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Unit root test, cointegration test, Granger causality test.

Does each variable have a stable mean?<br> a) Unit root test for performance variable<br> b) Unit root test for each marketing variable<br>Relationship marketing & performance:<br> a) In long-term equilibrium? Cointegration test<br> b) Which drives which? Granger Causality test Quantifying marketing effects in model<br> a) Cointegration: Vector Error Correction <br> b) No Cointegration: Vector Autoregressive<br>

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Unit root test, cointegration test, Granger causality test.

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  1. OZYEGIN UNIVERSITY • Data Analyst: Benson Nwaorgu

  2. Measurement steps needed • Does each variable have a stable mean? a) Unit root test for performance variable b) Unit root test for each marketing variable • Relationship marketing & performance: a) In long-term equilibrium? Cointegration test b) Which drives which? Granger Causality test 3. Quantifying marketing effects in model a) Cointegration: Vector Error Correction b) No Cointegration: Vector Autoregressive

  3. Assumption

  4. Do we see any trend? Are this variables really stationary??

  5. How many lags would be appropriate?

  6. Why Stationarizing(we desire)? To smooth data from spurious outcome! • How: Stationarizing variables: Differentiation Dsales=D(Sales) and DAdvertising=D(Advertising) • Test on EView: Augmented Dickey–Fuller test (ADF) is a test for a unit root in a time series • VARIABLES: ADVERTISING(M) and SALES(P) • STATIONARITY (FIXED MEAN AND VARIANCE) AND EVOLVING (NON FIXED MEAN AND VARIANCE)

  7. OUTCOME: UNIT ROOT ; Dataset: Lydia Pinkham

  8. ANY QUESTION SO FAR?? RECAP • Now we know how to read chart • How to stationarize our Variables • Why its important to sometimes employ the lag selection criteria • What UNIT ROOT is all about and how to test variables using ADF • Interpretation of outcomes! • Now lets see if these variables we measured (Advertising and sales) cointegrates in the long run? Do they??

  9. Stationarized Variables: JohanssenCointegration test and Granger causality Test • We want to know if there exist any form relationship in the short run and also in the long run? • Whether Sales Granger cause Advertising , vice versa • Question: When running JohanssenCointegration test which of the variables should we use? The first difference variable(stationarized variable) or Initial variable?

  10. Initial Variable Outcome: (1)No intercept, Trend or Test VAR, (3) Intercept(No trend) in CE and test VAR

  11. Differenced Variable Outcome: (1)No intercept, Trend or Test VAR, (2) Intercept(No trend) in CE and test VAR

  12. Initial Outcome: Which drives which? Granger Causality TEST

  13. Differenced Outcome: Which drives which? Granger Causality TEST

  14. Any Questions so far??? • RECAP! • Initial variable: We rejected our NULL Hypothesis @ *None*(No CE), FAILED to Reject at *Most 1* because we saw that variables are cointegrated meaning ADV and SALES have LR association (VEC) • First Differenced: Both *None* and at *most 1* (No CE) meaning ADV and Sales have no LR Association (VAR) • Granger causality: we REJECTED NULL: Sales does not Granger cause advertising: because P < 0.05 :*initial and differenced* Sales does granger cause Advertising • When we have Cointegration we should employ : Vector Error Correction • When variables are not Cointegrated we should use : Vector Autoregressive

  15. VEC; How do we make sense from this??

  16. Analysis: Predicting CE in short run and Long run! Analysis: Which is our target model? Advertising. We estimated our target model : As its our dependent variable . C(1)= Speed of adjustment towards the long run equilibrium, and its must be significant with negative sign: meaning long run causality from the independent variable sales. So we can say that there is LR causality running from Sales to Advertising. We can accept the result looking that the Negative coefficient and significant p value. Whether Sales have short run causality or not on Advertising? We use the WALD statistics to check short run from sales to advertising (C5,C6,C7) Null C(5)=C(6)=C(7)= 0 if we fail to reject the Null ; implies no short run causality running from sales to advertising. Wald test: Chi-square (0.0038) < 0.05, based on our NULL, we can say that c5=c6=c7 is not equal to zero. implies that we have a SR causality between sales to advertising

  17. THANK YOU FOR LISTENING Lots of Information! I guess

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