Question

In: Statistics and Probability

You are applying for a data job, and your assignment is to analyze the following data...

You are applying for a data job, and your assignment is to analyze the following data set for monthly average temperatures at St Catherines in the programming language R.

(a) Prepare some plots that visualize the data.

(b) Find the appropriate time series model and fit the data. Explain your choice of parameters.

(c) Make predictions for the next 3 years, plot these predictions.

(d) Summarize your findings.

The Data is provided below. Please show the R codes as well. Thank you!

"Month","Average monthly temperatures St Cathrines"

“1980-01", 3.3

“1980-02", 5.5

“1980-03", 0.5

“1980-04", 7.4

“1980-05", 14.4

“1980-06", 16.6

“1980-07", 21.8

“1980-08", 22.8

“1980-09", 16.9

“1980-10", 8.4

“1980-11", 3.4

“1980-12", 4.3

“1981-01", 7.6

“1981-02", 0.6

“1981-03”, 1.6

“1981-04", 8.5

“1981-05", 12.4

“1981-06", 19.2

“1981-07", 22.1

“1981-08", 20.7

“1981-09", 16.0

“1981-10", 7.7

“1981-11", 4.5

“1981-12", 1.3

“1982-01", 7.7

“1982-02", 5.3

“1982-03", 0.3

“1982-04", 5.7

“1982-05", 14.0

“1982-06", 15.9

“1982-07", 21.9

“1982-08", 18.4

“1982-09", 15.9

“1982-10", 11.2

“1982-11", 5.8

“1982-12", 3.0

“1983-01", 2.3

“1983-02", 1.6

“1983-03", 1.9

“1983-04", 6.5

“1983-05", 11.6

“1983-06", 19.6

“1983-07", 23.3

“1983-08”, 21.5

“1983-09", 17.5

“1983-10", 10.8

“1983-11", 4.9

“1983-12", 4.2

“1984-01", 6.1

“1984-02", 0.4

“1984-03", 3.0

“1984-04", 7.5

“1984-05", 11.0

“1984-06", 19.6

“1984-07", 21.0

“1984-08", 22.0

“1984-09", 15.4

“1984-10", 11.3

“1984-11", 4.6

“1984-12", 0.9

“1985-01", 6.0

“1985-02", 4.0

“1985-03", 2.3

“1985-04", 8.7

“1985-05", 14.3

“1985-06", 17.0

“1985-07", 21.1

“1985-08", 20.7

“1985-09", 18.3

“1985-10”, 10.9

“1985-11", 4.9

“1985-12", 3.2

“1986-01", 3.6

“1986-02", 4.8

“1986-03", 1.9

“1986-04", 8.1

“1986-05", 15.0

“1986-06", 17.7

“1986-07", 21.9

“1986-08", 19.7

“1986-09", 16.1

“1986-10", 10.4

“1986-11", 2.9

“1986-12", 0.4

“1987-01”, 3.1

“1987-02", 3.7

“1987-03", 2.7

“1987-04", 9.0

“1987-05", 15.0

“1987-06", 20.2

“1987-07", 23.5

“1987-08", 20.3

“1987-09", 16.8

“1987-10", 8.3

“1987-11", 5.3

“1987-12", 1.1

“1988-01", 3.3

“1988-02", 4.5

“1988-03”, 1.1

“1988-04", 6.7

“1988-05", 14.6

“1988-06", 18.4

“1988-07", 23.7

“1988-08", 22.2

“1988-09", 16.4

“1988-10", 8.4

“1988-11", 6.0

“1988-12", 1.1

“1989-01", 0.7

“1989-02", 4.7

“1989-03", 0.3

“1989-04", 5.6

“1989-05", 13.2

“1989-06", 19.2

“1989-07", 22.2

“1989-08", 20.7

“1989-09", 16.8

“1989-10", 11.1

“1989-11", 3.7

“1989-12", 7.5

“1990-01", 0.7

“1990-02", 1.8

“1990-03", 2.1

“1990-04”, 8.9

“1990-05", 12.1

“1990-06", 19.4

“1990-07", 21.5

“1990-08", 21.0

“1990-09", 16.2

“1990-10", 10.7

“1990-11", 5.8

“1990-12", 0.6

“1991-01", 3.9

“1991-02", 0.6

“1991-03", 2.9

“1991-04", 9.1

“1991-05", 16.8

“1991-06", 20.6

“1991-07", 22.1

“1991-08", 21.8

“1991-09", 16.4

“1991-10", 11.4

“1991-11", 4.2

“1991-12”, 0.1

“1992-01", 2.5

“1992-02", 2.1

“1992-03", 0.1

“1992-04", 6.1

“1992-05", 12.8

“1992-06", 16.9

“1992-07", 18.8

“1992-08", 18.9

“1992-09", 15.9

“1992-10", 8.5

“1992-11", 4.2

“1992-12", 0.3

“1993-01", 1.8

“1993-02", 6.8

“1993-03”, 1.7

“1993-04", 7.4

“1993-05", 12.7

“1993-06", 17.8

“1993-07", 22.4

“1993-08", 21.7

“1993-09", 15.1

“1993-10", 9.0

“1993-11", 3.9

“1993-12", 1.7

“1994-01”, 9.1

“1994-02", 6.2

“1994-03", 0.2

“1994-04", 8.2

“1994-05", 11.6

“1994-06", 19.3

“1994-07", 22.2

“1994-08", 19.6

“1994-09", 16.4

“1994-10", 10.6

“1994-11", 6.8

“1994-12", 1.0

“1995-01", 1.2

“1995-02", 5.7

“1995-03", 3.0

“1995-04", 5.2

“1995-05", 13.6

“1995-06", 20.0

“1995-07", 22.1

“1995-08", 21.9

“1995-09", 15.4

“1995-10”, 12.0

“1995-11", 2.4

“1995-12", 3.4

“1996-01", 5.2

“1996-02", 4.4

“1996-03", 2.0

“1996-04", 6.0

“1996-05", 12.2

“1996-06", 19.4

“1996-07", 20.5

“1996-08”, 21.7

“1996-09", 17.3

“1996-10", 10.7

“1996-11", 2.4

“1996-12", 0.8

“1997-01", 4.1

“1997-02", 0.9

“1997-03", 0.4

“1997-04", 6.2

“1997-06", 20.0

“1997-07", 20.7

“1997-08", 19.6

“1997-09", 16.3

“1997-10", 10.1

“1997-11", 3.3

“1997-12", 0.5

“1998-01", 0.6

“1998-02", 0.7

“1998-03", 3.3

“1998-04", 9.0

“1998-05", 16.9

“1998-06", 19.5

“1998-07", 21.8

“1998-08”, 22.1

“1998-09", 19.0

“1998-10", 11.6

“1998-11", 6.1

“1998-12", 2.5

“1999-01", 4.7

“1999-02", 0.5

“1999-03", 0.7

“1999-04", 8.1

“1999-05”, 15.4

“1999-06", 21.2

“1999-07", 24.6

“1999-08", 20.3

“1999-09", 18.5

“1999-10”, 10.6

“1999-11", 6.8

“1999-12", 0.5

Expert Solution

rm(list=ls())

## Import Data as data set named rdata

temp<-c(3.3, 5.5, 0.5, 7.4, 14.4, 16.6, 21.8, 22.8, 16.9, 8.4, 3.4, 4.3, 7.6, 0.6, 1.6, 8.5, 12.4, 19.2,

22.1, 20.7, 16, 7.7, 4.5, 1.3, 7.7, 5.3, 0.3, 5.7, 14, 15.9, 21.9, 18.4, 15.9, 11.2, 5.8, 3, 2.3,

1.6, 1.9, 6.5, 11.6, 19.6, 23.3, 21.5, 17.5, 10.8, 4.9, 4.2, 6.1, 0.4, 3, 7.5, 11, 19.6, 21, 22,

15.4, 11.3, 4.6, 0.9, 6, 4, 2.3, 8.7, 14.3, 17, 21.1, 20.7, 18.3, 10.9, 4.9, 3.2, 3.6, 4.8, 1.9,

8.1, 15, 17.7, 21.9, 19.7, 16.1, 10.4, 2.9, 0.4, 3.1, 3.7, 2.7, 9, 15, 20.2, 23.5, 20.3, 16.8, 8.3,

5.3, 1.1, 3.3, 4.5, 1.1, 6.7, 14.6, 18.4, 23.7, 22.2, 16.4, 8.4, 6, 1.1, 0.7, 4.7, 0.3, 5.6,

13.2, 19.2, 22.2, 20.7, 16.8, 11.1, 3.7, 7.5, 0.7, 1.8, 2.1, 8.9, 12.1, 19.4, 21.5, 21, 16.2, 10.7,

5.8, 0.6, 3.9, 0.6, 2.9, 9.1, 16.8, 20.6, 22.1, 21.8, 16.4, 11.4, 4.2, 0.1, 2.5, 2.1, 0.1, 6.1,

12.8, 16.9, 18.8, 18.9, 15.9, 8.5, 4.2, 0.3, 1.8, 6.8, 1.7, 7.4, 12.7, 17.8, 22.4, 21.7, 15.1, 9,

3.9, 1.7, 9.1, 6.2, 0.2, 8.2, 11.6, 19.3, 22.2, 19.6, 16.4, 10.6, 6.8, 1, 1.2, 5.7, 3, 5.2, 13.6,

20, 22.1, 21.9, 15.4, 12, 2.4, 3.4, 5.2, 4.4, 2, 6, 12.2, 19.4, 20.5, 21.7, 17.3, 10.7, 2.4, 0.8, 4.1,

0.9, 0.4, 6.2, 0, 20, 20.7, 19.6, 16.3, 10.1, 3.3, 0.5, 0.6, 0.7, 3.3, 9, 16.9, 19.5, 21.8, 22.1, 19,

11.6, 6.1, 2.5, 4.7, 0.5, 0.7, 8.1, 15.4, 21.2, 24.6, 20.3, 18.5, 10.6, 6.8, 0.5)

# conevert data into time series data

ts_data<-ts(data = temp, start = c(1980,1),end = c(1999,12),frequency = 12)

#### (a) Time series plot

plot(ts_data,xlab="Year",ylab="Temperature",main="Time Series")

#### (b) Appropriate model fitting

fit<-forecast::auto.arima(ts_data)

# Series: ts_data

# ARIMA(1,0,0)(1,1,0)[12] with drift

# Coefficients:

# ar1 sar1 drift

# 0.0466 -0.4651 0.0031

# s.e. 0.0666 0.0586 0.0090

#

# sigma^2 estimated as 5.134: log likelihood=-509.97

# AIC=1027.94 AICc=1028.12 BIC=1041.66

#### (c) prediction for next 3 year

pred<-forecast::forecast(fit,h=36)

Month	Forecast
Jan-00	2.79
Feb-00	0.64
Mar-00	1.96
Apr-00	8.57
May-00	16.15
Jun-00	20.46
Jul-00	23.35
Aug-00	21.19
Sep-00	18.79
Oct-00	11.12
Nov-00	6.53
Dec-00	1.48
Jan-01	3.73
Feb-01	0.63
Mar-01	1.43
Apr-01	8.41
May-01	15.86
Jun-01	20.86
Jul-01	23.99
Aug-01	20.83
Sep-01	18.71
Oct-01	10.93
Nov-01	6.71
Dec-01	1.08
Jan-02	3.35
Feb-02	0.69
Mar-02	1.73
Apr-02	8.54
May-02	16.05
Jun-02	20.73
Jul-02	23.74
Aug-02	21.05
Sep-02	18.80
Oct-02	11.07
Nov-02	6.68
Dec-02	1.32

orchestra answered 2 years ago

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