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The Relation between Drinks and Bread

The Relation between Drinks and Bread. Chia -chi Liu Stat, NCU 1/4/2011. Outline. Introduction and Motivation Data The Proposal Model Data Analysis Conclusions References. Introduction And Motivation. Nowadays, drinks have become indispensable in our life.

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The Relation between Drinks and Bread

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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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