# Expert Answer:STA137 UC Davis Time series method with the applic

Solved by verified expert:Hi， There is a statistics project that needs to be finished. I wanna the project to be formally engaged and correctly answered. so plz clearly read the assignment first. let me know if it is possible and then I will give u more materials related to the R codes that needed. thx.
project.docx

temp_nh.xlsx

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Project
(Due on Thursday, March 21)
Statistics 137
Winter Quarter, 2019
This project is due on March 21. You may work in a group (max group size=3) of registered
students in the course. Only one report per group needs to be submitted. Please write down the
names of the students in the group on submitted work. Please attach the R codes in an appendix
[Data source: Climate Research Center, University of East Anglia, UK]
Please find attached a data set on annual temperature anomalies (1850–2018) for the northern
hemisphere. Analyze the data using time series methods. You are free to use any number of
methods that we have covered in this course. You may consider the following points in your
analysis (with appropriate comments/explanations at each step):

Explain the data, why it is a time series, why it is important to analyze it.
Use graphical techniques to understand the nature of variation in the data.
Determine if the series is stationary or not. If you need to transform, then transform the
data, and estimate the trend in order to carry out the analysis. Make appropriate plots for
the trend (using loess) and the rough etc. Some of the subsequent analyses such as
modeling can be done on the rough part.
Obtain the appropriate ACF, PACF plots and periodogram (and its smoothed version),
and use these to make a preliminary identification of a time series model.
Fit an ARIMA model obtained via preliminary identification, and examine the residuals
and their properties.
Select the final model using a model selection criterion such as AICC. [If you fit
ARIMA(p,d,q), it may be enough to consider the 25 models with p=0,…,4 and q=0,…,4,
where p is the AR order and q is the MA order. The R function auto.arima (‘forecast
package’) or sarima (‘astsa’ package) may be used.]
Plot the spectral density of the final model as well as the smoothed periodogram on the
same graph.
Perform the necessary diagnostics on the residuals of the final model including the ACF
plot as well as the smoothed periodogram.
Write down the final model, the estimated parameters and the standard errors.
Refit the final model (i.e., use AR and MA orders of the final model, but not the
parameter estimates) using all the data except for last 6 years and use this model to
forecast temperature anomalies for the last 6 years. Plot the available observed and the
forecasted values against time (6 years) on the same graph. [If you need to extrapolate the
trend, often a linear extrapolation is reasonable.]

Summarize your findings from the analysis and explain your conclusion. If you feel the
analysis done by you can be improved, please provide a brief explanation.
Your report may include the following Sections:

Introduction: Statement of the problem.
Materials and Methods: Description of the data and the methods used in the analysis.
Results: Explanation of the results of your analyses. You can cut and paste the relevant
parts of your computer outputs and refer to them in explaining your results.
Conclusion and Discussion: Highlight the main points and discuss them.

Format:

The report should be typed and well formatted as a complete stand-alone document (not a
list or bullet points, etc).
The report should not contain code or raw R output. The R codes should be in an
appendix.
There should be a title page with names and student IDs of all group members.
Year
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
Temp-NH
-0.6
-0.214
-0.359
-0.489
-0.136
-0.614
-0.665
-0.545
-0.425
0.02
-0.73
-0.432
-0.832
0.101
-0.839
-0.348
-0.279
-0.654
-0.287
-0.259
-0.46
-0.691
-0.215
-0.369
-0.23
-0.896
-0.487
-0.256
0.163
-0.44
-0.407
-0.45
-0.306
-0.628
-0.776
-0.741
-0.558
-0.534
-0.665
-0.299
-0.324
-0.474
-0.58
-0.688
-0.295
-0.513
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
-0.343
-0.258
-0.315
-0.252
-0.169
-0.106
-0.435
-0.386
-0.496
-0.351
-0.126
-0.608
-0.432
-0.395
-0.289
-0.352
-0.554
-0.318
-0.104
-0.119
-0.37
-0.679
-0.392
-0.358
-0.239
0.007
-0.231
-0.215
-0.265
-0.083
-0.038
-0.183
-0.144
-0.501
-0.034
0.023
-0.057
-0.364
0.077
-0.106
-0.088
0.052
0.256
0.134
-0.045
-0.019
-0.059
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
0.125
0.158
-0.145
-0.005
0.036
0.111
-0.021
-0.294
-0.051
-0.064
0.25
-0.114
-0.14
-0.444
-0.093
0.043
0.046
-0.017
0.046
0.075
0.084
-0.297
-0.275
-0.129
-0.072
-0.2
-0.23
-0.107
-0.188
-0.334
0.129
-0.269
0.005
-0.361
0.1
-0.056
0.008
0.091
0.414
-0.057
0.318
-0.066
-0.101
0.106
0.227
0.397
0.31
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
0.608
0.454
0.09
0.177
0.402
0.717
0.23
0.574
0.894
0.699
0.633
0.831
0.893
0.892
0.787
0.996
0.987
1.125
0.845
0.815
1.101
0.912
0.944
0.957
1.01
1.36
1.536
1.3
1.072

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