The model, the relevant algorithm, formulae involved and useful explanation of your calculations
School of Computer Science and Mathematics
Faculty of Science, Engineering and Computing
Time Series Analysis and Further Inference with Applications Including Insurance Models (ST6300)
Retake Coursework  201920
Submission deadline of this coursework:
Instructions to Candidates:
 1. Answer Both Questions 1 and 2
 2. Q1 and Q2 each carries 100 marks
 3. Use 4 decimal places in your calculations
 4. Candidates are required to write their solutions VERY CLEARY, and showing ALL calculations (Page numbering is also required)
 5. All of your answers must be incorporated into a single document (Word or Pdf)
 6. The assessment must be submitted electronically via Canvas
 7. Any assignment showing evidence of copying may result in a mark of zero
General Guidelines to Candidates
 As this is a coursework assessment there is no extra time allocated for students with a SOSN.
 If you experience technical difficulties, e.g. access and upload issues, or identify a potential error in a question please email the module leader [email protected] .
 This is an open book assessment so you may consult your notes, textbooks and the Internet.
 You must not collaborate with someone else on this assessment, it should be wholly your own work. Your work will be checked for evidence of plagiarism and/or collusion using Turnitin.
 If you include graphics in your answer, please embed these into the Word document (e.g. a photograph of a handdrawn graphic). The source of any copied and pasted figures should be cited. If you have embedded any scanned/photographed diagrams and graphs, then your submission file cannot exceed 100MB.
Total number of pages including this page: 4
N Saebi
1: The monthly sales of personal computers by an electric outlet for the past 8 years are tabulated
below:
(The data is read columnwise)
Year

2012

2013

2014

2015

2016

2017

2018

2019


↓

↓

↓

↓

↓

↓

↓

↓

January

128

124

135

132

138

157

161

165

February

120

114

123

131

142

146

147

161

March

116

110

114

115

121

127

134

143

April

108

103

105

112

124

123

124

135

May

85

93

99

101

109

107

112

114

June

96

98

101

96

106

111

122

112

July

95

96

100

110

122

125

124

120

August

93

94

104

114

110

112

119

115

September

118

125

126

131

130

124

120

162

October

124

123

125

129

132

145

137

160

November

124

124

132

138

147

143

152

168

December

134

137

142

141

150

158

158

169

Plot the time series and comment on your visual observation of the graph. Then, by applying the following two methods, determine the outlet’s sales forecasts of computers for the months of 20122019, where applicable.
1: The Multiplicative Decomposition Method.
2: The Single Exponential Smoothing Method (SES).
In each of the above two methods you need to include at least the following set of guidelines:
(a): The model, the relevant algorithm, formulae involved and useful explanation of your calculations. (20 marks)
(b): Your Excel worksheets compactly presented with suitable titles and column headings. (10 marks)
(c): Calculations of the optimum values (where applicable, using the Excel Solver) for the parameter involved. (10 marks)
(d): The sales forecasts for periods 20122019, where applicable, and the corresponding forecast errors.
(20 marks)
(e): The Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE), for the test period of November 2012to December 2019 (inclusively). (10 marks)
In addition, the following needs to be provided:
(f): The comparative assessment table for the above two forecasting techniques using the MSE and the
MAPE. (10 marks)
(g): For each method, illustrate its forecast plot individually. Furthermore, in a single diagram, also show all
forecast plots and critically compare them with the time series plot of the data. Hence, using both assessment criteria table in (f) and the forecast plots, decide on the optimum forecasting method for the sales of personal computers. (10marks)
(h): Forecast of the monthly sales of personal computers by the electric outlet for the year 2020, using
your optimal model. (10 marks)
Retake Coursework Continued …
2: A random sample is drawn from a distribution with probability density function with mean and variance and, respectively.
An estimator of given by for a constant and the sample mean, is being considered
(a) Show that and. (20 marks)
(b) Show that the bias of this estimator in terms of is .
(10 marks)
(c) For show that is an asymptotically unbiased and a consistent estimator
of (25 marks)
(d) Given that that , use this to find the CramérRao lower bound for the variance of an unbiased estimator of.
(30 marks)
(e) For determine the efficiency of (that is, the ratio of the CramérRao lower bound to the MSE of ), and comment on its value.
(15 marks)
You may use the shortcut formula
You may also use either of the two formulae below to derive the CramérRao lower bound for the variance an unbiased estimator
End of Retake Coursework
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