Work 2

First

Below I load the data, then make a boxplot of temperatures by month.Then I decomposed the data and plotted it. I used the aggregate function to remove the seasons and then plotted the data.

setwd("C:/Users/Faythe/Downloads")
load("kbli.Rdata")
kbli.ts

##             tMaxF    tAvgF    tMinF
## Jan 1976 45.61290 40.77419 35.80645
## Feb 1976 44.79310 39.82759 34.68966
## Mar 1976 45.64516 39.35484 32.96774
## Apr 1976 56.30000 47.60000 38.53333
## May 1976 58.54839 52.48387 44.83871
## Jun 1976 64.40000 56.83333 49.16667
## Jul 1976 70.64516 62.61290 54.32258
## Aug 1976 66.54839 61.06452 55.35484
## Sep 1976 66.63333 58.73333 50.60000
## Oct 1976 58.83871 51.35484 43.64516
## Nov 1976 52.16667 44.46667 36.66667
## Dec 1976 48.25806 42.96774 37.45161
## Jan 1977 41.12903 35.54839 29.93548
## Feb 1977 52.53571 45.35714 38.00000
## Mar 1977 48.77419 43.90323 39.16129
## Apr 1977 59.13333 51.40000 43.36667
## May 1977 60.00000 53.35484 46.58065
## Jun 1977 67.93333 60.66667 53.00000
## Jul 1977 69.00000 61.77419 54.29032
## Aug 1977 75.61290 66.64516 57.70968
## Sep 1977 64.73333 57.60000 50.13333
## Oct 1977 59.12903 51.12903 43.12903
## Nov 1977 49.00000 43.80000 38.93333
## Dec 1977 42.77419 37.90323 32.83871
## Jan 1978 43.29032 38.74194 34.12903
## Feb 1978 49.71429 43.28571 37.03571
## Mar 1978 54.25806 47.22581 39.70968
## Apr 1978 56.73333 50.16667 43.16667
## May 1978 63.29032 55.38710 47.03226
## Jun 1978 70.06667 61.70000 53.13333
## Jul 1978 71.70968 63.32258 54.77419
## Aug 1978 69.83871 62.48387 55.03226
## Sep 1978 62.63333 56.90000 50.76667
## Oct 1978 58.51613 50.58065 42.54839
## Nov 1978 44.26667 38.20000 32.13333
## Dec 1978 39.93548 35.25806 30.51613
## Jan 1979 36.03226 30.22581 24.48387
## Feb 1979 44.53571 38.85714 33.14286
## Mar 1979 52.93548 44.83871 36.45161
## Apr 1979 54.60000 47.90000 41.20000
## May 1979 61.93548 54.22581 46.58065
## Jun 1979 65.53333 57.86667 50.13333
## Jul 1979 72.12903 63.45161 54.77419
## Aug 1979 69.83871 62.54839 55.35484
## Sep 1979 67.90000 60.03333 52.03333
## Oct 1979 58.58065 51.74194 44.70968
## Nov 1979 48.25000 40.75000 33.38333
## Dec 1979 48.25806 43.54839 38.41935
## Jan 1980 38.38710 32.80645 27.09677
## Feb 1980 48.34483 42.75862 37.13793
## Mar 1980 48.22581 42.74194 37.35484
## Apr 1980 59.10000 50.43333 41.46667
## May 1980 59.70968 52.93548 46.45161
## Jun 1980 63.20000 56.90000 50.53333
## Jul 1980 67.87097 60.87097 53.61290
## Aug 1980 66.41935 59.64516 52.70968
## Sep 1980 64.80000 57.83333 50.93333
## Oct 1980 60.00000 51.00000 41.93548
## Nov 1980 50.83333 45.13333 39.23333
## Dec 1980 44.41935 40.22581 36.03226
## Jan 1981 48.83871 41.83871 34.93548
## Feb 1981 48.14286 41.71429 35.10714
## Mar 1981 53.83871 46.06452 37.93548
## Apr 1981 54.60000 47.73333 40.76667
## May 1981 60.22581 53.96774 47.61290
## Jun 1981 61.46667 56.13333 50.46667
## Jul 1981 67.61290 61.38710 54.96774
## Aug 1981 72.35484 63.77419 55.35484
## Sep 1981 65.96667 58.00000 49.66667
## Oct 1981 55.87097 48.77419 41.54839
## Nov 1981 52.06667 45.70000 39.33333
## Dec 1981 43.58065 39.19355 34.45161
## Jan 1982 38.96774 35.03226 30.77419
## Feb 1982 45.10714 39.89286 34.71429
## Mar 1982 49.06452 41.77419 34.32258
## Apr 1982 53.83333 45.43333 36.83333
## May 1982 59.90323 52.29032 44.67742
## Jun 1982 68.73333 60.06667 51.53333
## Jul 1982 66.22581 59.96774 53.93548
## Aug 1982 68.64516 60.77419 53.16129
## Sep 1982 66.26667 58.50000 50.13333
## Oct 1982 58.06452 50.38710 42.45161
## Nov 1982 46.80000 40.30000 33.66667
## Dec 1982 45.16129 39.35484 33.64516
## Jan 1983 49.03226 43.25806 37.45161
## Feb 1983 51.14286 44.46429 37.82143
## Mar 1983 54.67742 47.48387 40.09677
## Apr 1983 56.96667 48.26667 39.50000
## May 1983 63.54839 55.54839 47.70968
## Jun 1983 64.33333 58.16667 52.03333
## Jul 1983 67.32258 60.64516 53.64516
## Aug 1983 70.64516 62.93548 55.03226
## Sep 1983 63.10000 55.26667 47.10000
## Oct 1983 54.96774 47.80645 40.58065
## Nov 1983 50.06667 46.03333 41.76667
## Dec 1983 35.93548 31.19355 26.41935
## Jan 1984 44.19355 39.25806 33.80645
## Feb 1984 48.13793 42.62069 36.93103
## Mar 1984 51.96774 45.41935 38.96774
## Apr 1984 53.96667 47.20000 40.36667
## May 1984 57.58065 51.16129 44.58065
## Jun 1984 62.70000 56.73333 50.73333
## Jul 1984 69.64516 61.29032 52.70968
## Aug 1984 69.48387 61.77419 54.19355
## Sep 1984 63.70000 55.83333 47.36667
## Oct 1984 53.41935 47.12903 40.74194
## Nov 1984 48.63333 44.00000 39.16667
## Dec 1984 36.48387 32.03226 27.64516
## Jan 1985 39.67742 34.16129 28.09677
## Feb 1985 43.03571 38.46429 33.67857
## Mar 1985 48.19355 42.45161 36.35484
## Apr 1985 55.03333 48.56667 41.76667
## May 1985 61.32258 54.06452 46.58065
## Jun 1985 66.06667 58.53333 50.90000
## Jul 1985 76.80645 66.64516 56.38710
## Aug 1985 71.96774 62.80645 53.54839
## Sep 1985 64.53333 56.70000 48.83333
## Oct 1985 56.16129 50.93548 45.58065
## Nov 1985 37.13333 32.53333 27.66667
## Dec 1985 40.09677 34.54839 29.09677
## Jan 1986 51.54839 45.16129 38.96774
## Feb 1986 47.10714 40.35714 33.50000
## Mar 1986 53.64516 46.96774 40.12903
## Apr 1986 52.30000 46.43333 40.26667
## May 1986 61.51613 54.22581 46.80645
## Jun 1986 67.86667 59.96667 51.76667
## Jul 1986 66.16129 59.58065 52.83871
## Aug 1986 73.96774 64.48387 55.25806
## Sep 1986 64.53333 57.33333 50.00000
## Oct 1986 60.00000 51.64516 43.16129
## Nov 1986 47.90000 43.33333 38.60000
## Dec 1986 47.38710 40.64516 33.70968
## Jan 1987 45.29032 39.90323 34.35484
## Feb 1987 50.39286 44.57143 38.39286
## Mar 1987 54.64516 47.29032 39.80645
## Apr 1987 58.10000 50.76667 43.43333
## May 1987 62.74194 54.96774 47.12903
## Jun 1987 68.20000 59.90000 51.43333
## Jul 1987 69.06452 61.80645 54.51613
## Aug 1987 71.96774 62.51613 52.87097
## Sep 1987 68.70000 59.03333 49.20000
## Oct 1987 62.12903 51.64516 41.41935
## Nov 1987 52.83333 47.33333 41.96667
## Dec 1987 43.06452 37.74194 32.45161
## Jan 1988 44.22581 38.09677 32.25806
## Feb 1988 48.20690 42.24138 36.20690
## Mar 1988 50.83871 44.48387 37.83871
## Apr 1988 55.90000 49.26667 42.36667
## May 1988 61.29032 54.16129 46.93548
## Jun 1988 65.16667 57.90000 50.46667
## Jul 1988 70.61290 62.12903 53.64516
## Aug 1988 70.54839 62.29032 53.83871
## Sep 1988 65.46667 57.03333 48.20000
## Oct 1988 58.80645 52.67742 46.90323
## Nov 1988 49.73333 45.50000 41.13333
## Dec 1988 45.67742 40.87097 35.87097
## Jan 1989 42.96774 38.54839 34.00000
## Feb 1989 39.75000 32.85714 25.85714
## Mar 1989 48.61290 42.54839 36.09677
## Apr 1989 60.50000 51.70000 42.73333
## May 1989 60.77419 54.00000 47.22581
## Jun 1989 68.90000 60.86667 53.03333
## Jul 1989 69.16129 61.80645 54.64516
## Aug 1989 69.03226 61.80645 54.48387
## Sep 1989 69.86667 59.00000 48.10000
## Oct 1989 58.38710 51.45161 44.22581
## Nov 1989 49.50000 44.80000 40.10000
## Dec 1989 45.54839 40.87097 36.16129
## Jan 1990 45.64516 41.19355 36.61290
## Feb 1990 44.10714 37.96429 31.85714
## Mar 1990 52.93548 44.87097 36.90323
## Apr 1990 57.40000 50.96667 44.53333
## May 1990 60.90323 54.83871 48.67742
## Jun 1990 65.20000 58.70000 52.33333
## Jul 1990 74.19355 65.45161 56.74194
## Aug 1990 74.09677 65.61290 56.80645
## Sep 1990 68.20000 60.00000 51.76667
## Oct 1990 55.48387 49.90323 44.12903
## Nov 1990 50.13333 45.30000 40.40000
## Dec 1990 38.67742 33.48387 28.22581
## Jan 1991 40.41935 35.54839 30.38710
## Feb 1991 52.50000 46.32143 40.07143
## Mar 1991 48.83871 42.38710 35.74194
## Apr 1991 55.40000 48.63333 42.00000
## May 1991 59.51613 53.67742 47.90323
## Jun 1991 63.40000 57.23333 50.96667
## Jul 1991 71.83871 63.64516 55.09677
## Aug 1991 71.51613 63.80645 55.87097
## Sep 1991 67.80000 59.03333 50.23333
## Oct 1991 57.09677 48.90323 40.58065
## Nov 1991 50.26667 45.03333 40.03333
## Dec 1991 47.32258 42.58065 37.80645
## Jan 1992 49.45161 43.38710 37.29032
## Feb 1992 52.13793 44.96552 37.62069
## Mar 1992 57.48387 48.54839 39.32258
## Apr 1992 59.40000 51.83333 43.96667
## May 1992 65.54839 57.00000 48.45161
## Jun 1992 69.60000 62.30000 54.96667
## Jul 1992 69.64516 63.03226 56.41935
## Aug 1992 70.32258 62.58065 54.64516
## Sep 1992 63.50000 55.96667 48.30000
## Oct 1992 58.22581 52.00000 45.74194
## Nov 1992 48.56667 43.63333 38.13333
## Dec 1992 40.25806 35.67742 31.09677
## Jan 1993 38.64516 32.45161 26.00000
## Feb 1993 46.50000 38.57143 30.32143
## Mar 1993 53.38710 46.16129 38.83871
## Apr 1993 55.16667 49.96667 44.53333
## May 1993 65.48387 58.09677 50.80645
## Jun 1993 64.43333 58.73333 53.16667
## Jul 1993 65.03226 59.96774 54.74194
## Aug 1993 69.22581 62.09677 54.64516
## Sep 1993 66.80000 57.16667 47.33333
## Oct 1993 59.32258 52.41935 45.41935
## Nov 1993 45.90000 39.16667 32.00000
## Dec 1993 45.19355 39.74194 34.09677
## Jan 1994 49.67742 44.64516 39.35484
## Feb 1994 43.96429 38.53571 33.21429
## Mar 1994 54.16129 46.41935 38.58065
## Apr 1994 57.03333 51.10000 44.90000
## May 1994 63.00000 55.80645 48.45161
## Jun 1994 64.83333 58.00000 50.80000
## Jul 1994 72.16129 63.74194 55.25806
## Aug 1994 72.06452 64.03226 55.93548
## Sep 1994 67.63333 59.50000 51.36667
## Oct 1994 56.77419 50.35484 43.22581
## Nov 1994 46.30000 41.13333 35.60000
## Dec 1994 44.80645 39.58065 34.29032
## Jan 1995 47.67742 40.67742 33.64516
## Feb 1995 48.71429 42.89286 36.85714
## Mar 1995 52.58065 44.74194 37.03226
## Apr 1995 56.46667 49.10000 41.66667
## May 1995 64.90323 57.03226 48.96774
## Jun 1995 68.76667 60.90000 53.00000
## Jul 1995 70.74194 63.51613 56.25806
## Aug 1995 67.12903 60.16129 53.09677
## Sep 1995 69.80000 61.06667 52.30000
## Oct 1995 55.45161 50.09677 44.19355
## Nov 1995 53.13333 47.20000 41.16667
## Dec 1995 45.48387 40.19355 34.74194
## Jan 1996 40.25806 35.87097 31.19355
## Feb 1996 48.20690 40.68966 33.37931
## Mar 1996 51.03226 44.22581 37.38710
## Apr 1996 56.46667 50.66667 44.70000
## May 1996 58.32258 52.22581 46.19355
## Jun 1996 65.10000 58.16667 51.23333
## Jul 1996 73.16129 63.96774 55.00000
## Aug 1996 72.51613 63.96774 55.22581
## Sep 1996 62.43333 55.83333 49.03333
## Oct 1996 56.35484 49.70968 43.03226
## Nov 1996 44.93333 40.00000 34.86667
## Dec 1996 38.06452 33.58065 28.87097
## Jan 1997 43.09677 38.25806 33.35484
## Feb 1997 46.92857 40.35714 33.75000
## Mar 1997 48.77419 43.19355 37.25806
## Apr 1997 55.93333 47.93333 39.66667
## May 1997 64.96774 57.25806 49.22581
## Jun 1997 65.33333 59.16667 53.06667
## Jul 1997 69.45161 62.70968 55.70968
## Aug 1997 74.51613 65.93548 57.38710
## Sep 1997 68.56667 60.56667 52.10000
## Oct 1997 56.41935 50.96774 45.35484
## Nov 1997 53.56667 46.16667 38.73333
## Dec 1997 46.87097 40.96774 34.93548
## Jan 1998 45.03226 40.29032 35.25806
## Feb 1998 52.03571 46.03571 39.71429
## Mar 1998 53.12903 46.61290 39.87097
## Apr 1998 57.73333 49.43333 40.93333
## May 1998 60.58065 54.61290 48.87097
## Jun 1998 65.60000 59.36667 53.40000
## Jul 1998 71.51613 64.58065 57.74194
## Aug 1998 72.90323 64.93548 56.90323
## Sep 1998 68.90000 59.00000 49.20000
## Oct 1998 58.48387 50.38710 42.45161
## Nov 1998 50.23333 45.50000 40.66667
## Dec 1998 43.80645 39.03226 34.38710
## Jan 1999 45.48387 41.12903 36.70968
## Feb 1999 47.89286 42.57143 37.53571
## Mar 1999 49.87097 43.06452 35.83871
## Apr 1999 56.06667 46.46667 37.23333
## May 1999 58.93548 50.90323 43.29032
## Jun 1999 63.26667 56.63333 50.13333
## Jul 1999 68.54839 60.19355 52.48387
## Aug 1999 70.25806 62.35484 54.77419
## Sep 1999 66.63333 56.06667 46.20000
## Oct 1999 58.29032 47.96774 38.51613
## Nov 1999 50.56667 45.16667 39.73333
## Dec 1999 44.38710 39.83871 35.19355
## Jan 2000 42.87097 37.67742 32.32258
## Feb 2000 49.14424 43.10345 37.11073
## Mar 2000 52.97183 50.00000 47.35211
## Apr 2000 54.26056 50.00000 46.49296
## May 2000 58.38301 51.35484 44.55111
## Jun 2000 63.60000 56.86667 50.00000
## Jul 2000 69.83871 61.19355 53.03226
## Aug 2000 62.30645 57.91935 55.09677
## Sep 2000 65.80000 56.76667 47.76667
## Oct 2000 58.48387 49.90323 42.06452
## Nov 2000 47.80000 40.73333 33.53333
## Dec 2000 42.54839 36.83871 30.54839
## Jan 2001 46.48387 39.87097 33.32258
## Feb 2001 45.78571 38.00000 30.00000
## Mar 2001 51.25806 44.09677 36.64516
## Apr 2001 55.03333 46.96667 39.86667
## May 2001 61.00000 52.48387 44.54839
## Jun 2001 63.33333 55.66667 48.43333
## Jul 2001 68.32258 60.41935 52.90323
## Aug 2001 69.77419 61.48387 53.74194
## Sep 2001 64.50000 56.16667 48.23333
## Oct 2001 55.00000 48.09677 41.67742
## Nov 2001 51.16667 45.46667 39.50000
## Dec 2001 43.70968 38.48387 33.41935
## Jan 2002 43.70968 38.83871 34.09677
## Feb 2002 46.50000 39.71429 33.00000
## Mar 2002 44.03226 38.03226 31.83871
## Apr 2002 54.56667 46.70000 39.10000
## May 2002 59.22581 51.12903 43.96774
## Jun 2002 67.50000 59.06667 51.33333
## Jul 2002 70.06452 61.58065 53.41935
## Aug 2002 71.45161 61.70968 52.58065
## Sep 2002 66.20000 56.23333 46.83333
## Oct 2002 55.67742 47.54839 39.67742
## Nov 2002 52.86667 45.56667 38.30000
## Dec 2002 47.32258 41.45161 35.61290
## Jan 2003 49.64516 43.03226 36.35484
## Feb 2003 46.25000 39.21429 32.28571
## Mar 2003 50.48387 45.09677 39.48387
## Apr 2003 54.83333 48.46667 42.46667
## May 2003 60.74194 52.87097 45.38710
## Jun 2003 68.76667 59.66667 51.10000
## Jul 2003 73.80645 63.58065 54.25806
## Aug 2003 73.22581 62.54839 52.70968
## Sep 2003 67.93333 58.23333 49.16667
## Oct 2003 58.32258 52.19355 46.38710
## Nov 2003 46.40000 39.86667 33.30000
## Dec 2003 45.67742 40.41935 34.90323
## Jan 2004 43.51613 38.41935 33.38710
## Feb 2004 49.06897 41.75862 34.41379
## Mar 2004 53.09677 46.03226 38.64516
## Apr 2004 61.36667 50.66667 40.80000
## May 2004 63.03226 54.41935 46.87097
## Jun 2004 68.83333 59.93333 51.50000
## Jul 2004 73.45161 64.77419 56.74194
## Aug 2004 72.32258 64.32258 57.00000
## Sep 2004 63.16667 55.80000 49.03333
## Oct 2004 57.41935 50.32258 43.74194
## Nov 2004 48.90000 43.00000 36.76667
## Dec 2004 45.38710 40.80645 36.35484
## Jan 2005 43.61290 38.19355 32.80645
## Feb 2005 48.89286 39.46429 29.78571
## Mar 2005 54.09677 46.58065 38.77419
## Apr 2005 57.73333 49.53333 41.73333
## May 2005 65.06452 56.67742 48.83871
## Jun 2005 65.13333 58.03333 51.56667
## Jul 2005 71.48387 62.19355 53.70968
## Aug 2005 72.29032 62.54839 53.29032
## Sep 2005 64.36667 55.20000 46.46667
## Oct 2005 58.25806 51.51613 45.06452
## Nov 2005 46.03333 41.06667 36.00000
## Dec 2005 45.09677 39.48387 33.83871
## Jan 2006 48.48387 44.09677 39.77419
## Feb 2006 45.75000 39.60714 33.14286
## Mar 2006 51.54839 43.80645 35.83871
## Apr 2006 55.90000 47.76667 39.90000
## May 2006 63.16129 53.54839 44.70968
## Jun 2006 68.93333 59.76667 51.50000
## Jul 2006 71.58065 62.61290 54.48387
## Aug 2006 70.74194 61.29032 52.48387
## Sep 2006 67.36667 57.16667 47.53333
## Oct 2006 57.25806 48.70968 40.54839
## Nov 2006 47.86667 43.00000 37.76667
## Dec 2006 47.22581 40.83871 34.48387
## Jan 2007 42.77419 36.45161 30.19355
## Feb 2007 47.32143 41.82143 36.32143
## Mar 2007 51.45161 45.19355 39.12903
## Apr 2007 55.80000 48.00000 40.06667
## May 2007 62.25806 53.19355 44.58065
## Jun 2007 64.90000 57.36667 50.53333
## Jul 2007 72.45161 63.87097 55.77419
## Aug 2007 70.29032 60.96774 52.16129
## Sep 2007 64.60000 55.80000 47.46667
## Oct 2007 56.41935 48.74194 41.80645
## Nov 2007 47.90000 41.16667 34.53333
## Dec 2007 43.16129 38.03226 33.25806
## Jan 2008 41.32258 36.35484 31.35484
## Feb 2008 47.34483 40.72414 33.96552
## Mar 2008 47.90323 41.16129 34.96774
## Apr 2008 51.80000 44.66667 38.03333
## May 2008 60.29032 52.77419 45.67742
## Jun 2008 62.60000 55.10000 48.16667
## Jul 2008 68.54839 60.32258 52.74194
## Aug 2008 69.83871 61.12903 52.87097
## Sep 2008 66.40000 56.30000 46.73333
## Oct 2008 56.45161 47.83871 39.70968
## Nov 2008 52.16667 45.90000 39.63333
## Dec 2008 37.58065 32.77419 27.87097
## Jan 2009 42.00000 36.29032 30.45161
## Feb 2009 45.53571 37.82143 30.03571
## Mar 2009 47.35484 40.06452 33.06452
## Apr 2009 57.13333 47.73333 38.70000
## May 2009 62.87097 53.19355 44.29032
## Jun 2009 69.53333 60.83333 52.70000
## Jul 2009 75.51613 65.16129 55.29032
## Aug 2009 71.19355 62.29032 53.80645
## Sep 2009 69.13333 59.10000 49.60000
## Oct 2009 57.19355 49.45161 42.16129
## Nov 2009 50.86667 45.56667 40.23333
## Dec 2009 40.93548 35.19355 29.29032
## Jan 2010 51.25806 45.38710 39.22581
## Feb 2010 52.39286 45.07143 37.57143
## Mar 2010 53.29032 45.25806 37.80645
## Apr 2010 56.60000 48.86667 41.86667
## May 2010 59.74194 51.90323 44.90323
## Jun 2010 64.10000 56.90000 50.76667
## Jul 2010 71.09677 61.87097 53.29032
## Aug 2010 71.70968 62.67742 54.06452
## Sep 2010 66.96667 59.50000 52.73333
## Oct 2010 59.93548 52.03226 44.61290
## Nov 2010 46.66667 41.50000 36.20000
## Dec 2010 47.38710 42.35484 37.29032
## Jan 2011 45.16129 40.09677 35.19355
## Feb 2011 44.03571 38.35714 32.89286
## Mar 2011 51.70968 45.58065 39.45161
## Apr 2011 52.00000 45.33333 39.00000
## May 2011 59.00000 51.87097 45.38710
## Jun 2011 65.63333 59.00000 52.33333
## Jul 2011 70.03226 61.29032 52.96774
## Aug 2011 71.96774 62.93548 54.51613
## Sep 2011 71.00000 60.36667 50.66667
## Oct 2011 57.67742 49.93548 42.74194
## Nov 2011 48.70000 41.53333 34.26667
## Dec 2011 44.87097 39.51613 34.12903
## Jan 2012 44.74194 38.93548 33.09677
## Feb 2012 49.82759 42.86207 35.86207
## Mar 2012 48.45161 42.29032 36.41935
## Apr 2012 57.73333 49.36667 41.60000
## May 2012 61.93548 53.25806 44.96774
## Jun 2012 63.90000 56.26667 48.76667
## Jul 2012 69.51613 61.61290 54.35484
## Aug 2012 73.25806 63.83871 54.87097
## Sep 2012 69.43333 57.83333 47.00000
## Oct 2012 58.45161 50.80645 43.41935
## Nov 2012 52.10000 46.10000 39.96667
## Dec 2012 43.80645 40.25806 36.64516
## Jan 2013 42.45161 37.12903 31.83871
## Feb 2013 49.00000 44.00000 38.75000
## Mar 2013 53.58065 45.64516 37.16129
## Apr 2013 55.30000 48.63333 41.40000
## May 2013 63.90323 55.77419 47.12903
## Jun 2013 69.53333 60.96667 51.96667
## Jul 2013 73.77419 64.80645 55.41935
## Aug 2013 74.06452 65.54839 56.45161
## Sep 2013 67.13333 60.23333 52.76667
## Oct 2013 57.00000 49.41935 41.25806
## Nov 2013 50.03333 43.90000 37.23333
## Dec 2013 41.38710 36.22581 30.48387
## Jan 2014 47.32258 41.06452 34.32258
## Feb 2014 42.82143 37.78571 32.35714
## Mar 2014 52.22581 45.87097 39.03226
## Apr 2014 58.50000 50.93333 42.73333
## May 2014 66.00000 57.64516 48.87097
## Jun 2014 68.06667 60.50000 52.50000
## Jul 2014 74.83871 65.51613 55.87097
## Aug 2014 75.48387 66.51613 57.06452
## Sep 2014 70.63333 61.43333 51.60000
## Oct 2014 62.83871 56.48387 49.87097
## Nov 2014 50.60000 44.13333 37.30000
## Dec 2014 48.51613 42.58065 36.19355
## Jan 2015 50.00000 42.67742 34.90323
## Feb 2015 54.17857 47.32143 39.78571
## Mar 2015 56.67742 48.77419 40.32258
## Apr 2015 58.00000 49.26667 40.16667
## May 2015 66.00000 57.70968 48.87097
## Jun 2015 73.60000 64.30000 54.46667
## Jul 2015 76.77419 67.48387 57.67742
## Aug 2015 75.87097 66.03226 55.64516
## Sep 2015 66.00000 57.06667 47.60000
## Oct 2015 62.32258 54.74194 46.70968
## Nov 2015 49.20000 42.33333 34.93333
## Dec 2015 46.70968 42.16129 36.93548

tMaxF <- kbli.ts[,"tMaxF"]
summary(tMaxF)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   35.94   48.63   57.07   57.25   66.00   76.81

boxplot(tMaxF~cycle(tMaxF),xlab="Month",ylab="Temp")

tmaxf.d<-decompose(tMaxF)
plot(tmaxf.d)

tmaxf.ag<-aggregate(tMaxF,FUN=mean)
plot(tmaxf.ag,ylab="Max Temp F")

Standard deviation

sd(tMaxF)

## [1] 9.972925

sd(tmaxf.ag)

## [1] 1.288124

acf(tmaxf.ag,lag.max = NULL, plot=TRUE)

pacf(tmaxf.ag)

The standard deviation of the data without the seasons is much smaller than the data with the season.

I do not see any significant correlations. Maybe using aggregate was the wrong option here?

Second - simulations

n <- 500
epsilon <- rnorm(n = n,mean = 0,sd = 1) # white noise
x <- numeric(length = n)
phi1 <- 0.25
phi2<-0.75
for(i in 3:n){
  x[i] <- phi1 * x[i-1] + phi2*x[i-2]+epsilon[i]  
}
plot(x,type="l")

acf(x)

pacf(x)

n2 <- 500
epsilon2 <- rnorm(n = n2,mean = 0.25,sd = 0.75) # white noise
x2 <- numeric(length = n2)
phi1.2 <- 0.4
phi2.2<-0.5
for(i in 3:n2){
  x2[i] <- phi1.2 * x2[i-1] + phi2.2*x2[i-2]+epsilon2[i]  
}
plot(x2,type="l")

acf(x2)

pacf(x2)

I did two simulations. In the first, I did not change the mean and standard and the plot looks similar to the given example. In the second, I changed the mean to 0.25 and the sd to 0.75. To me, the second simulation looks more rollercoaster-y than the first. The acf of my first simulation looks nice and gradual and the pacf has that second spike that indicates the second time step correlation. The same acf/pacf patterns were observed for the second simulation as well.

Third

The data I chose were the Coloured fox fur production, Nain, Labrador, 1834-1925 set from the time series data market.

foxfur<-read.csv("foxfur.csv",header=T)
FUR<-foxfur$fur
fur<- ts(FUR,start=c(1834,1),end=c(1925,1),frequency=1)
plot(fur,ylab="Fox fur production")

summary(fur)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00   23.75   42.50   42.04   61.25   80.00

var(fur)

## [1] 510.5036

sd(fur)

## [1] 22.59433

acf(fur)

pacf(fur)

fur.ag<-aggregate(fur,FUN=mean)
plot(fur.ag)

acf(fur.ag)

pacf(fur.ag)

fur.ar<-ar(fur.ag)
fur.ar

## 
## Call:
## ar(x = fur.ag)
## 
## Coefficients:
##       1  
## -0.2178  
## 
## Order selected 1  sigma^2 estimated as  491.7

First I plotted the data. Then I called for the summary of the data. It is interesting the the mean and mediana are very close. I then looked at the variance and standard deviation. The acf and pacf correlograms of the data show no correlations in time. This is interesting because the data seem to follow each other in series. I then aggregated the data to see what the acf and pacf would look like. I think I was unable to decompose my data because the time increment was yearly so there was no season to observe in it.