Question

The table below is the data set of the Shiller Real Home Price Index for the years 1946-1956.

                        Home Price

Year                 Index               

1946                 106.5058955

1947                 109.3296707

1948                 101.2225795

1949                 100.0466076

1950                 105.8948393

1951                 103.8986687

1952                 103.9743275

1953                 114.7133093

1954                 114.199126

1955                 115.4621261

1956                 115.3166155

Setting k = 3, determine the simple moving average forecasts for the years 1950, 1951, and 1952.

Answer 1

The formula for 3 years moving average is:-

To calculate the 3 point moving averages form a list of numbers, follow these steps:

1. Add up the first 3 numbers in the list and divide your answer by 3. Write this answer down as this is your first 3 point moving average.

2. Add up the next 3 numbers in the list and divide your answer by 3. Write this answer down as this is your second 3 point moving average.

3. Keep repeating step 2 until you reach the last 3 numbers.

Here 3 year moving average for index of the year 1948 is  

SUM = index for 1948(current year) + index for 1947(previous year of the current year) + index for 1946(previous year of the previous year)

the 3 years moving average for an index of the year 1948 is = SUM / 3

= 101.22 + 109.33 + 106.51 / 3 = 317.06 / 3 = 105.69

Answer:- 105.69

similarly for the year 1950

Here 3 year moving average for the index of the year 1950 is  

SUM = index for 1950(current year) + index for 1949(previous year of the current year) + index for 1948(previous year of the previous year)

the 3 years moving average for an index of the year 1950 is = SUM / 3

= 105.9 + 100.05 + 101.22 / 3 = 307.17 / 3 = 102.39

Answer:- 102.39

similarly, we have calculated table

year	index	3 year Sum	3 Year Moving Average
1946	106.51
1947	109.33
1948	101.22	317.06	105.69
1949	100.05	310.6	103.53
1950	105.9	307.17	102.39
1951	103.9	309.85	103.28
1952	103.97	313.77	104.59
1953	114.71	322.58	107.53
1954	114.2	332.88	110.96
1955	115.46	344.37	114.79
1956	115.32	344.98	114.99

The 3 years moving average for

1950 is 102.39

1951 is 103.28

1952 is 104.59