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QBUS6840 Predictive Analytics

创建日期：2024-05-13 17:36:36

所属分类：商业分析business analysis

标签： QBUS6840

Predictive Analytics

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QBUS6840

Predictive Analytics
Mid-term Exam Practice Questions
The purpose of these practice questions is to give you sample questions to practise for the mid-
term exam, and to give you some ideas about the details and format of the exam questions. Please
note that the set of questions below is not meant to cover all the topics tested in the midterm
exam.
Question 1
The file beer.txt contains two named columns ’Time’ (month) and ’Sales’ (numerical). Read
the following Python program:
[ 1 ] import pandas as pd
[ 2 ] import matp lo t l i b . pyplot as p l t
[ 3 ] import numpy as np
[ 4 ] beer = pd . r ead c sv ( ’ beer . txt ’ )
[ 5 ] s a l e s = beer [ ’ Sa les ’ ]
[ 6 ] s a l e s v = s a l e s . va lue s
[ 7 ] p l t . f i g u r e ( )
[ 7 ] p l t . p l o t ( s a l e s )
[ 8 ] p l t . t i t l e ( ’ Beer Sa les ’ )
[ 9 ] p l t . x l ab e l ( ’Month ’ )
[ 1 0 ] p l t . y l ab e l ( ’ Sa les ’ )
[ 1 1 ] myT = s a l e s v . r o l l i n g (12 , c en t e r=True ) . mean ( )
[ 1 2 ] T = s a l e s . r o l l i n g (2 , c en t e r=True ) . mean ( )
[ 1 3 ] T1 = T. r o l l i n g (12 , c en t e r = True ) . mean ( ) ;
[ 1 4 ] What i s th i s = beer [ ’ Sa les ’ ] . ewm( alpha =0.05 , ad jus t=True ) . mean ( )
[ 1 5 ] p l t . f i g u r e ( )
[ 1 6 ] p l t . p l o t ( s a l e s )
[ 1 7 ] p l t . p l o t (T1)
[ 1 8 ] p l t . p l o t ( What i s th i s )
[ 1 9 ] p l t . t i t l e ( ’ Beer Sa les ’ )
[ 2 0 ] p l t . x l ab e l ( ’Month ’ )
[ 2 1 ] p l t . y l ab e l ( ’ Sa les ’ )
Please answer the following questions:
(a) Explain the meaning of statement [4] in the program. What is the data type for variable
beer?
(b) What is the data type of the variable sales in statement [5]? What is the difference
between sales and sales v from statement [6]
(c) Do you have any concerns about this program? At which line would you expect an error
message when running this program or not? Why?
(d) How to handle the issue you identified in (c)?
(e) Write out the mathematical formula to replicate T from sales in statement [12].
(f) Explain the meaning of T1 in statement [13]. How many number of values/data have we
lost on the both ends of T1. Explain the reason for this.
(g) Explain the meaning of statement [14].
(h) Roughly sketch the figure given by statements [15]-[21]? You may assume a monthly
seasonal plot for the beer sales
Question 2
What is a scenario based forecast? What is an ex-ante forecast and an ex-post forecast? Give
an example where ex-post forecasts can be used.
Question 3
Which forecasting method forms a forecast by weighting the most recent data (in time) more
highly than less recent data and how?
Question 4
Describe/List the main differences between qualitative and quantitative forecasting methods.
Question 5
Which measure of forecast accuracy should be used in the following situations? Give their
definition in formulas.
(a) A small number of large forecast errors may be allowed
(b) Errors need to be measured in percentage terms.
(c) Whether a model’s forecasts are biased or not is more important than the magnitude of
errors.
Page 2
Question 6
Consider the following time series plot showing annual labour force data in Australia.
(a) Describe the main features or components apparent in the data
(b) List three quantitative forecast models that might be tried for this data, with brief
motivation for each choice.
Question 7
Describe the multiplicative decomposition method by showing each major step.
Question 8
Describe the additive decomposition method by showing each major step.
Question 9
(a) Find the weights for the smoother Centred MA-6
(b) Indicate how many missing observations there will be at the start and end of the smoothed
series in (a).
(c) Identify the smoothing method in (a) as a Weighted MA-k. What are k and the weights?
(d) Devise a symmetric smoother that is an WMA-5 so that the weight on time t is 1.5 times
the weight at times t− 1 and t+ 1, and double the weight at times t− 2, t+ 2.
Question 10
The trend corrected exponential smoothing model is given by the equations:
lt = αyt + (1− α)(lt−1 + bt−1), 0 ≤ α ≤ 1 (1)
bt = γ(lt − lt−1) + (1− γ)bt−1 0 ≤ γ ≤ 1 (2)
yt+1 = lt + bt + ϵt+1, with ϵt+1 ∼ N (0, σ2) (3)
Page 3
(a) Put this model in the error correction form.
(b) Derive the 1, 2 and 3 step-ahead forecasts from this model. Explain briefly why this
model is called the ’local-linear’ forecasting model.
(c) Discuss exactly how the model in (b) is different to simple applying a linear trend (with
normal errors) as follows:
yt = β0 + β1t+ ϵt
(d) The h-step ahead forecast and forecast variances from the model in (b) are:
Yˆt+h = lt + h× bt (4)
V ar(Yt+h|y1:t) = σ2
(
1 + α2
h−1∑
k=1
(1 + γk)2
)
(5)
Prove the above formulas when h = 2.
What happens to the forecasts and forecast intervals as h gets larger? What happens as
h tends to infinity? Explain how and why this behaviour can reasonable in a statistical
model
Question 11
Consider the damped Holt’ s linear model:
yt+1 = lt + ϕbt + ϵt+1
lt = αyt + (1− α) (lt−1 + ϕbt−1)
bt = γ (lt − lt−1) + (1− γ)ϕbt−1
Figure 1
(a) Explain the meaning of lt and bt.
Page 4
(b) How do you choose the optimal α and γ?
(c) How would we modify the model to get the estimations on the blue line?
(d) Write down the expression for the h-step-ahead forecast. What is the h-step-ahead
forecasting value when h becomes large enough? explain the reason.

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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