Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
In this paper, corss-correlation functions are used to investigate the relationship between retail sales value index for the two industries (food and jewellery) and the three sources of visitor arrivals (Mainland China under individual travel scheme (IVS) , Mainland China under non-IVS and countries other than Mainland China) between January 2005 and April 2015. The results indicate that only IVS visitor arrivals retail sales. Moreover, transfer function models generally have better performance than ARIMA models in forecasting retail sales value and both ARIMA and transfer function models predict declining retail sales value in the future months of 2015. These findings are important to government and business sectors.
JEL Codes: C32, C53, E32
In the past ten years, visitor arrivals to Hong Kong grow rapidly from 23.4 million in 2005 to
60.8 million in 2014. The top six source markets of visitor arrival to Hong Kong in 2014 were Mainland China (77.7% of total arrivals), Taiwan (3.3%), South Korea (2.1%), US
(1.9%), Japan (1.8%) and Macau (1.6%). (Hong Kong Tourism Board). Visitors from
Mainland China are divided into two types: (a) under individual travel scheme (IVS) and (b) non-IVS. As seen in Figure 1, the percentage share of IVS visitors to total Mainland Visitors increases from 44.3% in 2005 to 66.3% in 2014.
With the increase in the number of visitors, tourism shopping expenditure also rises greatly by 396% from HK$42,143 million in 2005 to HK$208,883 million in 2014 (Hong Kong
Tourism Board). Tourist shopping expenditure contributes greatly to the total retail sales in
Hong Kong. From 2005 to 2014, total retail sales value increases by 141% from
HK$204,372 million to HK$493,236 million.
In comparing the value of retail sales by different types of retail outlet in April and May 2015 with the corresponding months in 2014, the value of retail sales of “jewellery, watches and clocks, and va luable gifts” decreased by the largest percentage (19.5% and 14.9% respectively), and attracted the attention of Government and business sectors. As
“jewellery” industry accounts for 21% of the total retail sales in 2014, the continuing fall impacts the retail market and the economy. On the other hand, the value of retail sales of
“Food, alcoholic drinks and tobacco (other than supermarkets)" is one of the few industry groups that records a significant increase and will be studied together with “jewellery” industry as a comparison. This paper focuses on the relationship between retail sales value index of two outlet types (jewellery and food) and three different sources of visitor arrivals to Hong Kong (IVS, non-IVS and Others).
*Dr. Iris M H Yeung, Department of Management Sciences, City University of Hong Kong, Hong Kong.
Email : msiris@cityu.edu.hk
; Tel: (852)34428566
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
As the retail sales value index and visitor arrivals data are auto-correlated, cross-correlation functions will be used to explore the relationship between retail sales and visitor arrivals.
Both ARIMA and transfer function models will be used to forecast the retail sales value for the next 8 months (May 2015 to December 2015) for future planning.
Various forecasting methods have been used to forecast retail sales. For example, Alon
(1996) concluded that Winters’ exponential smoothing method outperformed simple and
Holt’s exponential smoothing method in forecasting aggregate sales. Alon et al. (2001) found that Winters' exponential smoothing and ARIMA models performed well under stable macro-economic conditions using US monthly aggregate retail sales data. However, when economic conditions are not stable, artificial neural networks (ANNs) produced the best results due to their ability to “capture the dynamic nonlinear trend and seasonal patterns, as well as the interactions between them.”
Chu and Zhang (2003) compared the performance of linear (ARIMA, regression with dummy variables, and regression with trigonometric variables) and nonlinear (neural networks) seasonal forecasting models for the US monthly aggregate retail sales and found that neural network models using deseasonalized data outperformed the rest of the models. They also found that seasonal dummy variables can be useful for predicting retail sales, but their performance may not be robust, and that trigonometric models are not useful in aggregate retail sales forecasting.
Cheung (2013) applied regression analysis to investigate the relationship between retail sales in Hong Kong and visitor arrivals from Mainland China. The results demonstrated that the relationship was significant after the launch of the IVS scheme. Also, the relationship between total retail sales value and IVS visitors was stronger than that of non-IVS visitors.
When the retail sales was split into different retail outlets, the relationship between IVS visitors and retail sales of outlets such as supermarkets; and “jewellery, watches and clo cks, and valuable gifts” was strong.
3.1. Data
Monthly data of retail sales value and visitor arrivals between January 2005 and April 2015 are obtained from Hong Kong Tourism Board and Census and Statistics Department.
Monthly retail sales value index is calculated with respect to the base period (Oct 2009 –
Sept 2010) and used as the dependent variable. The three sources of visitor arrivals (IVS, non-IVS and Others) will be used as the explanatory variables. The forecasting models are estimated and built using the data from January 2005 to December 2012, and the remaining data from January 2013 to April 2015 are used to assess the out-of-sample forecasting performance of the models.
3.2. ARIMA Model
Prior to the analysis, all data are natural logarithmic transformed to stabilize the variance.
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
Suppose the transformed series is denoted as order ( p, d, q ) for the series

Z
1
, Z
2
,  , Z n

Z
1
, Z
2

is given by:
,  , Z n

. The general ARIMA model of
 p
( B )( 1

B ) d
Z t
  q
( B ) a t
(1)
Where a t
is the white noise series for Z t
; B is the backward shift operator; d is the order of differencing;
 p
( B )

( 1
 
1
B
 
2
B
2     p
B p
) is the nonseasonal autoregressive operator of order p and
 q
( B )

( 1
 
1
B
1  
2
B
2     q
B q
) is the nonseasonal moving average operator of order q .
3.3. Cross-correlation Function
To identify a preliminary transfer function model describing the relationship between the output series Y t
and the input series X t between the prewhitened input series α t
, the sample cross-correlation function (SCC)
and the prewhitened output series β t
at lag k is calculated.
SCC k
 t n 

1 n
 k  t

1
  t
  t
 
  
2
 
 t n 

1 t
 k

 t





2

(2) where
 and

are the sample means of
 t and
 t
respectively.
3.4. Transfer Function Model
The general form of the transfer function model for the output series Y t
and one single input series X t is
Where
 
Y t



0 with parameters


 
  B b
X t

N t
(3)
 
1
B
    s
B s

is the operator in the numerator of the transfer function
 i
, i = 0, 1, 2, …, s ;
 

1
 
1
B
    r
B r

is the operator in the denominator of the transfer function with parameters
 i
, i = 0, 1, 2, …, r ; b is the delay time for the input at time t to produce an effect on the output; and N t
is an autocorrelated noise process at time t which is independent of the input process and represents the combined effects of all other common factors influencing Y t and can be modeled by an appropriate
ARIMA process.
The above model can be easily extended to the multiple-input case.
Y t


1

 
B
 
1 b
1
X
1 t


2

 
B
 
2 b
2
X
2 t
  
 k
 k
 
B
  b k
X kt

N t
(4)
For this multiple-input model, the input series X
1 t
, X
2 t
,  should be independent of one another for ease of interpretation and analysis.
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
4. The Findings
4. 1. Time series plot of the data
The time series plot of monthly retail sales index and visitor arrivals between 2005 January and 2015 April are given in Figure 1 and 2 respectively. The retail sales index and visitor arrivals data generally exhibit an upward trend. Relatively speaking, retail sales index of the
“jewellery” industry and IVS increase rapidly since 2010. In the seasonality plot, it can be observed that both retail sales value indices ( “jewellery” and “food” ) are high in January and December. As for visitor arrivals, IVS and non-IVS Mainland tourists come to Hong
Kong more in August and December whereas tourists from “Others” countries travel to
Hong Kong more in October to December.
4. 2. Seasonal ARIMA Models for Retail Value Index
Seasonal ARIMA models are fitted to the monthly log-transformed data from 2005 to 2012.
The best ARIMA model which is selected based on the Akaike Information Criteria (1974) and Schwarz Information Criteria (1978) and diagnostic checking results will be used to forecast the retail sales value index for the period of January 2013 and April 2015. The results of the fitted models are presented in Table 1.
4.3. Cross-correlation Function
Table 2 shows the cross-correlation results for different pairs of input and output variables which are presented in row and columns respectively. From Table 2, it can be seen that retail sales value index of both industries are affected by IVS visitor arrivals, but has no effective relationship with Non_IVS and “Others” visitors. So only IVS is used as input variable to forecast the retail sales value index.
4. 4. Transfer Function Models for Retail Value Index
Transfer function models using IVS visitor arrival as input variable are fitted to the monthly log-transformed data from 2005 to 2012. The best transfer function model which is selected based on the Akaike Information Criteria (1974) and Schwarz Information Criteria (1978) and diagnostic checking results will be used to forecast the retail sales value index for the period of January 2013 and April 2015. The results of the fitted models are presented in
Table 3.
4.5. Forecast of retail sales value index
The toot mean squared error (RMSE) and mean absolute percentage error (MAPE) of the fitted ARIMA and transfer function models to the in-sample (January 2005
– December
2012) and out-of-sample (January 2013 – April 2015) are given in Table 4. It is found that for “food” industry, transfer function model outperforms ARIMA model in both in-sample and out-of-sample periods
. On the other hand, for the “jewellery” industry, transfer function models outperform ARIMA models only in the in-sample period. These results indicate that
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
IVS tourist arrivals are useful to predict retail sales value index of “food” industry, but not for the “jewellery” industry in out-of-sample period
The forecasts of the retail sales value index for “jewellery” industry in May – December of
2015 are given in Figure 3. Both models point to declining retail sales values for the next several months. This projection results are important to policy makers and the business man to balance the tourist arrivals from Mainland China and the growth of retail sales
The transfer function models revealed that there is a significant relationship between total retail sales value index and IVS visitor arrivals from Mainland China. However, no significant relationship between retail sales value index and non-
IVS and “Others” visitors.
Compared with the “food” industry, the effect of IVS visitors on “jewellery” industry was weaker. The impact of IVS visitors on retail sales value index of “food” industry is stronger than that of “jewellery” industry. In this paper, only the effect of tourist arrivals on retail sales are studied. Further research on other independent variables such as exchange rates will be used to improve the fitted models.
The author would like to thank Mr. Mathew Chua for his help to prepare some data.
Alon I 1997, Forecasting aggregate retail sales: the winters' model revisited, in: Goodale J
C (Ed.), The 1997 Annual Proceedings, Midwest Decision Science Institute, 1997, pp.
234 –236.
Alon I, Qi M, Sadowski RJ 2001, Forecasting aggregate retail sales: a comparison of artificial neural networks and traditional methods.
Journal of Retailing and Consumer
Services, vol. 8 (3), pp. 147
–156.
Census and Statistics Department, Report on Monthly Survey of Retail Sales. Census and
Statistics Department, Hong Kong.
Chu C W and Zhang P G Q 2003. A comparative study of linear and nonlinear models for aggregate retail sales forecasting. International Journal of Production Economics, Vol.
86, pp. 217
–231.
Hong Kong Tourism Board, A Statistical Review of Hong Kong Tourism.
Hong Kong
Tourism Board.
Hong Kong Tourism Board, Tourism Expenditure Associated to Inbound Tourism.
Hong
Kong Tourism Board.
Peterson R T 1993, Forecasting practices in the retail industry. Journal of Business
Forecasting, Vol 12, pp. 11-14.
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
Dependent variable: Retail sales value i ndex of “Food” industry
Model: d=1, D=1, Q=(1) (12 13)

1

B
 
1

B
12
 ln y t


1
 
1
B
 
1
 
1 , 12
B
12  
1 , 13
B
13
 a t
Explanatory variable
Q=1
Coefficient
.803*** t-statistics (p value)
11.85 (<0.0001)
Q=12 0.647*** 6.70 (<0.0001)
Q=13 -0.242**
AIC = -223.898, SBC = -216.641
-2.5 (0.0145)
Dependent variable: R etail sales value index of “Jewellery” industry
Model: d=1, D=1, Q=(1) (12 14)

1

B
 
1

B
12
 ln y t


1
 
1
B
 
1
 
1 , 12
B
12  
1 , 14
B
14
 a t
Explanatory variable
Q=1
Coefficient
.228 t-statistics (p value)
2.08 (0.0406)
Q=12 0.497 4.94 (<0.0001)
Q=14
AIC = -218.876, SBC = -211.62
0.288 2.81 (0.0062)
Notes:
1. d represents the degree of non-seasonal differencing
2. D represents the degree of seasonal differencing
3. B represents the backshift operator
4. Q represents the moving average terms
5. * , ** , *** indicate the variable is significant at 10%, 5% and 1% level respectively
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
Sources of visitors
IVS
Non-IVS
Others
Retail sales value index of
“Food”
Lag 0, 1
No effective relationship
No effective relationship
Retail sales value index of
“Jewellery”
Lag 0
No effective relationship
No effective relationship
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
Dependent variable: Retail sales value index of “Food” industry
Model: d=1, D=1, P=3, Q=(1) (12 18), b=0, s =1 z t

C ( 1
 
1
B ) x t


1
 
1
B
 
1


1

1 , 12
B
12
 
3
B
3

 
1 , 18
B
18
 a t
Explanatory variable
C

1
P=3
Q=1
Coefficient
0.287***
0.154***
-0.262**
.548*** t-statistics (p value)
5.38 (<0.0001)
2.96 (0.0041)
-2.25 (0.0276)
5.36 (<0.0001)
Q=12 0.569*** 5.51 (<0.0001)
Q=13 -0.265**
AIC = -237.012, SBC = -222.572
-2.52 (0.0137)
Dependent variable: Retail sales value index of “Jewellery” industry
Model: d=1, D=1, Q = (12 14), b=0 z t

Cz t x 

1
 
1 , 12
B
12  
1 , 14
B
14
 a t
Explanatory variable
C
Coefficient
0.219*** t-statistics (p value)
5.45 (<0.0001)
Q=12 .379*** 3.55 (0.0006)
Q=14 0.413***
AIC = -239.031, SBC = -231.774
Notes:
3.77 (0.0003)
1. Z t
= output variable = ln(retail sales value index) at time t
2. X t
= input variable = ln(IVS visitors) at time t
3. d represents the degree of non-seasonal differencing
4. D represents the degree of seasonal differencing
5. B represents the backshift operator
6. P represents the autoregressive terms
7. Q represents the moving average terms
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
8. b = number of period before the input variable begin to affect the output variable
9. * , ** , *** indicate the variable is significant at 10%, 5% and 1% level respectively
Dependent variable: Retail sales value index of “Food” industry
RMSE
MAPE
In-sample
ARIMA model
Out-of-sample
Transfer function model
In-sample Out-sample
5.7833*
0.0404*
10.1479
0.0519
5.1335*
0.0405
Dependent variable: Retail sales value index of “Jewellery” industry
10.1229*
0.0463*
RMSE
MAPE
In-sample
6.3859
0.05184
ARIMA model
Out-sample
69.6336*
0.3258*
Transfer function model
In-sample
6.0013*
0.0445*
Out-sample
72.8872
0.3434
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
300
250
200
150
100
50
0
Food
Jewellery
Year-Month
5
4
3
7
6
2
1
0
IVS
NONIVS
OTHERS
Total
Year-Month
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Proceedings of 10th Annual London Business Research Conference
10 - 11 August 2015, Imperial College, London, UK , ISBN: 978-1-922069-81-8
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