trend Analysis feature of Minitab to obtain a linear trend for funding. Comment on the average annual increase in funding. Task 3 Use the Decomposition module in the Time Series menu to obtain Seasonal Indices for the data. Specify the worst and best months for funding, explaining the meaning of the corresponding indexes. Using the multiplicative decomposition model obtain trend-seasonal (TS) forecasts for 1998. Task 4 Take a first difference of the time series data and construct an autocorrelation plot of the differenced data with 60 lags. Do you think the data is stationary? Explain you answer. Task 5 Now take a difference of Lag 12 and draw the autocorrelation and partial autocorrelation plots. Task 6 Based on the plots obtained in Task 5, use the ARIMA feature in Minitab to obtain two potential seasonal ARIMA models, one based on the autoregressive components and the other on the moving average components. Write out the autoregressive equations for the two models. Obtain monthly forecasts for 1998 for these two models. Task 7 Using MAPE as a measure of forecast accuracy compare your time series decomposition forecasts for 1998 with your ARIMA forecasts based on the two ARIMA models. Based on these results specify your recommended forecasting model. Hint: For this part of the assignment, it is easiest to use Excel