EQC7006: Time Series Analysis 2020/2021
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ACADEMIC SESSION 2020/2021: SEMESTER II
EQC7006: Time Series Analysis
1. Answer the following questions.
a) For each of the following series, what sort of time patterns (trend and seasonal) would you expect to see?
i) Monthly retail sales of personal computer for the past 10 years at a local store.
ii) Hourly pulse rate of a person for one week.
iii) Daily sales at a fast-food store for six months.
b) Given below are plots of three time series data along with their ACFs. Which ACF goes with which time series? Give justifications.
Series 1: Accidental deaths in USA (monthly)
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ACF A:
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Series 2: International airline passengers (monthly)
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ACF B:
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Series 3: Mink trappings in Canada (annual)
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ACF C:
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2. Answer the following questions.
a) The following table gives the estimation results of Holt-Winters Additive Seasonal model. Y denotes the monthly series of new passenger vehicle sales in Australia (in thousands of units). Compute forecast values for January and February of 2018 (97 and 98 ).
Sample: 2010M01 2017M12
Included observations: 96
Method: Holt-Winters Additive Seasonal
Original Series: Y
Parameters: |
Alpha |
0.2400 |
Beta |
0.1000 |
|
Gamma |
0.1000 |
|
Sum of Squared Residuals |
288.5198 |
|
Root Mean Squared Error |
1.733613 |
End of Period Levels:
Mean Trend Seasonals:
2017M01
2017M02
2017M03
2017M04
2017M05
2017M06
2017M07
2017M08
2017M09
2017M10
2017M11
2017M12
36.03122
-0.274020
-4.948309
-2.594565
2.586789
-5.583590
- 1.024372
11.12648
- 1.811568
-0.954772
1.380597
-0.689081
0.833595
1.678802
*Mean = , Trend = , Seasonal =
b) The following tables give the estimation results of three regression models. Y denotes the monthly series of new passenger vehicle sales in Australia (in thousands of units). C is an intercept and @TREND+1 represents time trend (@TREND+1 = 1, 2, 3, …, 96). @MONTH’s are seasonal dummies where @MONTH=1 is equal to 1 for January and 0 otherwise, and @MONTH=2, @MONTH=3, @MONTH=4, @MONTH=5, @MONTH=6, @MONTH=7, @MONTH=8, @MONTH=9, @MONTH=10, and @MONTH=11 are similarly defined for February, March until November, respectively.
Model 1
Dependent Variable: Y
Method: Least Squares
Sample: 2010M01 2017M12
Included observations: 96
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
44.56778 |
0.582672 |
76.48867 |
0.0000 |
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R-squared 0.000000 Mean dependent var 44.56778 |
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Adjusted R-squared 0.000000 S.D. dependent var 5.708993 |
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S.E. of regression 5.708993 Akaike info criterion 6.332324 |
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Sum squared resid 3096.297 Schwarz criterion 6.359036 |
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Model 2 Dependent Variable: Y Method: Least Squares Sample: 2010M01 2017M12 Included observations: 96 |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
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C @TREND+1 |
50.64034 -0.125207 |
0.934760 0.016734 |
54.17472 -7.482021 |
0.0000 0.0000 |
R-squared 0.373252 Mean dependent var 44.56778 |
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Adjusted R-squared 0.366585 S.D. dependent var 5.708993 |
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S.E. of regression 4.543638 Akaike info criterion 5.885946 |
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Sum squared resid |
1940.597 |
Schwarz criterion |
5.939370 |
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Model 3
Dependent Variable: Y
Method: Least Squares
Sample: 2010M01 2017M12
Included observations: 96
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
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C 52.48405 0.835670 62.80477 0.0000 |
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@TREND+1 -0.130577 0.007632 - 17.10828 0.0000 |
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@MONTH=1 -6.470475 1.031505 -6.272851 0.0000 |
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@MONTH=2 -4.068023 1.030912 -3.946045 0.0002 |
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@MONTH=3 1.099179 1.030375 1.066776 0.2892 |
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@MONTH=4 -7.112368 1.029894 -6.905923 0.0000 |
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@MONTH=5 -2.631416 1.029470 -2.556089 0.0124 |
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@MONTH=6 9.399286 1.029102 9.133486 0.0000 |
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@MONTH=7 -3.376636 1.028790 -3.282143 0.0015 |
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@MONTH=8 -2.504184 1.028535 -2.434709 0.0170 |
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@MONTH=9 -0.284232 1.028337 -0.276399 0.7829 |
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@MONTH=10 -2.290405 1.028196 -2.227596 0.0286 |
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@MONTH=11 -0.759952 1.028111 -0.739174 0.4619 |
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R-squared 0.886668 Mean dependent var 44.56778 |
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Adjusted R-squared 0.870283 S.D. dependent var 5.708993 |
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S.E. of regression 2.056165 Akaike info criterion 4.404888 |
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Sum squared resid |
350.9085 |
Schwarz criterion |
4.752143 |
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i) Based on Model 3, interpret the estimated coefficients of @TREND+1.
ii) Based on Model 3, determine the estimated seasonal factors for January and June.
iii) By assuming that all estimated models are adequate, perform a hypothesis testing to determine if there is seasonal variation in the series .
iv) Based on the finding in (b)(iii), compute the forecast of new passenger vehicle sales in February 2018.
v) Compare forecasts of new passenger vehicle sales in February 2018 calculated in (a) and (b)(iii) and determine which method produced better forecast. [Given that the actual value of new passenger vehicle sales in February 2018 is equal to 33.167 thousand units].
2022-06-01