Contiguous U.S. Average Temperature Units: Degrees Fahrenheit Base Period:...

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Contiguous U.S. Average Temperature Units: Degrees Fahrenheit Base Period: XXXXXXXXXX Missing: -99 Date Value 189901 29.68 189902 25.5 189903 37.63 189904 50.61 189905 59.9 189906 68.65 189907 73.08...

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Contiguous U.S.     Average Temperature
Units: Degrees Fahrenheit
Base Period: XXXXXXXXXX
Missing: -99
Date    Value
189901    29.68
189902    25.5
189903    37.63
189904    50.61
189905    59.9
189906    68.65
189907    73.08
189908    71.74
189909    64.8
189910    53.98
189911    44.92
189912    31.62
190001    34.11
190002    30.76
190003    41.27
190004    51.6
190005    61.74
190006    70.3
190007    73.13
190008    72.86
190009    65.14
190010    56.35
190011    41.54
190012    34.48
190101    31.62
190102    29.86
190103    40.71
190104    49.39
190105    61.18
190106    68.43
190107    76.24
190108    73.2
190109    63.25
190110    55.45
190111    41.68
190112    31.48
190201    30.06
190202    31.46
190203    41.58
190204    50.85
190205    61.99
190206    68.04
190207    72.05
190208    71.37
190209    62.76
190210    54.43
190211    43.68
190212    30.79
190301    30.88
190302    28.42
190303    42.21
190304    50.22
190305    59.54
190306    65.89
190307    71.92
190308    70.97
190309    62.73
190310    53.94
190311    40.23
190312    30.54
190401    27.55
190402    31.59
190403    41.76
190404    49.46
190405    60.13
190406    67.26
190407    71.35
190408    70.72
190409    64.96
190410    53.92
190411    43.14
190412    32.02
190501    27.1
190502    26.94
190503    45.12
190504    50.49
190505    59.14
190506    68
190507    71.98
190508    72.37
190509    65.95
190510    51.64
190511    42.24
190512    30.99
190601    32.88
190602    33.69
190603    36.1
190604    52.72
190605    59.58
190606    67.32
190607    72.36
190608    71.85
190609    66.25
190610    52.54
190611    40.44
190612    34.97
190701    30.69
190702    35.46
190703    45.7
190704    47.53
190705    55.89
190706    65.7
190707    72.52
190708    70.79
190709    64.22
190710    53.78
190711    40.82
190712    34.7
190801    32.45
190802    33.01
190803    43.92
190804    52.75
190805    58.82
190806    66.92
190807    73.18
190808    70.68
190809    65.59
190810    51.76
190811    42.53
190812    33.31
190901    32.31
190902    35.02
190903    40.35
190904    48.96
190905    58.14
190906    68.94
190907    72.63
190908    72.93
190909    64.4
190910    52.88
190911    45.03
190912    25.61
191001    29.61
191002    29.3
191003    49.44
191004    53.62
191005    59.22
191006    68.29
191007    74.12
191008    71.11
191009    65.68
191010    55.62
191011    41.13
191012    31.93
191101    32.9
191102    33.66
191103    44.02
191104    50
191105    61.21
191106    70.75
191107    72.68
191108    70.9
191109    66.09
191110    52.66
191111    37.27
191112    32.2
191201    24.76
191202    31.08
191203    35.76
191204    50.58
191205    60.48
191206    66.7
191207    72.25
191208    70.12
191209    62.73
191210    53.17
191211    42.21
191212    32.95
191301    30.47
191302    29.5
191303    38.71
191304    51.39
191305    60.13
191306    68.22
191307    73
191308    73.36
191309    63.64
191310    51.64
191311    45.12
191312    33.33
191401    34.5
191402    29.52
191403    40.75
191404    51.04
191405    61.14
191406    69.35
191407    74.08
191408    71.69
191409    64.58
191410    55.24
191411    43.41
191412    26.78
191501    28.44
191502    35.94
191503    36.95
191504    54.57
191505    58.17
191506    66.07
191507    71.01
191508    70.16
191509    64.42
191510    55.35
191511    43.11
191512    33.17
191601    28.22
191602    33.03
191603    42.15
191604    50.25
191605    59.31
191606    66.31
191607    74.28
191608    71.82
191609    63.5
191610    52.14
191611    40.23
191612    28.94
191701    28.27
191702    30.09
191703    38.35
191704    48.63
191705    55.13
191706    66.97
191707    74.61
191708    71.02
191709    64.09
191710    50.41
191711    43.54
191712    29.64
191801    23.86
191802    33.82
191803    45.75
191804    49.03
191805    60.8
191806    71.15
191807    72.45
191808    72.5
191809    61.92
191810    56.17
191811    40.51
191812    34.45
191901    31.82
191902    32.25
191903    40.89
191904    51.35
191905    60.03
191906    69.3
191907    74.35
191908    72.27
191909    65.64
191910    52.59
191911    39.31
191912    28.78
192001    29.23
192002    33.69
192003    40.28
192004    46.78
192005    59.31
192006    67.37
192007    72.7
192008    70.63
192009    65.44
192010    54.63
192011    39.7
192012    33.13
192101    34.36
192102    36.9
192103    46.63
192104    51.01
192105    60.1
192106    70.36
192107    74.66
192108    72.03
192109    66.54
192110    55.35
192111    42.58
192112    35.08
192201    26.8
192202    31.95
192203    40.42
192204    50.31
192205    61.18
192206    70.14
192207    73
192208    72.81
192209    67.28
192210    55.02
192211    41.86
192212    33.55
192301    34.59
192302    29.57
192303    38.3
192304    49.91
192305    59.52
192306    68.04
192307    73.76
192308    71.11
192309    65.07
192310    51.24
192311    42.58
192312    35.98
192401    26.26
192402    35.19
192403    37.18
192404    50.27
192405    57.9
192406    68.59
192407    71.89
192408    72.07
192409    62.74
192410    54.97
192411    42.4
192412    27.59
192501    29.08
192502    38.3
192503    44.24
192504    54.72
192505    60.01
192506    69.84
192507    74.14
192508    71.4
192509    66.67
192510    48.92
192511    40.41
192512    32.5
192601    30.31
192602    37.67
192603    39.65
192604    50.04
192605    61.02
192606    68.2
192607    73.36
192608    72.34
192609    64.11
192610    54.95
192611    40.46
192612    31.33
192701    31.55
192702    37.9
192703    42.26
192704    51.58
192705    59.76
192706    67.21
192707    72.68
192708    69.37
192709    64.98
192710    55.9
192711    44.35
192712    28.22
192801    31.98
192802    34.34
192803    43.12
192804    48.06
192805    61.52
192806    65.91
192807    73.4
192808    71.82
192809    63.27
192810    55.08
192811    41.58
192812    32.94
192901    26.31
192902    26.92
192903    43.56
192904    51.17
192905    58.86
192906    67.5
192907    73.6
192908    72.63
192909    63.41
192910    53.92
192911    38.41
192912    33.96
193001    23.54
193002    40.1
193003    40.41
193004    54.41
193005    59.23
193006    68.41
193007    75.04
193008    72.9
193009    65.75
193010    51.69
193011    41.09
193012    31.17
193101    32.99
193102    37.94
193103    39.42
193104    51.06
193105    59.43
193106    70.7
193107    75.81
193108    71.96
193109    68.13
193110    56.57
193111    43.38
193112    35.06
193201    31.55
193202    36.7
193203    37.36
193204    51.6
193205    60.51
193206    69.24
193207    74.1
193208    72.57
193209    64.69
193210    52.32
193211    40.75
193212    29.41
193301    34.3
193302    29.59
193303    41.83
193304    49.84
193305    59.83
193306    71.56
193307    75.13
193308    71.92
193309    67.73
193310    55.2
193311    42.53
193312    36.43
193401    35.08
193402    34.32
193403    42.78
193404    53.74
193405    64.71
193406    70.68
193407    76.37
193408    73.53
193409    63.84
193410    56.52
193411    45.01
193412    32.67
193501    31.51
193502    36.01
193503    43.61
193504    49.71
193505    57.33
193506    67.64
193507    75.13
193508    72.99
193509    64.8
193510    53.8
193511    39.49
193512    30.74
193601    27.36
193602    25.23
193603    43.43
193604    50.22
193605    63.46
193606    70.61
193607    76.8
193608    74.59
193609    66.36
193610    53.49
193611    39.81
193612    34.47
193701    24.84
193702    31.73
193703    38.84
193704    50.11
193705    61.93
193706    68.79
193707    74.59
193708    74.66
193709    65.7
193710    53.89
193711    40.82
193712    32.7
193801    32.14
193802    36
193803    45.01
193804    51.73
193805    59.85
193806    68.77
193807    73.78
193808    73.72
193809    66.63
193810    56.41
193811    39.94
193812    34.21
193901    33.91
193902    29.98
193903    42.51
193904    51.53
193905    62.71
193906    68.86
193907    74.88
193908    72.64
193909    67.37
193910    54.72
193911    42.3
193912    37.72
194001    23.83
194002    33.85
194003    41.52
194004    50.23
194005    60.85
194006    69.6
194007    74.14
194008    72.14
194009    65.35
194010    56.08
194011    39
194012    36.05
194101    32.2
194102    33.53
194103    39.2
194104    52.02
194105    62.33
194106    67.8
194107    73.98
194108    72.07
194109    64.53
194110    55.2
194111    42.91
194112    36.12
194201    29.84
194202    30.74
194203    41.31
194204    53.06
194205    59.09
194206    67.91
194207    73.96
194208    71.78
194209    63.66
194210    54.57
194211    43.16
194212    32.97
194301    29.41
194302    36.28
194303    38.5
194304    52.88
194305    59.72
194306    68.77
194307    74.26
194308    73.45
194309    64.33
194310    53.69
194311    40.91
194312    32.59
194401    32.02
194402    34.5
194403    38.5
194404    48.97
194405    62.02
194406    68.36
194407    72.79
194408    72.1
194409    65.26
194410    55.27
194411    41.5
194412    30.67
194501    30.49
194502    35.28
194503    45.54
194504    50.22
194505    58.28
194506    65.88
194507    72.93
194508    72.16
194509    64.99
194510    54.14
194511    42.01
194512    29.08
194601    31.39
194602    34.88
194603    46.78
194604    54.61
194605    58.75
194606    68.32
194607    73.85
194608    71.17
194609    64.54
194610    53.15
194611    41.74
194612    36.18
194701    31.78
194702    31.41
194703    38.75
194704    50.95
194705    60.13
194706    66.72
194707    72.81
194708    74.08
194709    66.54
194710    58.8
194711    38.1
194712    32.92
194801    27.88
194802    31.62
194803    38.71
194804    53.35
194805    60.24
194806    68.76
194807    73.26
194808    72.05
194809    66.07
194810    53.19
194811    41.59
194812    32.58
194901    25.92
194902    31.91
194903    40.77
194904    52.07
194905    61.72
194906    69.24
194907    74.21
194908    72.1
194909    63.73
194910    54.05
194911    45.27
194912    33.26
195001    30.43
195002    35.55
195003    38.84
195004    48.65
195005    59.45
195006    67.93
195007    71.22
195008    70.02
195009    63.5
195010    57.47
195011    40.64
195012    33.01
195101    30.2
195102    34.54
195103    38.55
195104    49.73
195105    60.76
195106    66.65
195107    73.69
195108    71.89
195109    64.09
195110    54
195111    38.08
195112    31.23
195201    32
195202    35.46
195203    37.69
195204    51.66
195205    60.58
195206    70.75
195207    74.1
195208    72.82
195209    65.89
195210    52.95
195211    39.92
195212    33.44
195301    36.43
195302    35.87
195303    43.75
195304    48.76
195305    59.18
195306    70.18
195307    74.17
195308    72.1
195309    66.16
195310    56.21
195311    43.88
195312    33.69
195401    30.9
195402    41.41
195403    39.25
195404    54.18
195405    58.59
195406    68.85
195407    75.47
195408    72.18
195409    66.45
195410    54.68
195411    44.06
195412    33.91
195501    29.35
195502    31.05
195503    40.06
195504    52.86
195505    61.29
195506    66.54
195507    74.44
195508    73.87
195509    65.88
195510    55.04
195511    38.23
195512    31.71
195601    31.01
195602    32.27
195603    40.75
195604    49.37
195605    61.77
195606    70.36
195607    73.06
195608    71.69
195609    65.1
195610    56.16
195611    40.32
195612    36.23
195701    27.07
195702    38.07
195703    41.27
195704    50.7
195705    59.65
195706    68.7
195707    74.28
195708    71.65
195709    64.18
195710    51.67
195711    40.26
195712    37
195801    31.6
195802    31.98
195803    37.67
195804    50.27
195805    62.42
195806    67.93
195807    72.63
195808    73.29
195809    65.43
195810    54.73
195811    43.02
195812    32.22
195901    29.5
195902    32.49
195903    41.45
195904    51.6
195905    60.84
195906    69.96
195907    73.58
195908    73.17
195909    64.74
195910    53.33
195911    38.66
195912    35.94
196001    29.46
196002    30.52
196003    35.91
196004    52.59
196005    59.31
196006    69.08
196007    73.89
196008    72.21
196009    66.45
196010    54.77
196011    42.73
196012    30.4
196101    29.71
196102    37.42
196103    43.47
196104    48.67
196105    58.87
196106    69.49
196107    73.24
196108    72.7
196109    63.41
196110    53.85
196111    40.5
196112    31.08
196201    26.96
196202    34.92
196203    37.9
196204    51.84
196205    62.24
196206    67.91
196207    72.07
196208    72.12
196209    64.18
196210    56.12
196211    43.18
196212    33.4
196301    24.44
196302    34.12
196303    43.72
196304    51.89
196305    61.02
196306    68.67
196307    73.6
196308    71.98
196309    66.34
196310    59.36
196311    44.04
196312    27.9
196401    31.53
196402    31.77
196403    38.82
196404    51.3
196405    61.43
196406    68
196407    74.66
196408    70.72
196409    63.7
196410    53.78
196411    42.33
196412    32.04
196501    31.8
196502    32.52
196503    35.44
196504    51.89
196505    60.8
196506    66.85
196507    72.61
196508    71.06
196509    61.77
196510    54.99
196511    44.65
196512    35.85
196601    26.38
196602    31.24
196603    43
196604    49.96
196605    60.19
196606    67.93
196607    75.07
196608    70.86
196609    64.54
196610    52.83
196611    43.21
196612    32.68
196701    33.1
196702    32.88
196703    43.63
196704    51.01
196705    57.63
196706    67.55
196707    72.52
196708    71.22
196709    64.06
196710    53.92
196711    41.54
196712    32.07
196801    28.94
196802    32.92
196803    43.56
196804    50.58
196805    58.17
196806    68.5
196807    72.86
196808    70.59
196809    63.9
196810    54.64
196811    41.14
196812    30.04
196901    29.37
196902    32.81
196903    36.03
196904    52.63
196905    61.41
196906    66.83
196907    74.1
196908    73.22
196909    65.55
196910    51.03
196911    41.59
196912    33.46
197001    27.14
197002    35.35
197003    38.5
197004    49.44
197005    61.07
197006    68.74
197007    73.96
197008    73.38
197009    64.58
197010    52.27
197011    41.31
197012    33.58
197101    29.41
197102    33.48
197103    39.65
197104    50.27
197105    58.26
197106    69.44
197107    72.36
197108    72.01
197109    64.33
197110    55.08
197111    41.61
197112    33.98
197201    29.93
197202    33.55
197203    44.04
197204    50.81
197205    60.53
197206    68.22
197207    72.18
197208    71.67
197209    64.44
197210    52.29
197211    38.93
197212    29.86
197301    29.59
197302    33.58
197303    44.29
197304    48.83
197305    59.23
197306    68.95
197307    73.26
197308    72.61
197309    64.4
197310    56.07
197311    42.93
197312    33.71
197401    31.01
197402    34.74
197403    44.38
197404    51.55
197405    60.37
197406    68.49
197407    74.08
197408    70.3
197409    62.31
197410    53.89
197411    42.39
197412    33.66
197501    32.34
197502    32.76
197503    38.7
197504    46.85
197505    60.35
197506    67.51
197507    73.56
197508    71.53
197509    62.89
197510    54.63
197511    42.6
197512    34.29
197601    29.93
197602    39.56
197603    42.31
197604    51.85
197605    59.04
197606    67.8
197607    72.9
197608    70.66
197609    64.18
197610    50
197611    38.48
197612    30.92
197701    23.09
197702    36.03
197703    43.18
197704    54.07
197705    61.66
197706    70.34
197707    74.43
197708    71.78
197709    65.93
197710    53.98
197711    42.87
197712    33.28
197801    25.86
197802    27.99
197803    41.31
197804    51.58
197805    59.74
197806    68.94
197807    73.8
197808    71.8
197809    65.84
197810    54.41
197811    41.47
197812    29.8
197901    21.9
197902    28.13
197903    42.06
197904    50.14
197905    59.13
197906    67.82
197907    73.13
197908    70.97
197909    66.09
197910    55.26
197911    39.94
197912    36.03
198001    31.12
198002    32.85
198003    39.36
198004    51.44
198005    60.28
198006    68.74
198007    75.76
198008    72.79
198009    66.24
198010    52.59
198011    42.31
198012    35.19
198101    32.41
198102    36.59
198103    42.85
198104    55.13
198105    58.96
198106    69.82
198107    73.96
198108    72.1
198109    64.92
198110    52.32
198111    44.74
198112    33.66
198201    26.22
198202    32.59
198203    42

assessment-task-2-dataset-v4tlgwph.txt document-cr4gtboz.pdf

Answered Same Day Dec 15, 2021 SIT718

Solution

Dominic answered on Dec 16 2021

141 Votes

2
ASSESSMENT TASK 2
Contents
Question 1: Summary    3
Question 2: Visualise    3
Question 3: Geometric Brownian Motion    4
Question 4:    4
Question 5:    7
Question 6:    8
Appendix    8
References    9
Question 1: Summary
The following table gives initial summary of the data
    Student ID

    Period
    Jan 1959 - Jan 1979
    Min
    23.09
    Median
    52.28
    Mean
    51.74
    Max
    75.07
Question 2: Visualise
R command for plotting data using ggplot package produces the following plot. The series seems to follow oscillate up and down about the mean across the time period.
Figure 1: Time series plot of the data

Visually, the plot doesn’t seem to give off any evidence towards upward or downward trends. The mean of the data is calculated to be 51.74 and the variance to be around 238.836.
The histogram also doesn’t seem to suggest any thing particular about the series.
Figure 2: Histogram of Value
Question 3: Geometric Brownian Motion
A stochastic process is a process that is random in time. That is, value Xi in each time period ti a random variable.
A geometric Brownian motion is a type of Stochastic process in which evolves in such a way that relative change of the series is a Brownian motion.
Solving for S and simplifying, we get;
μ and σ, are the instantaneous mean and instantaneous standard deviation of the process, that is mean per unit of time and standard deviation per unit of time
Question 4:
In order for a stochastic process to satisfy the condition of being a Geometric Brownian motion;
· E( = ,
· Since relative change in S is normally distributed, S will be log-normally distributed with parameters μ and σ, which are the instantaneous mean and instantaneous standard deviation of the process.
· Over a time t, he random component of a Geometric Brownian motion is normally distributed with mean 0 and variance t.
· Each St is iid, that is independent and identically distributed.
· The increments St1 – St2, St2 – St3, St3 – St4, etc… are jointly independent random variables.
· Distribution of St1 – St2 = Distribution of St1+1 – St2+1 = Distribution of Stn+k – St2+k . That is distribution depends only on the interval of time between the processes
Besides the above mentioned, we may also check for...

SOLUTION.PDF

Contiguous U.S. Average Temperature Units: Degrees Fahrenheit Base Period: XXXXXXXXXX Missing: -99 Date Value 189901 29.68 189902 25.5 189903 37.63 189904 50.61 189905 59.9 189906 68.65 189907 73.08...

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