1 KULKUNYA PRAYARACH, PH.D. Multiple Regression Analysis I. Basic - PowerPoint PPT Presentation

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work 1 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work OUTLINE Basic Concept: Multiple Regression MULTICOLLINEARITY AUTOCORRELATION HETEROSCEDASTICITY REASEARCH IN FINANCE 2 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work BASIC CONCEPTS: Multiple Regression 𝑍 𝑗 = 𝛾 1 + 𝛾 2 𝑌 1 𝑗 + 𝛾 3 𝑌 2 𝑗 + 𝛾 4 𝑌 3 𝑗 + 𝑣 𝑗 3 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work BASIC CONCEPTS: Normality Assumption for • CLRM assumes that each is distributed normally with 𝑍 𝑗 = 𝛾 1 + 𝛾 2 𝑌 1 𝑗 + 𝛾 3 𝑌 2 𝑗 + 𝛾 4 𝑌 3 𝑗 + 𝑣 𝑗 4 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work BASIC CONCEPTS: Why we need Normality Assumptions of 5 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work BASIC CONCEPTS: Why we need Normality Assumptions of 1. Influence of the omitted or neglected variables is small and at best  Central Limit Theorem (CLT) random 2. Even if the number of variables is not very large or if these variables are not strictly independent, their sum may still be normally distributed 3. Must be normally distributed in order to make assumption of OLS estimators , are normally distributed 4. Normal distribution is a comparatively simple distribution involving only two parameters (mean and variance) Let’s say sample < 100 , normality assumption assumes a critical 5. role. If the sample size is reasonably large, normality is relaxed. 6. Large samples, t and F statistics have appropriately. TEST ‘BLUE’ Condition 6 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: Seasonally Adjusted • …is statistical methods of removing the seasonal component of a time series that is used when analyzing non-seasonal trends • Many economic phenomena have seasonal cycles 140 Dubai Crude Oil Price Seasonally Adjusted : 140 120 Census X12 Method 120 100 100 80 80 60 60 40 40 OIL OIL_SA 20 20 0 2009 2010 2011 2012 0 ม.ค. - 09 ก.ค. - 09 ต.ค. - 09 ม.ค. - 10 ก.ค. - 10 ต.ค. - 10 ม.ค. - 11 ก.ค. - 11 ต.ค. - 11 ม.ค. - 12 เม.ย. - 09 เม.ย. - 10 เม.ย. - 11 เม.ย. - 12 Jan Feb Mar Apr MayJune Jul Aug Sep Oct Nov Dec 7 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: Seasonally Adjusted 8 KULKUNYA PRAYARACH, PH.D.

ALTERNATIVE MODELS Stationary Granger (Unit Root Test: ADF) Causality Test H 0 : Non Station (unit root) Stationary : I(0) Non Stationary : I(1) First Diff (Reject H0), p ≤ 0.05 D(data) (Fail to Reject H 0 ) p > 0.05 VAR/VECM Stationary Data at I(0) or I(1) ECONOMETRIC PROBLEMS Multicollinearity If Multicollinearity Run: Xi = f(X1, X2,..,Xk) VIF > 10, then drop variable Rule of Thumb : VIF ≤ 10 No Multi VIF (  i) = 1 / 1 – R 2 ) VIF ( β i) = 1 / (1-R 2 ) If Autocorrelation Autocorrelation D.W. not 2, then AR(1) Test: Durbin Watson (D.W.)  2 No Autocorrelation If Heteroscedasticity ( p ≤ 0.05) Heteroscedasticity Transform Regression Test: White Test Yi /xi = b0\Xi, +b1 H 0 : Homoscedasticity, p > 0.05 ARCH/GARCH Yi/Xi 2 = b0\ Xi 2 , +b1/Xi Yi/  2 i = b0, +b1Xi /  2 i Clean Econometrix Problems GO AHEAD!!! RUN OLS : William H. Greene, Dr. Kulkunya Prayarach 9 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: Stationary • …is a stochastic process whose joint probability distribution does not change when shifted in time or space >>> Parameters (mean, variance) will not change overtime or position Stationary at level I(0) 10 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: Random Walk (Unit Root Process) Random Walk without Drift Random Walk with Drift 11 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: Unit Root Test  … a test of stationary (or nonstationary) where  Where u t is a white noise error term.  Test Augmented Dickey-Fuller (ADF) Test for Unit Root Test  Test H 0 : then UNIT ROOT (nonstationary) ~ Random walk without drift >>> CANNOT simply regress Y t on its lagged value Y t-1 12 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: How to Solve Unit Root Problem STEP 1: First Differentiate STEP 2 : Test Unit Root again  Test H 0 : ~ >>> Unit root (ACCEPT) STEP 3 : Second Differentiate  Test H 0 : if reject then NO Unit root 13 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis KULKUNYA PRAYARACH, PH.D. I. Basic Concepts 27 29 31 33 35 37 1/1/2009 1/4/2009 1/7/2009 1/10/2009 Exchange Rate II. Multicollinearity 1/1/2010 1/4/2010 1/7/2010 1/10/2010 1/1/2011 1/4/2011 III. Autocorrelation 1/7/2011 1/10/2011 1/1/2012 1/4/2012 100 120 140 160 IV. Heteroscedasticity 20 40 60 80 0 1/3/2006 3/22/2006 6/8/2006 8/24/2006 11/9/2006 1/30/2007 4/18/2007 7/5/2007 9/20/2007 5 Dec 07 19 Feb 08 5 May 08 Oil Price (WTI) 18 Jul 08 2 Oct 08 V. Research & Group Work 17 Dec 08 3 Mar 09 18 May 09 31 Jul 09 15 Oct 09 30 Dec 09 16 Mar 10 31 May 10 13 Aug 10 28 Oct 10 12 Jan 11 29 Mar 11 13 Jun 11 14 26 Aug 11 10 Nov 11 25 Jan 12 10 Apr 12

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work DATA PREPARATION: Gaussian, Standard or Classical Linear Regression Model (CLRM) 15 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 1: Abnormal profit % # of stock 16 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 2: Nonlinear Regression Taylor Series Expansion Gauss-Newton iterative Newton-Raphson iterative Method 17 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 3: 18 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 4: 19 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 5: 20 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 6: There must be sufficient variability in the values taken by the regressors. I. Conceptual Framework II. Empirical Evidence IV. Linkages: III. My Mapping Internal Factor, External Factor, Shock 21 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work Assumption 7: • X variables Should be vary 22 KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis I. Basic Concepts II. Multicollinearity III. Autocorrelation IV. Heteroscedasticity V. Research & Group Work MULTICOLLINEARITY: Is Multicollinearity seriously Problem? Assumption 8: • W hat is the nature of multicollinearity? • I s Multicollinearity really a problem? • W hat are its practical consequences? • H ow does one detect it? • W hat remedial measures can be taken to alleviate the problem of multicollinearity? 23 KULKUNYA PRAYARACH, PH.D.