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The Impact of Drinks on the Bread Market: A Var Modeling Analysis

This study examines the correlation between drink sales and bread purchases using VAR modeling. The data analysis reveals negative correlation, suggesting that customers tend to buy drinks without bread. The study proposes the VAR(1) model due to its simplicity and desirable normality. Prediction results show potential for growth in the drinks market. Further tests, such as cointegration and Granger causality, are suggested for more comprehensive analysis.

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The Impact of Drinks on the Bread Market: A Var Modeling Analysis

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  1. The Relation between Drinks and Bread Chia-chi Liu Stat, NCU 1/4/2011

  2. Outline • Introduction and Motivation • Data • The ProposalModel • Data Analysis • Conclusions • References

  3. Introduction And Motivation • Nowadays, drinks have become indispensable in our life. • Maybe we buy a bread and a drink for breakfast, so I add the sale volume of bread into data • My reference is due to the data of Uni-PresidentGroup during 2006.01-2010.11

  4. Data

  5. Time Series Plot

  6. Time Series Plot

  7. The Proposed Model • At first, I proposed the SARIMA model when I only have the data of drinks. • After added another data and both of data are not difficult to get stationary, so I proposed the VAR model.

  8. Var model Suppose a collection of k output variable exist that are related to the input as for each of i=1,2,…,k output variables. Assume that for t=s and zero otherwise. In matrix notation, with being the vector of outputs, and , i=1,…,k, j=1,…,r being k×r matrix containing the regression coefficients, lead to

  9. Data analysis - drink

  10. Data analysis - bread

  11. Data analysis • The covariance matrix: • The correlation matrix:

  12. Data analysis – model selection or

  13. Data analysis – var(1)

  14. Data analysis – residual of var(1) of drink

  15. Data analysis – residual of var(1) of bread

  16. Data analysis – var(2)

  17. Data analysis – residual of var(2) of drink

  18. Data analysis – residual of var(2) of bread

  19. Data analysis Compare these two plots, model 1 is better than 2. Compare these two plots, model 2 is better than 1.

  20. Predition – var(1)

  21. Predition – var(2)

  22. Conclusion • Due to correlation matrix, we can conclude that the data had negative correlation. That means people buy drink didn’t buy bread. • The better normality and more simple model are we desired, so choose VAR(1). • The result of prediction is not good enough cause the data are too small, though the predictor are all in confidence interval. • There are more test we can do: cointegration, granger causility.

  23. More analysis - sarima • To analysis the data of drinks by SARIMA. • First we get stationary time series.

  24. Sarima – analysis • By ACF and PACF plots, we get four probably model. • Sarima(1,1,0,1,1,1,12) • Sarima(2,1,0,1,1,1,12) • Sarima(1,1,1,1,1,1,12) • Sarima(2,1,1,1,1,1,12)

  25. Sarima – model selection • Sarima(1,1,0,1,1,1,12), AIC=-4.474674

  26. Sarima – model selection • Sarima(2,1,0,1,1,1,12), AIC=-4.509912

  27. Sarima – residual test • Normality

  28. Sarima – prediction • We forecast 12 data ahead.

  29. Sarima – conclusion • From the plot of prediction we know DRINKS market is full of potential. • If we have enough money, then maybe we can choose nice place and have a tea shop. • Maybe we will get rich someday!!!

  30. References • Time series analysis and its application with R example • http://www.uni-president.com.tw/index.asp • http://finzi.psych.upenn.edu/R/library/vars/doc/vars.pdf • Data link: http://www.uni-president.com.tw/invest/investor01.asp

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