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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)

 

 

ACF A:

 

Series 2:

International airline passengers (monthly)

 

ACF B:

 

Series 3:

Mink trappings in Canada (annual)

 

ACF C:

 

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.

 

C

44.56778

0.582672

76.48867

0.0000

 

R-squared                              0.000000    Mean dependent var               44.56778

Adjusted R-squared               0.000000    S.D. dependent var                  5.708993

S.E. of regression                  5.708993    Akaike info criterion                 6.332324

Sum squared resid                 3096.297    Schwarz criterion                     6.359036

 

 

Model 2

Dependent Variable: Y

Method: Least Squares

Sample: 2010M01 2017M12

Included observations: 96

Variable

Coefficient

Std. Error

t-Statistic

Prob.

 

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

Adjusted R-squared               0.366585    S.D. dependent var                  5.708993

S.E. of regression                  4.543638    Akaike info criterion                 5.885946

Sum squared resid

1940.597

Schwarz criterion

5.939370

 


Model 3

Dependent Variable: Y

Method: Least Squares

Sample: 2010M01 2017M12

Included observations: 96

Variable

Coefficient

Std. Error

t-Statistic

Prob.

 

C                         52.48405         0.835670         62.80477        0.0000

@TREND+1               -0.130577         0.007632       - 17.10828        0.0000

@MONTH=1               -6.470475         1.031505       -6.272851        0.0000

@MONTH=2               -4.068023         1.030912       -3.946045        0.0002

@MONTH=3                1.099179         1.030375         1.066776        0.2892

@MONTH=4               -7.112368         1.029894       -6.905923        0.0000

@MONTH=5               -2.631416         1.029470       -2.556089        0.0124

@MONTH=6                9.399286         1.029102         9.133486        0.0000

@MONTH=7               -3.376636         1.028790       -3.282143        0.0015

@MONTH=8               -2.504184         1.028535       -2.434709        0.0170

@MONTH=9               -0.284232         1.028337       -0.276399        0.7829

@MONTH=10              -2.290405         1.028196       -2.227596        0.0286

@MONTH=11              -0.759952         1.028111       -0.739174        0.4619

R-squared                              0.886668    Mean dependent var               44.56778

Adjusted R-squared               0.870283    S.D. dependent var                  5.708993

S.E. of regression                  2.056165    Akaike info criterion                 4.404888

Sum squared resid

350.9085

Schwarz criterion

4.752143

 

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].