Dynamic Hierarchical Factor Model Application in Marketing:

Dynamic Hierarchical Factor Model Application in Marketing:

June 26, 2017 Yuxuan Yang Supervisor/ University Keyvan Dehmamy Felix Eggers Student number: 3009335

Master thesis, MSc Marketing, specialization Marketing Intelligent University of Groningen, Faculty of Economics and Business

ABSTRACT

1. INTRODUCTION

Price competition is a common weapon of retailers, but a price war takes the intensity of the competition to a new level. Price war is defined as “competing firms struggling to undercut one other’s prices” (Assael, 1990). It is one of the most severe competitions in the business battlefield. Even though a price war seems to boost brand sales in the beginning (Sotgiu & Gielens, 2015), from a long-term perspective, it eventually leads to irreversible, permanent damage to the market in several ways. A price war can damage brand loyalty, squeeze margins, and destroy the distribution channels of supermarket chains and brands (Heil & Helsen, 2001). Consumers are the only winners in this game because they benefit from price reductions. However, consumers also have to undertake upcoming quality reductions thanks to a price war.

Price promotion, as an essential marketing tool, has been widely adopted by marketers to attract customers’ attention, decrease manufacturers’ and retailers’ inventories, and boost sales performance in the short term. Previous researchers who have studied price segments have indicated that brands from different price segments have different price promotion patterns. Premium-priced brands usually tend to undertake more intensive price promotion than economy-priced brands, because they have a large revenue space that can be sacrificed to penetrate economy-priced segments. However, under the pressure of a price war, all manufacturers and retailers have to adapt their marketing strategies to survive. Limited studies exist on price promotion pattern change under a price war from the perspective of brands. The literature only shows that price promotion can weaken a price war’s efficiency at generating sales (Heil & Helsen, 2001). However, no study has explained how marketers adapt their price promotion strategy during a price war.

We use sales data on deodorants in major supermarket chains in the current study. The dataset consists of eight national deodorant brands and five major supermarket chains in the Netherlands sold over a period of 124 weeks. We manipulate and clean the dataset first, and then we extract the price promotion as well as the sales for the subsequent analysis.

The unique contributions of the current study are as follows: (1) The study applies a four-level DHFM in price promotion to estimate the price promotion pattern during a price war. (2) It decomposes the variance and looks into the main triggers of price promotion. (3) It assesses whether the common factor of price promotion has a strong capability to explain sales movement using FAVAR. In practice, this research provides a latent model for marketers to form rich insights on price promotion patterns under the impact of a price war. Therefore, this empirical evidence can guide marketers to form price promotions more rational and react more rapidly.

2. RELATED LITERATURE REVIEW

Price Promotion

Price Promotion is a topic in the marketing field that never goes out of fashion. Blattberg, Briesch, and Fox give the definition of price promotion as follows: “Temporary price discounts offered to a customer” (Blattberg, Briesch, & FOX, How Promotions Work, 1995). Price promotion, as a marketing tool, has a strong influence in different aspects (Kuntner & Teichert, 2016).

Price promotion is like a double-bladed sword for marketers. There is a great confrontation in the literature about the effect of price promotions (Ataman, Van Heerde, & Mela, 2010). On the one hand, price promotion can significantly boost sales in the short term (Bijmolt, Heerde, & Pieters, 2005). Brands conduct price promotion to enhance their market penetration without hurting customer retention (Ailawadi, Lehmann, & Neslin, 2001). On the other hand, price promotion contains destructive aspects for the market. Overusing price promotion can lead to high price sensitivity (Kopalle, Mela, & Marsh, 1999), weaker customer brand loyalty, and decreased base price elasticity (Bogomolova, Szabo, & Kennedy, 2017).

Nevertheless, price promotion attracts a lot of attention from both marketers and researchers because the expenditure on price promotion amounts to more than half their budget for many manufacturers (Ailawadi, Beauchamp, Donthu, Gauri, & Shankar, 2009). Furthermore, price promotion by both retailers and manufacturers influences sales performance (Ailawadi, Beauchamp, Donthu, Gauri, & Shankar, 2009). Bogomolova, Szabo, and Kennedy (2017) have indicated the three characteristics of marketers making price promotion decisions: (1) The decisions are made mainly based on intuition and untested assumptions. (2) Marketers lack empirical evidence to guide their actions, and their price promotion patterns usually confronts with academic findings. (3) Price promotion’s results are often ignored by marketers, and they are failed from learning from the previous price promotion experience.

Price promotion can lower the effectiveness of a price war (Sotgiu & Gielens, 2015). Price promotion lowers consumers’ expected price level of a brand because they expect more intense promotion in the near future (Mela, Gupta, & Lehmann, 1997).

Price War

price war: (1) Manufacturers and retailers’ actions and reactions are based on competitors’ actions and reactions. (2) Price changes are undesirable for all the players in the market. (3) None of the retailers and manufacturers intend to launch a price war. (4) Price changes do harm to market norms. (5) Price changes occur rapidly. (6) Decreasing prices are a major trend during a price war. (7) Price interaction is not sustainable. (Heil & Helsen, 2001)

Unlike price promotion, price wars are usually not well communicated to consumers. Retailers tend to misrepresent a price war to consumers as a permanent price reduction (Sotgiu & Gielens, 2015). There are several reasons a price war can start. For instance, marketers who lack an understanding of the market and the industry are more willing to launch a price war to penetrate the market and expect to win a larger market share from their competitors’ grasp (Ramaswamy, Gatignon, & Reibstein, 1994).

Regarding the impact of price wars, from a short-term perspective, manufacturers and retailers can benefit from it. Retailers often launch price wars on national brands to drive more traffic (Sotgiu & Gielens, 2015). Sales are boosted in the beginning as well (Heil & Helsen, 2001). However, in the long term, price wars tend to have a severe negative influence on the market. The consequences can be as follows: (1) A price war can damage brand equity. Heavy price reduction can even strongly affect consumers’ brand loyalty (Blattberg, Briesch, & FOX, How Promotions Work, 1995). (2) The overall revenue of both retailers and brands can decrease (Heil & Helsen, 2001). (3) An intensive price war can even lead to a radical change in the distribution channel (Heil & Helsen, 2001). Sotgiu and Gielen (2015) divided price wars into three distinctive stages. First, prices remain on a high level (pre-price war constant stage); subsequently, retailers reduce prices significantly and keep them at a low level for a long period (post-price war constant stage). Finally, retailers decide to end the price war and increase prices back to the normal level (post-price war lift stage), which represents the end of the price war. Because a price war has a permanent impact on reduction of the price baseline, it might also have a lasting effect on a brand’s price promotion decisions.

Price Segmentations

price sensitive. Thus, when an economy-priced brand launches its price promotion, it can be more influential among customers from other economy-priced brands. Moreover, a premium-priced brand’s loyal consumers are more quality driven, and so an economy-premium-priced brand’s price promotion has less influence on their choices. However, economy-priced loyalty customers can be easily induced by premium-priced brands if they launch a large price promotion (Blattberg &Kenneth,1989). Thus, price promotion by premium-priced brands is more effective on both segments, and its overall influence is better than economy-priced brands’ price promotion. However, price promotion also has some side effects for premium-priced brands. It can lead to the misconception among consumers that the brand has overestimated its value.

3. ECONOMETRIC FRAMEWORK

3.1. Dynamic Hierarchical Factor Model

In the current study, we introduce the DHFM, which was proposed by Moench and Ng in 2011. The literature has shown great interest in examining the co-movement of a brand’s price promotion under the influence of a price war. The dynamic factors model (DFM), which was introduced by Geweke in 1977, has been naturally implemented in macroeconomic analysis, especially by corporates with stochastic latent factor processes in cross-sectional data (Aguilar & West, 2000). DFM is capable of being applied in a dataset in which the number of time series is much more than the observations within each of the time series (Stock & Watson, 2011). Even though the DFM was originally introduced in economics, it has been widely applied in different fields, such as processing mentoring, the energy market (electronic price), the telecommunication market, and marketing research.

A structural DFM called DHFM was introduced by Moench and Ng in 2011 as one of DFM’s extensions. Compared to the DFM, the advantages of the DHFM is that it can capture co-movement from different levels (aggregate, block-specific, subblock-specific components, and idiosyncratic noises) in large and dynamic panel data, and it also allows us to estimate and interpret results more easily (Moench, Ng, & Potter, 2013). Based on model building and the notations by Moench et al. (2011), the four-level decomposition has been written below (from low to high level).

𝑍_"#$%= Λ_(."#$ 𝐿 𝐻_"#%+ 𝑒_("#$% (3.1) 𝐻_"#% = Λ_.."# 𝐿 𝐺_"% + 𝑒_0"#% (3.2) 𝐺_"% = Λ_1." 𝐿 𝐹_%+ 𝑒_."% (3.3) Ψ₁(𝐿)𝐹_% = 𝜖_1% (3.4)

block specific levels respectively. The highest level reflects to the evolvement of the common factor Ft.

The four-level DHFM aims to capture the co-movement of different deodorant brands’ price promotion patterns and to estimate and interpret the variance of different blocks’ reaction to the price war. More specifically, 𝐹_% denotes the common movement of the market (level 4). 𝐹_% has an influence on the block-specific factor (level 3), the premium-priced brand segment (𝐺_9%), and the economy-priced segment (𝐺_:%). In level 2, the sub-block specific factor is characterized as 𝐻_"#%, which consists of eight deodorant brands. Based on the previous literature, brands within the same price segments have relatively similar price promotion strategies. Thus, high-level correlation is expected among them. Level 1 classification is denoted as 𝑍_"#$%, which includes the individual price promotion of different brands in each supermarket chain. Each price promotion movement is decomposed to a brand level common factor 𝐻_"#% and idiosyncratic noise 𝑒_("#$%. Based on the description above, the structure of the model is presented in Table 1 (Appendix B).

For the estimation, each factor in this DHFM (the common factor, group specific factor, sub-group specific factor, and idiosyncratic noises) was assumed to be stationary, normally distributed, and in the form of autoregression. To conclude, following Emanuel Moench and Serena Ng (2011), the equation below has been written as follows:

𝜖_("#$%= 𝜓_("#$ 𝐿 𝑒_("#$% 𝜖_("#$% ~ 𝑁(0, 𝜎_("#$: _{) (3.5)}

𝜖_0"#% = 𝜓_0"# 𝐿 𝑒_0"# 𝜖_0"# ~ 𝑁(0, 𝜎_0"#: _{) (3.6)}

𝜖_."%= 𝜓_." 𝐿 𝑒_("#$% 𝜖_("#$% ~ 𝑁(0, 𝜎_.": _{) (3.7)}

𝜖_1% = 𝜓₁(𝐿)𝐹_% 𝜖_1% ~ 𝑁(0, 𝜎₁:_{) (3.8)}

Estimation Method

time were applied in principle component analysis to estimate the initial value of factors 𝐹%,

𝐺_%, and 𝐻_%.

3.2. Factor Augmented Vector Autoregressive Model

The FAVAR model was first introduced by Bernank, Boivin, and Eliasz in 2005. FAVAR combines the standard vector autoregressive model with factor analysis. The latent factor in this autoregressive cannot be captured by simple aggregation of low-dimension variables. This model only obtains a limited number of factors but to capture valid information from a large dataset. Thus, compared to VAR, the FAVAR model finds a balance point between information deficiency and degree-of-freedom problems (Bai, Li, & Lu, 2016). We closely followed the notions of Bernank, Boivin, and Eliasz (2005). The formula we used is shown below:

1@ A@ = Φ 𝐿 1@CD A@CD + 𝑣% (3.9) 𝑋_%` <sub>= Λ</sub>H<sub>𝐹</sub> %`+ ΛI𝑌%`+ 𝑒%` (3.10)

The simple mathematical description of the model is provided in this paper. An in-depth description of the model can be found in the original paper by Bernank, Boivin, and Eliasz (2005). We proposed FAVAR models with different lags and chose the most appropriate model with the least Akaike information criterion (AIC). After constructing the FAVAR model, a pure autoregressive model was selected as the benchmark model in the current study to assess the predictive performance. The autoregressive model of order p is shown below:

𝑦%= 𝛿 + 𝜃9𝑦%N9+ 𝜃:𝑦%N:+ 𝜃O𝑦%NO+ ⋯ + 𝜃Q𝑦%NQ + 𝑣% (3.11),

Where 𝛿 and 𝑣% represent the constant and error term respectively. 𝑦% shows the value at

4.

DATA

The University of Groningen provided the sales data on Dutch deodorants from major supermarkets. The dataset contained eight deodorant brands (DOVE, FA, NIVEA, SANEX, VOGUE, X8X4, and AXE) across five supermarket chains (Albert Heijn, Jumbo, C-1000, Super de Boer, and Edah) from November 10, 2003, to March 20,2006. Each chain and brand consisted of the following variables: time, sales, price, regular price, promotion on display, promotion and feature, promotion and both display and promotion. Only chains, sales, price, regular price, and date were selected as a sub-dataset and applied in the following analysis.

Next, we examined the validity of the dataset. First, the brand VOGUE in supermarket chain Edah had radical values in regular price, as well as missing values in actual price. To solve this, regular price, which was under two euro, was identified as an oddity value and replaced by the mean of VOGUE regular price, which was higher than 2.5 euro. The missing actual price of VOGUE in Edah was also replaced by the mean of VOGUE. Second, the regular price was calculated as the average price of specific brands in supermarkets that did not have any promotions that week, because there would be no regular price for a specific brand if all the supermarkets had launched a promotion. Therefore, the missing regular price was imputed by the mean of the regular price two weeks before and after the missing values. The basic statistics of the selected variables are summarized in Appendix A.

Defining Premium-Priced and Economy-Priced Segments

Figure 1. Boxplot of actual price in different brands

Price Promotion

We calculated the price promotion of each brand s in supermarket chain n at given time t. the formula is shown below. Price promotion PP of brand s in supermarket chain n at time t equals to the regular price RP minus price of brand s in supermarket chain n at given time t.

𝑃𝑃#$% = 𝑅𝑃#$T− 𝑃#$T (4.1)

The calculated price promotion contained negative values because the regular price represented the average price of the specific brand from supermarket chains. To have a more rational dataset, the negative value from the price promotion was replaced to 0. Figure 2 below gives an overview of the price promotion of each brand across all the supermarket chains from 2003 to 2006.

Figure 2. Brand price promotion performance across supermarket chains

Sales Data

5.

EMPIRICAL RESULTS

Variance Decomposition

To find out the main triggers behind the price promotion patterns, we applied a variance decomposition analysis. Variance decomposition can be used to disentangle the effects of various shocks, and moreover, it estimates the contribution of each level of the structure to the error terms. The total variance of price promotion of each brand 𝑉𝑎𝑟 𝑍_"#$ can be decomposed to

𝑉𝑎𝑟 𝑍_"#$ = g₁ 𝑉𝑎𝑟 𝐹 + g_. 𝑉𝑎𝑟 𝑒_." + g₀ 𝑉𝑎𝑟 𝑒_0"# + g₍ 𝑉𝑎𝑟 𝑒_("#$ （5.1）

where g is a composite of parameters Λ related to the equation (3.1) to (3.3). The following variance shares are calculated below. The first line is the share of the common factor. The second line is the block-specific factor. The third line is the sub-block specific factor. In the end, the fourth line is the idiosyncratic factor.

g₁ 𝑉𝑎𝑟 𝐹 ／𝑉𝑎𝑟 𝑍_"#$ (5.2) g_. 𝑉𝑎𝑟 𝑒_." ／𝑉𝑎𝑟 𝑍"#$ (5.3)

g₀ 𝑉𝑎𝑟 𝑒_0"# ／𝑉𝑎𝑟 𝑍_"#$ (5.4) g₍ 𝑉𝑎𝑟 𝑒_("#$ ／𝑉𝑎𝑟 𝑍"#$ (5.5)

Figure 4. Variance decomposition of different price segments

Posterior Mean (Standard Deviation)

Block Names Sub-block Names Share F Share G Share H Share Z

Economy-Priced Brands FA 0,024(0,0169) 0,035(0,009) 0,030(0,006) 0,910(0,0184) SANEX 0,003(0,004) 0,007(0,0106) 0,216(0,022) 0,774(0,0193) VOGUE 0,002(0,003) 0,003(0,004) 0,108(0,087) 0,888(0,088) X8X4 0,002(0,003) 0,005(0,007) 0,256(0,024) 0,738(0,023) Premium-Priced Brands DOVE 0,175(0,0224) 0,069(0,010) 0,0634(0,007) 0,692(0,023) NIVEA 0,0169(0,011) 0,007(0,004) 0,173(0,052) 0,803(0,056) REXONA 0,025(0,012) 0,010(0,005) 0,189(0,016) 0,775(0,005) AXE 0,002(0,004) 0,001(0,002) 0,246(0,0215) 0,750(0,022)

Table 1. Decomposition of Variance Table

Impulse Responses

To understand the different reactions of each brand and each price segment to the price war, we applied a positive shock of one standard deviation to the common factor 𝐹 to witness the diffusion of the influence from the upper level to the bottom level of the dynamic hierarchy.

Figure 5. Impulse responses of common F, block-specific Gb, and sub-block specific Hb, factors from a shock on the common factor.

Both price segments have similar patterns regarding the shock on the common factor. They have a sharp increase until week 4 and reach a peak. After that, they decay for approximately 20 weeks and disappear. However, the premium-priced segment reacts to a price war more intensively with regard to the depth of price promotion, compared to the economy-priced segment. In terms of the individual brands, only three brands (DOVE, REXONA, and FA) have a significant positive impulse response.

Forecasting

We also made predictions for eight brands in each supermarket chain, and we compared the prediction results with the test sample. The line charts in Appendix C shows that the DHFM is not capable of predicting the price promotion in this case. It cannot capture price promotion’s fluctuations in any of the brands.

Sales Prediction Through the FAVAR Model

The FAVAR model was applied to predict the sales performance of individual brands, different price segments, and the deodorant market. The common F was extracted from the previous DHFM model, and furthermore, it was considered to be an exogenous variable in FAVAR. We divided the deodorant data into two parts: the training sample (1–100 weeks) and the testing sample (101–124 weeks). The training sample was used to train the FAVAR model and compare the prediction outcome with the test sample. Furthermore, a first-order autoregressive model was introduced in this part as benchmark model. We compared the predictive validity through APE and ASPE.

Figure 7 The sales prediction on the common level

Figure 8. The sales prediction of the economy-priced segment

Figure 9. The sales prediction of the premium-priced segment

Figures 15 to 22 in the appendix predict the sales of individual brands in the Dutch market. Prediction performances varied among different brands. AXE, DOVE, and SANEX made for satisfying predictions, and the majority of the fluctuations were captured. However, FAVAR was not capable of predicting FA, NIVEA, REXONA VOGUE, and X8X4 because of extreme fluctuations in their data.

Then, the AR model was applied through the same procedures as the FAVAR model, and sales prediction was made accordingly. APE and ASPE assessed the estimation validation. The APE assessed whether the prediction had systematic away from the actual data. Both FAVAR and AR were acceptable as criteria and indicated that both models had a lack of bias. ASPE indicated the overall prediction performance. Table 2 below shows the assessment of predictive performance between FAVAR and AR in different levels. We did not witness a significant improvement with the FAVAR model compared to the benchmark.

Prediction Performance Comparison between FAVAR and AR

FAVAR AR

ASPE APE ASPE APE

Market in General 49179.82 39.54569 48866.54 31.40268

Premium-priced segment 52885.89 8.679442 50195.15 14.92877

NIVEA 5341.902 -9.790454 5292.348 -9.397633 REXONA 48189.52 2.73934 48652.86 1.6039 SANEX 2128.806 3.065669 2141.035 3.171246 VOGUE 8518.264 -14.63389 8471.548 -14.26633 X8X4 1443.739 55.42425 2528.707 45.59099 AXE 2546.768 37.68668 2147.985 36.1875

6.

CONCLUSION

To estimate the different price promotion patterns under the impact of a price war, the DHFM was introduced to capture the co-movement from different levels of the structure. Monte Carlo Markov Chain (MCMC) was used to extract the factors from the deodorant dataset.

Variance decomposition was first applied to estimate the main drivers of price promotion. It was found that supermarket chains dominate the movement of price promotion in the deodorant market. Individual brands also have a moderate capability to explain the price promotion pattern. However, a price promotion strategy is less likely to be affected by price segments and the deodorant market in general.

Then, an impulse response analysis was conducted to predict how brands from different price segments will respond if a price war starts. It was found that different segments do show distinctive differences under the pressure of a price war. Premium-priced brands tend to conduct a more in-depth price promotion of longer duration compared to economy-priced brands. The results are in line with Blattberg and Kenneth’s findings. They have indicated that the depth of price promotion in premium-priced brands is larger than in economy-priced brands because they can gain more advantages from this movement (Blattberg & Kenneth, 1989).

Further, the predictive performance of DHFM in price promotion was assessed. We took the first 100 weeks to train the model and predict the price promotion in the upcoming 24 weeks compared to the real data. As a result, the overall predictive validity was not found acceptable. The model could not capture the trend and the fluctuation properly. Thus, we concluded that the DHFM is not a capable method for predicting price promotion.

We were also interested in assessing the explanation capability of price promotion to sales and in another word, assessing whether price promotion can enhance the prediction of sales. The FAVAR method was applied to predict sales with the latent factor price promotion and was compared with the benchmark model AR. On the one hand, the prediction performance of FAVAR was satisfying, especially on the higher level (3 and 4). It could predict trends and capture most of the fluctuations. On the other hand, when we compared this model to the benchmark model, we found that the prediction validity was not significantly better than the benchmark. Thus, we concluded that price promotion does not have a significant influence on sales performance.

the price promotion pattern changes under the impact of a price war. In addition, this research also assesses the possibility of applying the common factor of price promotion on the explanation of sales performance.

The current study suggests that marketing managers can implement DHFM in the marketing field. Marketers can decompose competitors’ price promotion patterns. In this way, marketers gain a more objective insight into the main drivers behind their price promotion patterns and adjust their strategic reasoning accordingly. The impulse response provides extra evidence for managers to forecast price promotion patterns from different angles under the shock of a price war. Also, this research suggests marketers not to implement the common latent factor on the prediction of sales.

The current study had several limitations. First, the study was conducted based on a deodorant dataset in the Netherlands. Country of origin and product category can both have an influence on the results. Second, the study was restricted by the size of the database. It consisted of only eight brands in five supermarket chains assessed over a period of 124 weeks. Therefore, the co-movements between the eight brands was not salient because the DHFM could not sufficiently capture the information and benefit from the structure. At last, the price promotion data contained a series of radical fluctuations that made it difficult for our model to estimate trends.

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APPENDIX A. Basic Statistics of Deodorant Database

Statistic N Mean St. Dev. Min Max

DOVESales 620 25.774 20.206 5.490 195.780 FASales 620 30.958 32.164 3.480 395.880 NIVEASales 620 21.052 25.577 4.370 302.670 REXONASales 620 60.940 92.616 7.090 849.150 SANEXSales 620 30.949 35.133 5.820 374.810 VOGUESales 620 19.168 28.025 0.070 434.360 X8X4Sales 620 29.532 20.801 3.010 109.260 AXESales 620 57.883 49.231 9.740 545.680 DOVEPrice 620 2.423 0.375 1.578 3.067 FAPrice 620 1.673 0.180 1.049 2.420 NIVEAPrice 620 2.714 0.303 1.795 3.308 REXONAPrice 620 2.395 0.385 1.421 2.991 SANEXPrice 620 2.195 0.288 1.402 2.890 VOGUEPrice 620 2.237 0.311 1.086 2.751 X8X4Price 620 1.862 0.410 1.220 2.543 AXEPrice 620 2.987 0.340 2.050 3.691 DOVERPrice 620 2.454 0.371 0.983 3.072 FARPrice 620 1.700 0.168 1.255 2.444 NIVEARPrice 620 2.759 0.286 2.005 3.485 REXONARPrice 620 2.446 0.381 0.978 3.228 SANEXRPrice 620 2.223 0.285 1.787 2.892 VOGUERPrice 620 2.279 0.306 1.139 2.752 X8X4RPrice 620 1.875 0.408 1.220 2.543 AXERPrice 620 3.024 0.334 2.163 3.698 WEEKNR 620 26.048 16.232 1 53 YEAR 620 2,004.556 0.744 2,003 2,006

APPENDIX B. List of Brands and Hierarchical Classificaiton

Level 4 Level 3 Level 2 Level 1(Z)

The whole Dutch deodorant market

(F)

Premium-priced Brands

(𝐺₉)

Dove(𝐻₉₉) Albert Heijn

Edah Super de Boer

Jumbo C1000

Nivea(𝐻_9:) Albert Heijn

Edah Super de Boer

Jumbo C1000

Rexona(𝐻_9O) Albert Heijn

Edah Super de Boer

Jumbo C1000

Axe(𝐻_9Y) Albert Heijn

Edah Super de Boer Jumbo C1000 Economy-priced Brands (𝐺_:)

Fa(𝐻:9) Albert Heijn

Edah Super de Boer

Jumbo C1000

Sanex(𝐻::) Albert Heijn

Edah Super de Boer

Jumbo C1000

Vogue(𝐻_:O) Albert Heijn

Edah Super de Boer Jumbo C1000 X8X4(𝐻_:Y) Albert Heijn Edah Super de Boer Jumbo C1000

APPENDIX C. Prediction of Price Promotion through FAVAR

x

Figure 10. Prediction Charts of Price Promotion in EDAH

Figure 12. Prediction Charts of Price Promotion in Jumbo

Figure 13 Prediction Charts of Price Promotion in Super de Boer

APPENDIX D. FAVAR Prediction

Figure 15. The sales prediction of DOVE

Figure 16. The sales prediction of FA

Figure 17. The sales prediction of NIVEA

Figure 19 The sales prediction of SANEX

Figure 20The sales prediction of VOGUE

Figure 21 The sales prediction of X8X4

APPENDIX E. The formula of APE and ASPE

Leeflang, Wittink, Wedel and Naert (2000) discussed several methods to measure the predictive performance. These methods focus on the bias and variance. In other word, the model with a better predication capacity should have a smaller bias and also with a smaller variance. In this research, we choose APE and ASPE to measure the predict performance. The formula is shown in below:

𝐴𝑃𝐸 = (𝑦%− 𝑦%) \ %]\∗_{_9} 𝑇 − 𝑇∗ (𝐸. 1) 𝐴𝑆𝑃𝐸 = (𝑦%− 𝑦%) \ %]\∗_{_9} : 𝑇 − 𝑇∗ (𝐸. 2)

For both formula APE and ASPE in this research, the t = 1,...,T* denotes the training sample. t