Year Quarter Expenditure 1950 1 599 1950 2 583 1950 3 448 1950 4 451 1951 1 596 1951 2 573 1951 3 468 1951 4 485 1952 1 557 1952 2 575 1952 3 547 1952 4 485 1953 1 612 1953 2 713 1953 3 566 1953 4 571 1954 1 697 1954 2 664 1954 3 572 1954 4 562 1955 1 641 1955 2 702 1955 3 582 1955 4 568 1956 1 689 1956 2 746 1956 3 610 1956 4 652 1957 1 724 1957 2 734 1957 3 611 1957 4 623 1958 1 747 1958 2 755 1958 3 671 1958 4 656 1959 1 783 1959 2 821 1959 3 781 1959 4 697 1960 1 830 1960 2 840 1960 3 812 1960 4 767 1961 1 852 1961 2 844 1961 3 794 1961 4 738 1962 1 862 1962 2 887 1962 3 750 1962 4 863 1963 1 946 1963 2 961 1963 3 868 1963 4 923 1964 1 977 1964 2 982 1964 3 829 1964 4 855 1965 1 1038 1965 2 1059 1965 3 958 1965 4 959 1966 1 1015 1966 2 1031 1966 3 914 1966 4 892 1967 1 1039 1967 2 1085 1967 3 1018 1967 4 1031 1968 1 1154 1968 2 1134 1968 3 1111 1968 4 1108 1969 1 1132 1969 2 1177 1969 3 1122 1969 4 1149 1970 1 1286 1970 2 1305 1970 3 1165 1970 4 1174 1971 1 1363 1971 2 1359 1971 3 1167 1971 4 1212 1972 1 1363 1972 2 1325 1972 3 1187 1972 4 1265 1973 1 1368 1973 2 1411 1973 3 1368 1973 4 1326 1974 1 1453 1974 2 1462 1974 3 1342 1974 4 1360 1975 1 1539 1975 2 1566 1975 3 1405 1975 4 1485 1976 1 1546 1976 2 1525 1976 3 1466 1976 4 1496 1977 1 1640 1977 2 1677 1977 3 1572 1977 4 1533 1978 1 1734 1978 2 1749 1978 3 1675 1978 4 1667 1979 1 1761 1979 2 1773 1979 3 1774 1979 4 1789 1980 1 1844 1980 2 1896 1980 3 1812 1980 4 1875 1981 1 1999 1981 2 1959 1981 3 1906 1981 4 1891 1982 1 1991 1982 2 2041 1982 3 1999 1982 4 1970 1983 1 2159 1983 2 2103 1983 3 2058 1983 4 2125 1984 1 2215 1984 2 2203 1984 3 2161 1984 4 2196 1985 1 2255 1985 2 2368 1985 3 2244 1985 4 2198 1986 1 2417 1986 2 2470 1986 3 2361 1986 4 2374 1987 1 2505 1987 2 2585 1987 3 2505 1987 4 2486 1988 1 2598 1988 2 2630 1988 3 2573 1988 4 2586 1989 1 2724 1989 2 2707 1989 3 2688 1989 4 2691 1990 1 2821 1990 2 2941 1990 3 2841 1990 4 2868 1991 1 2978 1991 2 3060 1991 3 2916 1991 4 2933 1992 1 3045 1992 2 3124 1992 3 2998 1992 4 3067 1993 1 3207 1993 2 3243 1993 3 3200 1993 4 3211 1994 1 3363 1994 2 3381 1994 3 3363 1994 4 3340 1995 1 3509 1995 2 3547 1995 3 3557 1995 4 3524 1996 1 3634 1996 2 3761 1996 3 3655 1996 4 3686 1997 1 3864 1997 2 3898 1997 3 3820 1997 4 3872 1998 1 3997 1998 2 4048 1998 3 3942 1998 4 3967 1999 1 4206 1999 2 4234 1999 3 4158 1999 4 4164 2000 1 4310 2000 2 4407 2000 3 4279 2000 4 4309 2001 1 4528 2001 2 4553 2001 3 4556 2001 4 4575 2002 1 4752 2002 2 4817 2002 3 4754 2002 4 4756 2003 1 4945 2003 2 4947 2003 3 4885 2003 4 4914 2004 1 5106 2004 2 5197 2004 3 5165 2004 4 5219 2005 1 5387 2005 2 5429 2005 3 5447 2005 4 5431 2006 1 5596 2006 2 5633 2006 3 5608 2006 4 5742 2007 1 5825 2007 2 5903 2007 3 5875 2007 4 5943 2008 1 6122 2008 2 6151 2008 3 6092 2008 4 6148 2009 1 6310 2009 2 6431 2009 3 6404 2009 4 6424 2010 1 6579 2010 2 6751 2010 3 6685 2010 4 6751 2011 1 6894 2011 2 7002 2011 3 7004 2011 4 7068 2012 1 7241 2012 2 7303 2012 3 7270 2012 4 7334 2013 1 7571 2013 2 7620 2013 3 7636 2013 4 7664 2014 1 7861 2014 2 7983 2014 3 7922 2014 4 8027 2015 1 8196 2015 2 8326 2015 3 8294 2015 4 8373 2016 1 8596 2016 2 8703 2016 3 8632 2016 4 8780 2017 1 8957 2017 2 9056 2017 3 9041 2017 4 9126 2018 1 9339 2018 2 9440 2018 3 9445 2018 4 9496 2019 1 9802 2019 2 9845 2019 3 9846 2019 4 9976 2020 1 10181 2020 2 10285 2020 3 10300 2020 4 10403 Part B Time Series Decomposition 1 Fit a linear and quadratic trends to your series Then, create a line chart with your original series and the two trends Which trend seems to best t the series Explain 2 Fit a linear and quadratic trends to the log of your series Then, create a line chart with the log of your serill and the two trends Which trend seems to best t the serill Do you see a differs cs between the best trend in this question and in the previous one Explain Answer the following questions using the log of your series and the trends computed in question 2 3 Plot the detrended series using the trend that best t the series Briey describe what you see Do you better detect short term uctuations 4 Using a moving average of order 5, compute the cyclical component of your series Then, plot the cycle and briey describe what you see interpret the values of some peaks and troughs 5 Plot the low frequency of your series and briey describe What you see 5 Compute the seasonal component and represent it on a bar chart only the 4 quarters Interpret the four seasonal values

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Year Quarter Expenditure 1950 1 599 1950 2 583 1950 3 448 1950 4 451 1951 1 596 1951 2 573 1951 3 468 1951

Year	Quarter	Expenditure
1950	1	599
1950	2	583
1950	3	448
1950	4	451
1951	1	596
1951	2	573
1951	3	468
1951	4	485
1952	1	557
1952	2	575
1952	3	547
1952	4	485
1953	1	612
1953	2	713
1953	3	566
1953	4	571
1954	1	697
1954	2	664
1954	3	572
1954	4	562
1955	1	641
1955	2	702
1955	3	582
1955	4	568
1956	1	689
1956	2	746
1956	3	610
1956	4	652
1957	1	724
1957	2	734
1957	3	611
1957	4	623
1958	1	747
1958	2	755
1958	3	671
1958	4	656
1959	1	783
1959	2	821
1959	3	781
1959	4	697
1960	1	830
1960	2	840
1960	3	812
1960	4	767
1961	1	852
1961	2	844
1961	3	794
1961	4	738
1962	1	862
1962	2	887
1962	3	750
1962	4	863
1963	1	946
1963	2	961
1963	3	868
1963	4	923
1964	1	977
1964	2	982
1964	3	829
1964	4	855
1965	1	1038
1965	2	1059
1965	3	958
1965	4	959
1966	1	1015
1966	2	1031
1966	3	914
1966	4	892
1967	1	1039
1967	2	1085
1967	3	1018
1967	4	1031
1968	1	1154
1968	2	1134
1968	3	1111
1968	4	1108
1969	1	1132
1969	2	1177
1969	3	1122
1969	4	1149
1970	1	1286
1970	2	1305
1970	3	1165
1970	4	1174
1971	1	1363
1971	2	1359
1971	3	1167
1971	4	1212
1972	1	1363
1972	2	1325
1972	3	1187
1972	4	1265
1973	1	1368
1973	2	1411
1973	3	1368
1973	4	1326
1974	1	1453
1974	2	1462
1974	3	1342
1974	4	1360
1975	1	1539
1975	2	1566
1975	3	1405
1975	4	1485
1976	1	1546
1976	2	1525
1976	3	1466
1976	4	1496
1977	1	1640
1977	2	1677
1977	3	1572
1977	4	1533
1978	1	1734
1978	2	1749
1978	3	1675
1978	4	1667
1979	1	1761
1979	2	1773
1979	3	1774
1979	4	1789
1980	1	1844
1980	2	1896
1980	3	1812
1980	4	1875
1981	1	1999
1981	2	1959
1981	3	1906
1981	4	1891
1982	1	1991
1982	2	2041
1982	3	1999
1982	4	1970
1983	1	2159
1983	2	2103
1983	3	2058
1983	4	2125
1984	1	2215
1984	2	2203
1984	3	2161
1984	4	2196
1985	1	2255
1985	2	2368
1985	3	2244
1985	4	2198
1986	1	2417
1986	2	2470
1986	3	2361
1986	4	2374
1987	1	2505
1987	2	2585
1987	3	2505
1987	4	2486
1988	1	2598
1988	2	2630
1988	3	2573
1988	4	2586
1989	1	2724
1989	2	2707
1989	3	2688
1989	4	2691
1990	1	2821
1990	2	2941
1990	3	2841
1990	4	2868
1991	1	2978
1991	2	3060
1991	3	2916
1991	4	2933
1992	1	3045
1992	2	3124
1992	3	2998
1992	4	3067
1993	1	3207
1993	2	3243
1993	3	3200
1993	4	3211
1994	1	3363
1994	2	3381
1994	3	3363
1994	4	3340
1995	1	3509
1995	2	3547
1995	3	3557
1995	4	3524
1996	1	3634
1996	2	3761
1996	3	3655
1996	4	3686
1997	1	3864
1997	2	3898
1997	3	3820
1997	4	3872
1998	1	3997
1998	2	4048
1998	3	3942
1998	4	3967
1999	1	4206
1999	2	4234
1999	3	4158
1999	4	4164
2000	1	4310
2000	2	4407
2000	3	4279
2000	4	4309
2001	1	4528
2001	2	4553
2001	3	4556
2001	4	4575
2002	1	4752
2002	2	4817
2002	3	4754
2002	4	4756
2003	1	4945
2003	2	4947
2003	3	4885
2003	4	4914
2004	1	5106
2004	2	5197
2004	3	5165
2004	4	5219
2005	1	5387
2005	2	5429
2005	3	5447
2005	4	5431
2006	1	5596
2006	2	5633
2006	3	5608
2006	4	5742
2007	1	5825
2007	2	5903
2007	3	5875
2007	4	5943
2008	1	6122
2008	2	6151
2008	3	6092
2008	4	6148
2009	1	6310
2009	2	6431
2009	3	6404
2009	4	6424
2010	1	6579
2010	2	6751
2010	3	6685
2010	4	6751
2011	1	6894
2011	2	7002
2011	3	7004
2011	4	7068
2012	1	7241
2012	2	7303
2012	3	7270
2012	4	7334
2013	1	7571
2013	2	7620
2013	3	7636
2013	4	7664
2014	1	7861
2014	2	7983
2014	3	7922
2014	4	8027
2015	1	8196
2015	2	8326
2015	3	8294
2015	4	8373
2016	1	8596
2016	2	8703
2016	3	8632
2016	4	8780
2017	1	8957
2017	2	9056
2017	3	9041
2017	4	9126
2018	1	9339
2018	2	9440
2018	3	9445
2018	4	9496
2019	1	9802
2019	2	9845
2019	3	9846
2019	4	9976
2020	1	10181
2020	2	10285
2020	3	10300
2020	4	10403

Part B: Time Series Decomposition 1. Fit a linear and quadratic trends to your series. Then, create a line chart with your original series and the two trends. Which trend seems to best t the series? Explain. 2. Fit a linear and quadratic trends to the log of your series. Then, create a line chart with the log of your serill and the two trends. Which trend seems to best t the serill? Do you see a differs-cs between the best trend in this question and in the previous one? Explain. Answer the following questions using the log of your series and the trends computed in question 2. 3. Plot the detrended series using the trend that best t the series. Briey describe what you see: Do you better detect short term uctuations? 4. Using a moving average of order 5, compute the cyclical component of your series. Then, plot the cycle and briey describe what you see: interpret the values of some peaks and troughs. 5. Plot the low frequency of your series and briey describe What you see. 5. Compute the seasonal component and represent it on a bar chart {only the 4 quarters]. Interpret the four seasonal values