Question

A. Use the three- and seven-term moving averages to generate one-step ahead forecasts for 1981 to the end of the series. Graph the results, and comment on the difference between the two moving averages.

B. Compare the performance of the two procedures by calculating the RMSE and MAE. Why is Mape inappropriate in this case?

Please show to do this in excel, I am having a difficult time understanding how this is done.

Year | GDP Growth |

1963 | 4.4 |

1964 | 5.8 |

1965 | 6.4 |

1966 | 6.5 |

1967 | 2.5 |

1968 | 4.8 |

1969 | 3.1 |

1970 | 0.2 |

1971 | 3.4 |

1972 | 5.3 |

1973 | 5.8 |

1974 | -0.5 |

1975 | -0.2 |

1976 | 5.3 |

1977 | 4.6 |

1978 | 5.6 |

1979 | 3.2 |

1980 | -0.2 |

1981 | 2.5 |

1982 | -1.9 |

1983 | 4.5 |

1984 | 7.2 |

1985 | 4.5 |

1986 | 3.5 |

1987 | 3.4 |

1988 | 4.1 |

1989 | 3.5 |

1990 | 1.9 |

1991 | -0.2 |

1992 | 3.3 |

1993 | 2.7 |

1994 | 4 |

1995 | 2.5 |

1996 | 3.7 |

1997 | 4.5 |

1998 | 4.2 |

1999 | 4.5 |

2000 | 3.8 |

2001 | 0.8 |

2002 | 1.9 |

2003 | 3 |

2004 | 4.4 |

2005 | 2.9 |

2006 | 2.8 |

2007 | 2 |

Answer #1

1) 3 term moving average is calculated as

For example forecast for 1981 is calculated as

7 term moving average is calculated as

For example forecast for 1981 is calculated as

the following excel shows the calculations, starting from the year 1981

Get the following

Graph the results

select the data and use insert-->scatter-->lines as shown below

get the following

format as needed

We can see that the original GDP Growth series widely fluctuates. Some of these variations could be due to the irregular component of the time series. The purpose of the moving average forecasting is to smooth out the random fluctuations due to the irregular component. In this regard, we can see that 7 term moving average does a better job that 3 term moving average. 7 term moving average does not react as much as the 3 term moving average and it has smoothened out the fluctuations in the original GDP series.

b)

RMSE (Root means squared Error) is calculated as

where Actual(t) is the actual value of GDP Growth in period t and Forecast(t) is the forecasted value in period t. n=27 is the number of periods (from 1981 to 2007) for which the error is calculated.

Mean Absolute Error (MAE) is calculated as

where |value| is the absolute of "value"

The following excel shows the 2 calculations

The values are

7 term moving average has a lower RMSE as well as MAE. Hence 7 term moving average is a better forecasting method.

MAPE is calculated as

The Actual value in the denominator is the GDP growth. If the GDP growth is zero (which it can be), then this devision becomes not calculable. Hence MAPE meaure might not be appropriate for GDP growth as GDP growth can be 0.

Perform a hypothesis testing using Kendall’s Tau method to check
if the distribution of peak flows does not change as a function of
time. Data is below please show step by step. I will rate
afterwards.
Year
Peak Flow
1947
15500
1948
27400
1949
27500
1950
43000
1951
19100
1952
17600
1953
15800
1954
8600
1955
9950
1956
35400
1957
34700
1958
37000
1959
26000
1960
27000
1961
42300
1962
26300
1963
41600
1964
50500
1965
15500
1966
6710
1967...

Year-Year Percent Change in Commodities CPI
Year-Year Percent Change in Services CPI
Year
Commodities%
Services%
1960
0.9
3.4
1961
0.6
1.7
1962
0.9
2.0
1963
0.9
2.0
1964
1.2
2.0
1965
1.1
2.3
1966
2.6
3.8
1967
1.9
4.3
1968
3.5
5.2
1969
4.7
6.9
1970
4.5
8.0
1971
3.6
5.7
1972
3.0
3.8
1973
7.4
4.4
1974
11.9
9.2
1975
8.8
9.6
1976
4.3
8.3
1977
5.8
7.7
1978
7.2
8.6
1979
11.3
11.0
1980
12.3
15.4
1981
8.4...

Using Box-Jenkin’s four-step method, forecast the US quarterly
GDP for the second quarter of 2015.
observation_date
GDP (billion $)
1947-01-01
1934.5
1947-04-01
1932.3
1947-07-01
1930.3
1947-10-01
1960.7
1948-01-01
1989.5
1948-04-01
2021.9
1948-07-01
2033.2
1948-10-01
2035.3
1949-01-01
2007.5
1949-04-01
2000.8
1949-07-01
2022.8
1949-10-01
2004.7
1950-01-01
2084.6
1950-04-01
2147.6
1950-07-01
2230.4
1950-10-01
2273.4
1951-01-01
2304.5
1951-04-01
2344.5
1951-07-01
2392.8
1951-10-01
2398.1
1952-01-01
2423.5
1952-04-01
2428.5
1952-07-01
2446.1
1952-10-01
2526.4
1953-01-01
2573.4
1953-04-01
2593.5
1953-07-01
2578.9
1953-10-01
2539.8
1954-01-01
2528.0
1954-04-01
2530.7
1954-07-01...

please answer 1-3
year
catch
effort
1962
51.8
50.0567
1963
44.3
44.3
1964
48
44.54
1965
44.826
59.9788
1966
39.208
45.3769
1967
48.278
46.6083
1968
37.819
52.2453
1969
31.992
54.1197
1970
29.894
35.6082
1971
39.406
61.2475
1972
34.279
54.7616
1973
27.958
46.5664
1974
36.407
28.5148
1975
27.827
27.1653
1976
33.71
38.8333
1977
32.888
22.0711
1978
35.804
31.362
1979
38.95
25.6873
1980
29.157
19.38
1981
23.748
21.7888
1982
28.333
20.1047
1983
31.945
27.1808
1984
18.434
17.9237
1985
22.531
18.9703
1986
25.587...

Year
Total Tornadoes
1950
213
1951
272
1952
252
1953
434
1954
562
1955
605
1956
516
1957
870
1958
576
1959
616
1960
628
1961
709
1962
669
1963
475
1964
716
1965
909
1966
597
1967
938
1968
672
1969
620
1970
666
1971
901
1972
753
1973
1114
1974
957
1975
931
1976
846
1977
864
1978
801
1979
867
1980
878
1981
794
1982
1059
1983
943
1984
919
1985
696
1986
777
1987
668
1988...

(For this part, you MUST present sufficient solution steps, and
MUST apply specific Excel functions =NPV(…), =IRR(…), =AVERAGE(…),
=YIELD(…) whenever applicable.
We are given the information that Microthin’s stock price was
$21 in December 2013, $29 in December 2014, $27 in December 2015,
$20 in December 2016, and $26 in December 2017. It also pays annual
dividend amounts varying from 2013 through 2017.
Let's assume you do the following transactions:
a) In December 2013: buy 30,000 Microthin shares;
b) In...

Regress Consumption against the GDP from the data sheet. Include
the Excel ANOVA table.Although irrelevant run a "F" test as well as
individual coefficient test. Write a short paragraph discussing the
results. For example, how this information can be used to forecast
future consumption or any other interesting conclusions you can
draw material in your textbook as well as outside reading can be
very helpful.
Year
Personal Consumption Expenditure
Nominal GDP
1929-01-01
77.4
104.6
1930-01-01
70.1
92.2
1931-01-01
60.7
77.4...

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