The average monthly temperatures for Boulder, Colorado, from January 1991 to September2008 are given in Boulder.xlsx.a. Plot

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Question:

The average monthly temperatures for Boulder, Colorado, from January 1991 to September2008 are given in Boulder.xlsx.a. Plot the time series, create seasonal plot for the last four years of the series, andcomment on your results.

b. Compute the summary statistics (mean, median, MAD, and S) overall and for eachmonth. Comment on your results. Does it make sense to compute summary statisticsacross all values, rather than month by month? Explain why or why not.

c. Use the data in Boulder.xlsx,to generate forecast 12 months ahead; thatis, the forecast corresponds to the value for the same month in the previous year.Compute the ME, MAE, RMSE, and RMASE for these forecasts.

Year	Month	Temperature	Temp_Lag 12
1992	JAN	35.9	29.9
1992	FEB	40.6	40.9
1992	MAR	43.3	42.8
1992	APR	54.3	47.8
1992	MAY	59.1	58.2
1992	JUN	62.9	66.6
1992	JUL	68.3	70.5
1992	AUG	66.3	69.2
1992	SEP	64.4	61.7
1992	OCT	54.1	52.1
1992	NOV	34.1	36.8
1992	DEC	29.2	35.3
1993	JAN	28.3	35.9
1993	FEB	30.6	40.6
1993	MAR	42.4	43.3
1993	APR	47.6	54.3
1993	MAY	57.5	59.1
1993	JUN	64.5	62.9
1993	JUL	69.5	68.3
1993	AUG	67.3	66.3
1993	SEP	58.8	64.4
1993	OCT	48.7	54.1
1993	NOV	35.6	34.1
1993	DEC	35.4	29.2
1994	JAN	35.5	28.3
1994	FEB	31.9	30.6
1994	MAR	43.9	42.4
1994	APR	47.6	47.6
1994	MAY	60.8	57.5
1994	JUN	70.0	64.5
1994	JUL	71.2	69.5
1994	AUG	70.9	67.3
1994	SEP	65.0	58.8
1994	OCT	50.6	48.7
1994	NOV	36.6	35.6
1994	DEC	36.1	35.4
1995	JAN	34.5	35.5
1995	FEB	38.3	31.9
1995	MAR	42.1	43.9
1995	APR	45.1	47.6
1995	MAY	50.9	60.8
1995	JUN	62.4	70.0
1995	JUL	70.5	71.2
1995	AUG	74.0	70.9
1995	SEP	60.4	65.0
1995	OCT	50.5	50.6
1995	NOV	45.0	36.6
1995	DEC	36.3	36.1
1996	JAN	29.7	34.5
1996	FEB	37.7	38.3
1996	MAR	37.9	42.1
1996	APR	50.4	45.1
1996	MAY	58.9	50.9
1996	JUN	66.9	62.4
1996	JUL	71.5	70.5
1996	AUG	69.5	74.0
1996	SEP	60.8	60.4
1996	OCT	53.1	50.5
1996	NOV	40.6	45.0
1996	DEC	36.5	36.3
1997	JAN	31.3	29.7
1997	FEB	32.8	37.7
1997	MAR	45.5	37.9
1997	APR	42.8	50.4
1997	MAY	57.4	58.9
1997	JUN	66.5	66.9
1997	JUL	71.4	71.5
1997	AUG	68.7	69.5
1997	SEP	64.0	60.8
1997	OCT	52.7	53.1
1997	NOV	37.9	40.6
1997	DEC	33.9	36.5
1998	JAN	36.5	31.3
1998	FEB	36.4	32.8
1998	MAR	38.7	45.5
1998	APR	46.5	42.8
1998	MAY	58.8	57.4
1998	JUN	62.1	66.5
1998	JUL	72.8	71.4
1998	AUG	70.7	68.7
1998	SEP	67.1	64.0
1998	OCT	50.4	52.7
1998	NOV	44.0	37.9
1998	DEC	32.2	33.9
1999	JAN	36.4	36.5
1999	FEB	42.1	36.4
1999	MAR	46.0	38.7
1999	APR	44.5	46.5
1999	MAY	55.6	58.8
1999	JUN	64.8	62.1
1999	JUL	73.5	72.8
1999	AUG	69.3	70.7
1999	SEP	58.5	67.1
1999	OCT	51.9	50.4
1999	NOV	48.0	44.0
1999	DEC	36.9	32.2
2000	JAN	36.4	36.4
2000	FEB	41.0	42.1
2000	MAR	42.9	46.0
2000	APR	51.2	44.5
2000	MAY	61.0	55.6
2000	JUN	67.4	64.8
2000	JUL	74.7	73.5
2000	AUG	73.0	69.3
2000	SEP	63.1	58.5
2000	OCT	49.6	51.9
2000	NOV	31.4	48.0
2000	DEC	31.2	36.9
2001	JAN	33.0	36.4
2001	FEB	32.3	41.0
2001	MAR	40.8	42.9
2001	APR	50.7	51.2
2001	MAY	58.4	61.0
2001	JUN	68.9	67.4
2001	JUL	75.0	74.7
2001	AUG	71.8	73.0
2001	SEP	65.0	63.1
2001	OCT	53.8	49.6
2001	NOV	43.9	31.4
2001	DEC	35.0	31.2
2002	JAN	33.1	33.0
2002	FEB	36.0	32.3
2002	MAR	37.5	40.8
2002	APR	52.9	50.7
2002	MAY	56.2	58.4
2002	JUN	70.5	68.9
2002	JUL	76.8	75.0
2002	AUG	71.3	71.8
2002	SEP	64.0	65.0
2002	OCT	45.9	53.8
2002	NOV	40.3	43.9
2002	DEC	36.6	35.0
2003	JAN	40.2	33.1
2003	FEB	31.6	36.0
2003	MAR	43.7	37.5
2003	APR	50.6	52.9
2003	MAY	57.4	56.2
2003	JUN	62.8	70.5
2003	JUL	75.9	76.8
2003	AUG	72.9	71.3
2003	SEP	60.5	64.0
2003	OCT	57.4	45.9
2003	NOV	39.0	40.3
2003	DEC	36.4	36.6
2004	JAN	35.4	40.2
2004	FEB	33.6	31.6
2004	MAR	48.2	43.7
2004	APR	49.2	50.6
2004	MAY	59.9	57.4
2004	JUN	62.7	62.8
2004	JUL	69.2	75.9
2004	AUG	66.4	72.9
2004	SEP	62.9	60.5
2004	OCT	51.9	57.4
2004	NOV	39.7	39.0
2004	DEC	36.5	36.4
2005	JAN	35.5	35.4
2005	FEB	37.9	33.6
2005	MAR	42.0	48.2
2005	APR	48.4	49.2
2005	MAY	57.6	59.9
2005	JUN	65.4	62.7
2005	JUL	75.1	69.2
2005	AUG	69.7	66.4
2005	SEP	66.5	62.9
2005	OCT	52.6	51.9
2005	NOV	45.0	39.7
2005	DEC	33.3	36.5
2006	JAN	40.7	35.5
2006	FEB	33.7	37.9
2006	MAR	39.4	42.0
2006	APR	53.9	48.4
2006	MAY	61.0	57.6
2006	JUN	71.6	65.4
2006	JUL	74.4	75.1
2006	AUG	71.6	69.7
2006	SEP	58.4	66.5
2006	OCT	51.0	52.6
2006	NOV	43.4	45.0
2006	DEC	35.3	33.3
2007	JAN	27.2	40.7
2007	FEB	34.6	33.7
2007	MAR	47.6	39.4
2007	APR	47.9	53.9
2007	MAY	58.0	61.0
2007	JUN	67.7	71.6
2007	JUL	74.8	74.4
2007	AUG	73.7	71.6
2007	SEP	64.5	58.4
2007	OCT	55.2	51.0
2007	NOV	44.9	43.4
2007	DEC	30.2	35.3
2008	JAN	31.6	27.2
2008	FEB	36.1	34.6
2008	MAR	40.8	47.6
2008	APR	47.8	47.9
2008	MAY	57.1	58.0
2008	JUN	66.1	67.7
2008	JUL	75.0	74.8
2008	AUG	69.6	73.7
2008	SEP	60.9	64.5