The enrollment in the School of Business at the local colleg

The enrollment in the School of Business at the local college by Quarter since 2010 is as follows:

                                         Quarterly Data

Year

Winter

Spring

Summer

Fall

2010

2033

1871

714

2318

2011

2174

2069

840

2413

2012

2370

2254

927

2704

2013

2625

2478

1136

3001

2014

2803

2668

-

-

Using the Ratio-to- moving average method

a) Determine the four quarterly indexes

b) Interpret the Quarterly pattern of enrollment. Does the seasonal variation surprise

c) Compute the Trend equation, and forecast the 2015 enrollment by Quarter i.e Quarter 3 and 4.

Year	Winter	Spring	Summer	Fall
2010	2033	1871	714	2318
2011	2174	2069	840	2413
2012	2370	2254	927	2704
2013	2625	2478	1136	3001
2014	2803	2668	-	-

Solution

•Pick time period (number of years)

•Pick season period (month, quarter)

•Calculate average price for season

•Calculate average price over time

•Divide season average by over time average price x 100

Using Seasonal Index to Forecast

•Observe price in time t1 P1

•Forecast price in time t2 P2

• Start with P1/ I1 = P2 / I2

• Then P1 x I2 / I1 = P2

•Assume that cows are selling at $50/cwt in November. What is the forecast of February?

Seasonal indices are calculated so that their average is 1. This means that the sum of the seasonal indices equals the number of seasons. Thus, if the seasons are months, the seasonal indices add to 12. If the seasons are quarters, then the seasonal indices would add to 4, and so on. January has seasonal index of 1.1which means, January’s unemployment is 10% above average. September’s unemployment is 15% less than average.

Deseasonalising is the process that is used to remove the seasonal effects from a set of data. This allows any underline trend to be made clearer.

We can use seasonal indices to deseasonalise time series. To calculate deseasonalised data, each entry is divided by its seasonal index as follows.

                                   Deseasonalising data

Example: Deseasonalise the quarterly sales gures of Summer Year1 using the data and seasonal indices tables below.

Solution: Deseasonalised data for ‘Summer 1’ = Summer 1 data         =    920 = 893

                                                                Summer seasonal index     1.03

                                Calculating seasonal indices

Example: Mikki runs a shop and she wishes to determine quarterly seasonal indices

based on her last year’s sales, which are shown in the table below.

Solution: Using the above formula to find the seasonal index

seasonal index = value of the quarter

                          quarter average

Find the quarter average

quarter average = 920 + 1085 + 1241 + 446 = 923

                                            4

Find the seasonal index of each season

seasonal index Summer = 920 = 0.997

                                      923

seasonal index Autumn = 1085 = 1.176

                                      923

seasonal index Winter = 1241 = 1.345

                                      923

seasonal index Spring = 446 = 0.483

                                    923

                        Calculating seasonal indices (several years’ data)

Suppose that Mikki has in fact three years of data, as shown. Use the data to calculate seasonal indices, correct to two decimal places.

Solution: The seasonal average of year 1 was found previously

Find the quarter average for year 2

quarter average year 2 = 1035 + 1180 + 1356 + 541 = 1028

                                                        4

Find the seasonal index of each season

seasonal index Summer = 1035 = 1.007

                                      1028

seasonal index Autumn = 1180 = 1.148

                                      1028

seasonal index Winter = 1356 = 1. 319

                                     1028

seasonal index Spring = 541 = 0.526

                                    1028

Find the quarter average for year 3

quarter average year 2 = 1299 + 1324 + 1450 + 659 = 1183

                                                        4

Find the seasonal index of each season

seasonal index Summer = 1299 =1.098

                                      1183

seasonal index Autumn = 1324 = 1.119

                                      1183

seasonal index Winter = 1450 = 1.226

                                    1183

seasonal index Spring = 659 = 0.557

                                    1183

To find the seasonal indices of the 3 years we need to find the average seasonal index of each season.