University of Waterloo Time Series Decomposition Questions & Worksheet

Description

Answer the question using the data file. It is an artificial time series from 1950 to 2020. For the exercise, we assume that it is a series of consumption expenditure in thousands of dollars. For each chart that you create, add a main title and axis titles. When the chart contains more than one line, use a different color and shape for each line and add a legend.Part A: Visualization1. Plot the series using a line chart. Briefly describe what you see: Is it a positive or negative trend? Is the trend increasing? What kind of short term fluctuations do you observe?2. Answer the previous question using the log-scale. Can you tell if the growth rate is increasing or decreasing on average over the period?3. To better see how the growth rate evolves through time, plot the annualized growth rate of consumption expenditure. Describe what you see. Is it constant on average?Part B: Time Series Decomposition1. 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 fit 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 series and the two trends. Which trend seems to best fit the series? Do you see a difference 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 fit the series. Briefly describe what you see: Do you better detect short term fluctuations?4. Using a moving average of order 5, compute the cyclical component of your series. Then, plot the cycle and briefly describe what you see: interpret the values of some peaks and troughs.5. Plot the low frequency of your series and briefly describe what you see.6. Compute the seasonal component and represent it on a bar chart (only the 4 quarters). Interpret the four seasonal values.Part C: ComovementFor this part, select any other series in the file assignment1.zip and answer the following questions: Create a scatter plot of your series expressed in logs against the selected series also expressed in logs. Using the log of the selected series, compute its cyclical component. Then create a scatter plot of this cycle with the cycle of your series computed in Part B.• Looking at the two scatter plots, what can you say about the type of comovement between the two series?

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Year
Quarter
1950
1950
1950
1950
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1951
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1
2
3
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1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
Expenditure Decdate
507
1950.125
460
1950.375
512
1950.625
462
1950.875
499
1951.125
509
1951.375
555
1951.625
465
1951.875
488
1952.125
496
1952.375
508
1952.625
449
1952.875
498
1953.125
500
1953.375
548
1953.625
494
1953.875
526
1954.125
523
1954.375
587
1954.625
517
1954.875
581
1955.125
568
1955.375
634
1955.625
568
1955.875
595
1956.125
561
1956.375
600
1956.625
564
1956.875
604
1957.125
577
1957.375
665
1957.625
613
1957.875
624
1958.125
615
1958.375
700
1958.625
647
1958.875
634
1959.125
597
1959.375
644
1959.625
decdate2
3802987.52
3803962.64
3804937.89
3805913.27
3806888.77
3807864.39
3808840.14
3809816.02
3810792.02
3811768.14
3812744.39
3813720.77
3814697.27
3815673.89
3816650.64
3817627.52
3818604.52
3819581.64
3820558.89
3821536.27
3822513.77
3823491.39
3824469.14
3825447.02
3826425.02
3827403.14
3828381.39
3829359.77
3830338.27
3831316.89
3832295.64
3833274.52
3834253.52
3835232.64
3836211.89
3837191.27
3838170.77
3839150.39
3840130.14
Log – Scale
6.228511
6.13122649
6.23832463
6.13556489
6.2126061
6.23244802
6.31896811
6.14203741
6.19031541
6.20657593
6.23048145
6.10702289
6.21060008
6.2146081
6.30627529
6.20253552
6.26530121
6.25958146
6.37502482
6.24804287
6.36475076
6.34212142
6.45204895
6.34212142
6.38856141
6.32972091
6.39692966
6.33505425
6.4035742
6.35784227
6.49978704
6.41836494
6.43615037
6.42162227
6.55108034
6.47234629
6.45204895
6.39191711
6.46769873
1959
1960
1960
1960
1960
1961
1961
1961
1961
1962
1962
1962
1962
1963
1963
1963
1963
1964
1964
1964
1964
1965
1965
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1965
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1966
1966
1966
1967
1967
1967
1967
1968
1968
1968
1968
1969
1969
1969
1969
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
591
572
569
629
571
559
540
626
599
612
600
663
621
606
613
695
632
642
648
732
712
700
691
721
654
645
637
718
640
651
615
709
669
695
709
758
692
716
680
786
752
1959.875
1960.125
1960.375
1960.625
1960.875
1961.125
1961.375
1961.625
1961.875
1962.125
1962.375
1962.625
1962.875
1963.125
1963.375
1963.625
1963.875
1964.125
1964.375
1964.625
1964.875
1965.125
1965.375
1965.625
1965.875
1966.125
1966.375
1966.625
1966.875
1967.125
1967.375
1967.625
1967.875
1968.125
1968.375
1968.625
1968.875
1969.125
1969.375
1969.625
1969.875
3841110.02
3842090.02
3843070.14
3844050.39
3845030.77
3846011.27
3846991.89
3847972.64
3848953.52
3849934.52
3850915.64
3851896.89
3852878.27
3853859.77
3854841.39
3855823.14
3856805.02
3857787.02
3858769.14
3859751.39
3860733.77
3861716.27
3862698.89
3863681.64
3864664.52
3865647.52
3866630.64
3867613.89
3868597.27
3869580.77
3870564.39
3871548.14
3872532.02
3873516.02
3874500.14
3875484.39
3876468.77
3877453.27
3878437.89
3879422.64
3880407.52
6.38181602
6.34913899
6.34388043
6.44413126
6.34738921
6.32614947
6.29156914
6.43935037
6.3952616
6.41673228
6.39692966
6.49677499
6.43133108
6.40687999
6.41836494
6.54391185
6.44888939
6.4645883
6.4738907
6.59578051
6.56807791
6.55108034
6.53813982
6.58063914
6.48310735
6.46925032
6.45676966
6.57646957
6.46146818
6.47850964
6.42162227
6.56385553
6.50578406
6.54391185
6.56385553
6.63068339
6.53958596
6.57368017
6.5220928
6.66695679
6.62273632
1970
1970
1970
1970
1971
1971
1971
1971
1972
1972
1972
1972
1973
1973
1973
1973
1974
1974
1974
1974
1975
1975
1975
1975
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1976
1976
1976
1977
1977
1977
1977
1978
1978
1978
1978
1979
1979
1979
1979
1980
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
745
711
722
654
686
650
714
704
732
718
791
733
746
715
750
706
738
694
747
678
676
665
719
664
691
695
775
746
771
724
805
755
737
719
787
724
751
739
807
757
792
1970.125
1970.375
1970.625
1970.875
1971.125
1971.375
1971.625
1971.875
1972.125
1972.375
1972.625
1972.875
1973.125
1973.375
1973.625
1973.875
1974.125
1974.375
1974.625
1974.875
1975.125
1975.375
1975.625
1975.875
1976.125
1976.375
1976.625
1976.875
1977.125
1977.375
1977.625
1977.875
1978.125
1978.375
1978.625
1978.875
1979.125
1979.375
1979.625
1979.875
1980.125
3881392.52
3882377.64
3883362.89
3884348.27
3885333.77
3886319.39
3887305.14
3888291.02
3889277.02
3890263.14
3891249.39
3892235.77
3893222.27
3894208.89
3895195.64
3896182.52
3897169.52
3898156.64
3899143.89
3900131.27
3901118.77
3902106.39
3903094.14
3904082.02
3905070.02
3906058.14
3907046.39
3908034.77
3909023.27
3910011.89
3911000.64
3911989.52
3912978.52
3913967.64
3914956.89
3915946.27
3916935.77
3917925.39
3918915.14
3919905.02
3920895.02
6.61338422
6.56667243
6.58202514
6.48310735
6.53087763
6.47697236
6.57088296
6.55677836
6.59578051
6.57646957
6.67329797
6.5971457
6.6147256
6.57228254
6.62007321
6.55961524
6.60394382
6.54247196
6.61606519
6.51914729
6.51619308
6.49978704
6.57786136
6.49828215
6.53813982
6.54391185
6.65286303
6.6147256
6.64768837
6.58479139
6.69084228
6.62671775
6.60258789
6.57786136
6.66822825
6.58479139
6.62140565
6.60529792
6.69332367
6.62936325
6.67456139
1980
1980
1980
1981
1981
1981
1981
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
1986
1986
1987
1987
1987
1987
1988
1988
1988
1988
1989
1989
1989
1989
1990
1990
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
780
801
733
765
737
868
834
856
834
909
851
844
794
861
807
830
830
881
794
853
826
886
864
861
832
891
832
856
829
895
852
860
846
906
839
858
887
937
878
907
907
1980.375
1980.625
1980.875
1981.125
1981.375
1981.625
1981.875
1982.125
1982.375
1982.625
1982.875
1983.125
1983.375
1983.625
1983.875
1984.125
1984.375
1984.625
1984.875
1985.125
1985.375
1985.625
1985.875
1986.125
1986.375
1986.625
1986.875
1987.125
1987.375
1987.625
1987.875
1988.125
1988.375
1988.625
1988.875
1989.125
1989.375
1989.625
1989.875
1990.125
1990.375
3921885.14
3922875.39
3923865.77
3924856.27
3925846.89
3926837.64
3927828.52
3928819.52
3929810.64
3930801.89
3931793.27
3932784.77
3933776.39
3934768.14
3935760.02
3936752.02
3937744.14
3938736.39
3939728.77
3940721.27
3941713.89
3942706.64
3943699.52
3944692.52
3945685.64
3946678.89
3947672.27
3948665.77
3949659.39
3950653.14
3951647.02
3952641.02
3953635.14
3954629.39
3955623.77
3956618.27
3957612.89
3958607.64
3959602.52
3960597.52
3961592.64
6.65929392
6.68586095
6.5971457
6.63987583
6.60258789
6.76619171
6.7262334
6.75227038
6.7262334
6.81234509
6.74641213
6.73815249
6.67708346
6.7580945
6.69332367
6.7214257
6.7214257
6.78105763
6.67708346
6.74875955
6.71659477
6.78671695
6.76157277
6.7580945
6.72383244
6.79234443
6.72383244
6.75227038
6.72022016
6.79682372
6.74758653
6.75693239
6.74051936
6.80903931
6.73221071
6.7546041
6.78784498
6.84268328
6.77764659
6.81014245
6.81014245
1990
1990
1991
1991
1991
1991
1992
1992
1992
1992
1993
1993
1993
1993
1994
1994
1994
1994
1995
1995
1995
1995
1996
1996
1996
1996
1997
1997
1997
1997
1998
1998
1998
1998
1999
1999
1999
1999
2000
2000
2000
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
960
880
869
851
916
862
873
840
891
842
826
795
842
812
837
821
889
824
851
834
897
858
879
879
946
894
916
883
955
920
923
912
958
906
893
912
957
913
938
919
985
1990.625
1990.875
1991.125
1991.375
1991.625
1991.875
1992.125
1992.375
1992.625
1992.875
1993.125
1993.375
1993.625
1993.875
1994.125
1994.375
1994.625
1994.875
1995.125
1995.375
1995.625
1995.875
1996.125
1996.375
1996.625
1996.875
1997.125
1997.375
1997.625
1997.875
1998.125
1998.375
1998.625
1998.875
1999.125
1999.375
1999.625
1999.875
2000.125
2000.375
2000.625
3962587.89
3963583.27
3964578.77
3965574.39
3966570.14
3967566.02
3968562.02
3969558.14
3970554.39
3971550.77
3972547.27
3973543.89
3974540.64
3975537.52
3976534.52
3977531.64
3978528.89
3979526.27
3980523.77
3981521.39
3982519.14
3983517.02
3984515.02
3985513.14
3986511.39
3987509.77
3988508.27
3989506.89
3990505.64
3991504.52
3992503.52
3993502.64
3994501.89
3995501.27
3996500.77
3997500.39
3998500.14
3999500.02
4000500.02
4001500.14
4002500.39
6.86693328
6.77992191
6.76734313
6.74641213
6.82001636
6.75925527
6.77193556
6.73340189
6.79234443
6.73578001
6.71659477
6.67834211
6.73578001
6.69950034
6.72982407
6.71052311
6.79009724
6.71417053
6.74641213
6.7262334
6.79905586
6.7546041
6.7787849
6.7787849
6.85224257
6.79570578
6.82001636
6.7833252
6.86171134
6.82437367
6.82762923
6.81563999
6.86484778
6.80903931
6.79458658
6.81563999
6.86380339
6.81673588
6.84374995
6.82328612
6.89264164
2000
2001
2001
2001
2001
2002
2002
2002
2002
2003
2003
2003
2003
2004
2004
2004
2004
2005
2005
2005
2005
2006
2006
2006
2006
2007
2007
2007
2007
2008
2008
2008
2008
2009
2009
2009
2009
2010
2010
2010
2010
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
934
968
964
996
919
971
948
989
946
959
944
1027
962
950
995
1065
992
1021
994
1042
1002
1023
990
1030
952
966
946
1002
942
966
962
1021
954
977
974
1009
953
980
990
1021
976
2000.875
2001.125
2001.375
2001.625
2001.875
2002.125
2002.375
2002.625
2002.875
2003.125
2003.375
2003.625
2003.875
2004.125
2004.375
2004.625
2004.875
2005.125
2005.375
2005.625
2005.875
2006.125
2006.375
2006.625
2006.875
2007.125
2007.375
2007.625
2007.875
2008.125
2008.375
2008.625
2008.875
2009.125
2009.375
2009.625
2009.875
2010.125
2010.375
2010.625
2010.875
4003500.77
4004501.27
4005501.89
4006502.64
4007503.52
4008504.52
4009505.64
4010506.89
4011508.27
4012509.77
4013511.39
4014513.14
4015515.02
4016517.02
4017519.14
4018521.39
4019523.77
4020526.27
4021528.89
4022531.64
4023534.52
4024537.52
4025540.64
4026543.89
4027547.27
4028550.77
4029554.39
4030558.14
4031562.02
4032566.02
4033570.14
4034574.39
4035578.77
4036583.27
4037587.89
4038592.64
4039597.52
4040602.52
4041607.64
4042612.89
4043618.27
6.83947644
6.87523209
6.87109129
6.90374726
6.82328612
6.87832647
6.8543545
6.89669433
6.85224257
6.86589107
6.85012617
6.93439721
6.86901445
6.85646198
6.90274274
6.97073008
6.89972311
6.92853782
6.90173721
6.94889722
6.90975328
6.93049477
6.89770494
6.93731408
6.85856503
6.87316383
6.85224257
6.90975328
6.84800527
6.87316383
6.86901445
6.92853782
6.86066367
6.88448665
6.8814113
6.91671502
6.8596149
6.88755257
6.89770494
6.92853782
6.88346259
2011
2011
2011
2011
2012
2012
2012
2012
2013
2013
2013
2013
2014
2014
2014
2014
2015
2015
2015
2015
2016
2016
2016
2016
2017
2017
2017
2017
2018
2018
2018
2018
2019
2019
2019
2019
2020
2020
2020
2020
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
985
941
1010
978
984
966
1021
997
1025
996
1069
1003
1018
1042
1099
1025
1030
1026
1080
1015
1030
1001
1026
976
1015
1008
1073
994
1007
975
1033
966
996
956
1003
962
978
983
1041
999
2011.125
2011.375
2011.625
2011.875
2012.125
2012.375
2012.625
2012.875
2013.125
2013.375
2013.625
2013.875
2014.125
2014.375
2014.625
2014.875
2015.125
2015.375
2015.625
2015.875
2016.125
2016.375
2016.625
2016.875
2017.125
2017.375
2017.625
2017.875
2018.125
2018.375
2018.625
2018.875
2019.125
2019.375
2019.625
2019.875
2020.125
2020.375
2020.625
2020.875
4044623.77
4045629.39
4046635.14
4047641.02
4048647.02
4049653.14
4050659.39
4051665.77
4052672.27
4053678.89
4054685.64
4055692.52
4056699.52
4057706.64
4058713.89
4059721.27
4060728.77
4061736.39
4062744.14
4063752.02
4064760.02
4065768.14
4066776.39
4067784.77
4068793.27
4069801.89
4070810.64
4071819.52
4072828.52
4073837.64
4074846.89
4075856.27
4076865.77
4077875.39
4078885.14
4079895.02
4080905.02
4081915.14
4082925.39
4083935.77
6.89264164
6.84694314
6.91770561
6.88550967
6.8916259
6.87316383
6.92853782
6.90475077
6.93244789
6.90374726
6.97447891
6.91075079
6.9255952
6.94889722
7.00215595
6.93244789
6.93731408
6.93342303
6.98471632
6.92264389
6.93731408
6.90875478
6.93342303
6.88346259
6.92264389
6.91572345
6.97821374
6.90173721
6.91473089
6.88243747
6.94022247
6.87316383
6.90374726
6.86275791
6.91075079
6.86901445
6.88550967
6.89060912
6.94793707
6.90675478
Annualized Growth Rate
Expenditure
1200
1000
800
600
400
200
1950.125
1952.375
1954.625
1956.875
1959.125
1961.375
1963.625
1965.875
1968.125
1970.375
1972.625
1974.875
1977.125
1979.375
1981.625
1983.875
1986.125
1988.375
1990.625
1992.875
1995.125
1997.375
1999.625
0
Expenditure
Log – Scale
7.2
7
6.8
6.6
6.4
6.2
6
5.8
5.6
1
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
181
190
199
-9.728451411
10.70981356
-10.2759734
7.704120467
1.98419208
8.65200972
-17.69307082
4.827800027
1.626052087
2.390552085
-12.34585598
10.35771893
0.40080214
9.166718853
-10.37397698
6.276569555
-0.571974867
11.54433558
-12.69819453
11.67078823
-2.262933813
10.99275357
-10.99275357
4.643998682
-5.884050002
6.720874969
-6.187540372
6.851994644 log
-4.573193143 Year
14.19447741
-8.142210472
1.778543243
-1.452810056
12.94580672
-7.873404054
-2.029734006
-6.013184104
7.578161271
Xt
2015
2016
2017
2018
2019
35.7
36.1
36.5
37.1
37.6
log(Xt)
log(Xt)?log(Xt?1)
3.5752 -3.5863
1.10% 0.011142177
3.5973
1.10% 0.011019395
3.6136
1.60% 0.016304709
3.627
1.30%
Annualized Growth Rate
20
20
15
10
5
0
-5
1
9
17
25
33
41
49
57
65
73
81
89
97
105
113
121
129
137
145
153
161
169
177
185
-8.58827087
-3.267702603
-0.525855725
10.02508226
-9.674204704
-2.12397365
-3.45803336
14.77812315
-4.408877298
2.14706844
-1.98026273
9.984533497
-6.544390825
-2.445109586
1.148494987
12.55469096
-9.502245142
1.569890954
0.930239266
12.18898176
-2.770260255
-1.699757637
-1.294051128
4.249931352
-9.753178583
-1.385703466
-1.248066122
11.96999135
-11.50013927
1.704146585
-5.68873744
14.22332587
-5.80714664
3.812778544
1.994368097
6.682785911
-9.109743002
3.409421134
-5.158736879
14.48639943
-4.422046848
-10
-15
-20
part b
SUMMARY OUTPUT
c/d:e
Regression Statistics
Multiple R
0.970066471
R Square
0.941028959
Adjusted R Square
0.940609236
Standard Error 39.5441266
Observations
284
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
X Variable 2
SS
MS
F
2 7011880.23 3505940.11 2242.025345
281 439410.364 1563.73795
283 7451290.59
Coefficients Standard Error
t Stat
-238131.9479 24618.8551 -9.6727466
233.1154786 24.800495 9.39963007
-0.056791757 0.00624534 -9.0934666
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.96108027
R Square
0.923675285
Adjusted R Square0.92340463
Standard Error 44.90800793
Observations
284
c/d
P-value
2.73571E-19
1.99867E-18
1.79499E-17
ANOVA
df
Regression
Residual
Total
SS
MS
F
1 6882572.96 6882572.96 3412.740314
282 568717.628 2016.72918
283 7451290.59
Coefficients Standard Error
t Stat
-14270.75651 258.162178 -55.278262
7.595409766 0.13001683 58.4186641
Intercept
X Variable 1
P-value
2.3701E-153
1.4104E-159
Expenditure with a Linear Trend and a Quad
1200
1000
800
600
400
200
0
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
-0.935210557
-4.671178858
1.535270909
-9.891778744
4.777027627
-5.390526484
9.391059945
-1.410460618
3.90021578
-1.931094491
9.682839872
-7.615226588
1.757989832
-4.244305751
4.779066384
-6.045796904
4.432858711
-6.147186409
7.359322463
-9.691789719
-0.29542119
-1.640603539
7.807431707
-7.957920824
3.985767429
0.57720218
10.89511838
-3.813742915
3.296277336
-6.289698118
10.6050885
-6.412452817
-2.412985706
-2.472653447
9.03668907
-8.343685603
3.661425938
-1.610773082
8.802574732
-6.396041483
4.519813838
Expenditure
Line Trend
Log Expenditure with a Linear and a Quad
7.2
7
6.8
6.6
6.4
6.2
6
5.8
5.6
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
-1.526747213
2.656702738
-8.871524518
4.273013194
-3.728794164
16.36038225
-3.99583123
2.603697378
-2.603697378
8.611169182
-6.59329656
-0.825963398
-6.106903335
8.101104318
-6.477083616
2.810203252
0
5.963192515
-10.39741647
7.167608624
-3.216477397
7.012217708
-2.51441818
-0.347826438
-3.426206361
6.851198665
-6.851198665
2.843793532
-3.205022101
7.660356314
-4.923719145
0.934586242
-1.641302964
6.851994644
-7.682859958
2.239339302
3.324088282
5.483829993
-6.50366886
3.249585648
0
Log – Scale
L-Linear Trend
Part B – 2
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.945697285
R Square
0.894343355
Adjusted R Square
0.893968686
Standard Error 0.069836545
Observations
284
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
MS
F
1 11.6418518 11.6418518 2387.022851
282 1.37535432 0.00487714
283 13.0172061
Coefficients Standard Error
t Stat
-12.93846654 0.40146859 -32.227843
0.009878405 0.00020219 48.8571679
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.969503787
R Square
0.939937593
Adjusted R Square
0.939510103
Standard Error 0.052748133
P-value
1.52398E-96
1.1748E-139
5.679083435
-8.701137699
-1.257878221
-2.093099669
7.36042361
-6.076109401
1.268028518
-3.8533664
5.894253563
-5.656441323
-1.918524072
-3.825265887
5.743789959
-3.627967408
3.032373033
-1.930096104
7.957412606
-7.59267056
3.224159866
-2.017872621
7.28224597
-4.445176257
2.41807982
0
7.345767137
-5.653679388
2.43105895
-3.669116407
7.838613988
-3.733767044
0.325556446
-1.198924443
4.92077879
-5.580847193
-1.445272517
2.10534092
4.816340138
-4.706751086
2.701406841
-2.046382665
6.935551882
Observations
284
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
X Variable 2
SS
MS
F
2 12.2353614 6.11768068 2198.733596
281 0.78184473 0.00278237
283 13.0172061
Coefficients Standard Error
t Stat
-492.5407268 32.8392296 -14.998547
0.49303466 0.03308152 14.9036277
-0.000121671 8.3307E-06 -14.605175
P-value
9.26101E-38
2.04848E-37
2.47672E-36
-5.316520294
3.575564905
-0.414079267
3.265596297
-8.046113523
5.504034594
-2.397196604
4.233982937
-4.445176257
1.364850583
-1.576490874
8.427104378
-6.538275926
-1.255246607
4.628075256
6.798734098
-7.100697086
2.881471088
-2.680061151
4.716001566
-3.914394067
2.074148431
-3.278982282
3.96091381
-7.874904643
1.459879942
-2.092126516
5.751071259
-6.174800707
2.515855964
-0.414938355
5.95233675
-6.787414672
2.382298059
-0.30753484
3.530371671
-5.71001167
2.793766801
1.015237146
3.083287504
-4.507523175
0.917905476
-4.569850159
7.076247025
-3.21959398
0.611622702
-1.846206284
5.537398395
-2.37870482
2.769712161
-2.870063399
7.073165344
-6.372812306
1.484440915
2.33020252
5.325873209
-6.970806283
0.486618965
-0.389105549
5.129329439
-6.207242864
1.467018975
-2.855930191
2.466824642
-4.996043932
3.918130506
-0.692044284
6.2490294
-7.647653597
1.299368606
-3.229342172
5.778499812
-6.705863491
3.058342337
-4.098934453
4.799287491
-4.17363373
1.649521937
0.509945011
5.732794847
-4.118228997
1997.375
1999.625
2001.875
2004.125
2006.375
2008.625
2010.875
2013.125
2015.375
2017.625
2019.875
190
199
208
217
226
235
244
253
262
271
280
wth Rate
Line Trend Quadratic Trend
541.241957
494.0302591
543.140809
496.9300663
545.039662
499.8227745
546.938514
502.7083837
548.837367
505.586894
550.736219
508.4583053
552.635072
511.3226176
554.533924
514.1798309
556.432777
517.0299453
558.331629
519.8729607
560.230481
522.7088772
562.129334
525.5376946
564.028186
528.3594131
565.927039
531.1740327
567.825891
533.9815532
569.724744
536.7819748
571.623596
539.5752974
573.522449
542.3615211
575.421301
545.1406458
577.320153
547.9126715
579.219006
550.6775982
581.117858
553.435426
583.016711
556.1861548
584.915563
558.9297846
586.814416
561.6663155
588.713268
564.3957474
590.61212
567.1180803
592.510973
569.8333143
594.409825
572.5414493
596.308678
575.2424853
598.20753
577.9364223
600.106383
580.6232604
602.005235
583.3029995
603.904088
585.9756396
605.80294
588.6411808
607.701792
591.299623
609.600645
593.9509662
611.499497
596.5952105
613.39835
599.2323558
185
193
201
209
217
225
233
241
249
257
265
273
281
Significance F
1.8826E-173
Lower 95%
-286592.7385
184.2971403
-0.06908534
Upper 95% Lower 95.0%
-189671.16 -286592.74
281.933817 184.29714
-0.0444982 -0.0690853
Upper 95.0%
-189671.16
281.933817
-0.0444982
615.297202
617.196055
619.094907
620.99376
622.892612
624.791464
626.690317
628.589169
630.488022
632.386874
634.285727
636.184579
638.083432
639.982284
641.881136
643.779989
645.678841
647.577694
649.476546
651.375399
653.274251
655.173103
657.071956
658.970808
660.869661
662.768513
664.667366
666.566218
668.465071
670.363923
672.262775
674.161628
676.06048
677.959333
679.858185
681.757038
683.65589
685.554743
687.453595
689.352447
691.2513
601.8624021
604.4853494
607.1011978
609.7099472
612.3115977
614.9061491
617.4936016
620.0739552
622.6472097
625.2133653
627.772422
630.3243796
632.8692383
635.406998
637.9376587
640.4612205
642.9776833
645.4870472
647.989312
650.4844779
652.9725448
655.4535128
657.9273818
660.3941518
662.8538228
665.3063949
667.751868
670.1902422
672.6215173
675.0456935
677.4627708
679.872749
682.2756283
684.6714086
687.06009
689.4416723
691.8161558
694.1835402
696.5438257
698.8970122
701.2430997
162
169
176
183
190
197
204
211
218
225
232
239
246
253
260
267
274
281
693.150152
Significance F
695.049005
1.4104E-159
696.947857
698.84671
700.745562
702.644415
Lower 95%
Upper 95% Lower 95.0% Upper 95.0% 704.543267
-14778.92602 -13762.587 -14778.926 -13762.587 706.442119
7.339483082 7.85133645 7.33948308 7.85133645 708.340972
710.239824
712.138677
714.037529
715.936382
717.835234
and a Quadratic Trend
719.734086
721.632939
723.531791
725.430644
727.329496
729.228349
731.127201
733.026054
734.924906
736.823758
738.722611
740.621463
742.520316
744.419168
746.318021
748.216873
Quadratic Trend
750.115726
752.014578
753.91343
755.812283
757.711135
and a Quadratic Trend
759.609988
761.50884
763.407693
765.306545
767.205398
769.10425
703.5820883
705.9139779
708.2387685
710.5564601
712.8670528
715.1705465
717.4669413
719.756237
722.0384338
724.3135317
726.5815305
728.8424304
731.0962314
733.3429333
735.5825363
737.8150403
740.0404454
742.2587515
744.4699586
746.6740667
748.8710759
751.0609861
753.2437973
755.4195096
757.5881228
759.7496372
761.9040525
764.0513689
766.1915863
768.3247047
770.4507242
772.5696447
774.6814662
776.7861888
778.8838124
780.974337
783.0577627
785.1340894
787.2033171
789.2654458
791.3204756
155
162
169
176
183
190
197
204
211
218
225
232
239
246
253
260
267
274
281
771.003102
772.901955
774.800807
776.69966
778.598512
780.497365
782.396217
784.29507
786.193922
788.092774
L-Quadratic Trend
789.991627
791.890479
793.789332
795.688184
797.587037
799.485889
801.384741
803.283594
805.182446
807.081299
808.980151
810.879004
812.777856
814.676709
816.575561
Significance F
818.474413
1.1748E-139
820.373266
822.272118
824.170971
826.069823
Lower 95%
Upper 95% Lower 95.0% Upper 95.0% 827.968676
-13.72872209 -12.148211 -13.728722 -12.148211 829.867528
0.009480413 0.0102764 0.00948041 0.0102764 831.766381
833.665233
835.564085
837.462938
839.36179
841.260643
843.159495
845.058348
846.9572
793.3684064
795.4092382
797.4429711
799.469605
801.4891399
803.5015759
805.5069129
807.5051509
809.4962899
811.48033
813.4572711
815.4271132
817.3898564
819.3455006
821.2940458
823.2354921
825.1698394
827.0970877
829.0172371
830.9302874
832.8362389
834.7350913
836.6268448
838.5114993
840.3890548
842.2595114
844.122869
845.9791276
847.8282872
849.6703479
851.5053096
853.3331724
855.1539362
856.967601
858.7741668
860.5736337
862.3660016
864.1512705
865.9294404
867.7005114
869.4644834
Significance F
2.4756E-172
Lower 95%
Upper 95% Lower 95.0% Upper 95.0%
-557.1828487 -427.8986 -557.18285 -427.8986
0.427915603 0.55815372 0.4279156 0.55815372
-0.00013807 -0.0001053 -0.0001381 -0.0001053
848.856053
850.754905
852.653757
854.55261
856.451462
858.350315
860.249167
862.14802
864.046872
865.945724
867.844577
869.743429
871.642282
873.541134
875.439987
877.338839
879.237692
881.136544
883.035396
884.934249
886.833101
888.731954
890.630806
892.529659
894.428511
896.327364
898.226216
900.125068
902.023921
903.922773
905.821626
907.720478
909.619331
911.518183
913.417036
915.315888
917.21474
919.113593
921.012445
922.911298
924.81015
871.2213565
872.9711306
874.7138057
876.4493818
878.177859
879.8992372
881.6135164
883.3206967
885.020778
886.7137603
888.3996436
890.078428
891.7501134
893.4146999
895.0721873
896.7225758
898.3658654
900.0020559
901.6311475
903.2531402
904.8680338
906.4758285
908.0765242
909.670121
911.2566187
912.8360175
914.4083174
915.9735182
917.5316201
919.0826231
920.626527
922.163332
923.693038
925.2156451
926.7311532
928.2395623
929.7408724
931.2350836
932.7221958
934.202209
935.6751233
926.709003
928.607855
930.506707
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936.203265
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940.00097
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1004.56195
1006.46081
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1038.7413
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1003.580953
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1021.138182
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1024.023547
1024.971138
1025.911629
1026.845022
1027.771315
1028.69051
1029.602606
1030.507602
1031.4055
L-Linear Trend L-Quadratic Trend
6.325658073
6.2245113
6.328127674
6.229125356
6.330597275
6.233724203
6.333066876
6.238307841
6.335536478
6.24287627
6.338006079
6.24742949
6.34047568
6.251967501
6.342945281
6.256490304
6.345414883
6.260997897
6.347884484
6.265490282
6.350354085
6.269967458
6.352823686
6.274429424
6.355293288
6.278876182
6.357762889
6.283307731
6.36023249
6.287724072
6.362702091
6.292125203
6.365171693
6.296511125
6.367641294
6.300881839
6.370110895
6.305237343
6.372580496
6.309577639
6.375050098
6.313902725
6.377519699
6.318212603
6.3799893
6.322507272
6.382458901
6.326786732
6.384928503
6.331050983
6.387398104
6.335300026
6.389867705
6.339533859
6.392337307
6.343752484
6.394806908
6.347955899
6.397276509
6.352144106
6.39974611
6.356317104
6.402215712
6.360474892
6.404685313
6.364617472
6.407154914
6.368744844
6.409624515
6.372857006
6.412094117
6.376953959
6.414563718
6.381035703
6.417033319
6.385102239
6.41950292
6.389153565
Detrended
12.9697409
-36.930066
12.1772255
-40.708384
-6.586894
0.54169472
43.6773824
-49.179831
-29.029945
-23.872961
-14.708877
-76.537695
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14.0184468
-42.781975
-13.575297
-19.361521
41.8593542
-30.912671
30.3224018
14.564574
77.8138452
9.07021536
33.3336845
-3.3957474
32.8819197
-5.8333143
31.4585507
1.75751472
87.0635777
32.3767396
40.6970005
29.0243604
111.358819
55.700377
40.0490338
0.40478951
44.7676442
cycle
-11.815676
-14.301285
1.82020498
-10.451206
-8.1155186
-11.572732
-14.622846
-38.665862
-34.901778
-35.330596
-27.752314
-33.366934
-20.774454
-18.574876
-3.9681985
-12.954422
1.66645319
7.29442748
26.7295007
20.171673
33.0209442
26.2773143
29.9407835
13.2113516
17.6890186
11.3737847
29.4656497
29.3646137
38.6706766
38.1838386
60.1040995
53.8314593
55.3659182
47.307476
50.4561327
26.0118885
8.37474319
low frequency hif
488.007099
488.407099
507.407099
498.007099
503.207099
502.607099
502.407099
481.207099
487.807099
490.207099
500.607099
497.807099
513.207099
518.207099
535.607099
529.407099
546.807099
555.207099
577.407099
573.607099
589.207099
585.207099
591.607099
577.607099
584.807099
581.207099
602.007099
604.607099
616.607099
618.807099
643.407099
639.807099
644.007099
638.607099
644.407099
622.607099
607.607099
23.992901
-26.407099
-8.407099
10.992901
51.792901
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14.792901
20.192901
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2.19290103
34.792901
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3.59290103
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44.792901
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1.99290103
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55.992901
8.39290103
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36.392901
6.421972522
6.424442123
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6.431850927
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6.436790129
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6.449138135
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6.478773351
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6.486182154
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6.491121357
6.493590958
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6.542163095
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81.5155221
59.0274552
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33.0726182
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47.8097578
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29.127251
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10.3285914
21.9