+-------+ ----+ Title +------------------------------------------------------------
lmharch: OLS Heteroscedasticity Engle (ARCH) Test
+-------------------+ ----+ Table of Contents +------------------------------------------------
Syntax Description Options Saved Results References
*** Examples
Authors
+--------+ ----+ Syntax +-----------------------------------------------------------
lmharch depvar indepvars [if] [in] , [ noconstant lags(#) coll ]
+-------------+ ----+ Description +------------------------------------------------------
lmharch computes OLS Engle LM AutoRegressive Conditional Heteroscedasticity (ARCH) Test
R2, R2 Adjusted, and F-Test, are obtained from 4 ways: 1- (Buse 1973) R2. 2- Raw Moments R2. 3- squared correlation between predicted (Yh) and observed dependent variable (Y). 4- Ratio of variance between predicted (Yh) and observed dependent variable (Y).
- Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1). - F-Test=R2/(1-R2)*(N-K-1)/(K).
+---------+ ----+ Options +----------------------------------------------------------
lags(#) Order of Lag Length
noconstant Exclude Constant Term from Equation
coll keep collinear variables; default is removing collinear vari > ables.
+---------------+ ----+ Saved Results +----------------------------------------------------
lmharch saves the following in e():
e(lmharch_#) Engle LM ARCH Test AR(i) e(lmharchp_#) Engle LM ARCH Test AR(i) P-Value
+------------+ ----+ References +-------------------------------------------------------
Damodar Gujarati (1995) "Basic Econometrics" 3rd Edition, McGraw Hill, New York, USA.
Engle, Robert (1982) "Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation" Econometrica, 50(4), July, 1982; 987-1007.
+----------+ ----+ Examples +---------------------------------------------------------
clear all
sysuse lmharch.dta , clear
db lmharch
lmharch y x1 x2 , lags(4) -------------------------------------------------------------------------------
. clear all . sysuse lmharch.dta , clear . lmharch y x1 x2 , lags(4)
============================================================================== * Ordinary Least Squares (OLS) ============================================================================== y = x1 + x2 ------------------------------------------------------------------------------ Sample Size = 17 Wald Test = 273.3662 | P-Value > Chi2(2) = 0.0000 F-Test = 136.6831 | P-Value > F(2 , 14) = 0.0000 (Buse 1973) R2 = 0.9513 | Raw Moments R2 = 0.9986 (Buse 1973) R2 Adj = 0.9443 | Raw Moments R2 Adj = 0.9984 Root MSE (Sigma) = 5.5634 | Log Likelihood Function = -51.6471 ------------------------------------------------------------------------------ - R2h= 0.9513 R2h Adj= 0.9443 F-Test = 136.68 P-Value > F(2 , 14) 0.0000 - R2v= 0.9513 R2v Adj= 0.9443 F-Test = 136.68 P-Value > F(2 , 14) 0.0000 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | 1.061709 .2666739 3.98 0.001 .4897506 1.633668 x2 | -1.382986 .0838143 -16.50 0.000 -1.562749 -1.203222 _cons | 130.7066 27.09429 4.82 0.000 72.59515 188.8181 ------------------------------------------------------------------------------ ============================================================================== *** OLS Heteroscedasticity Engle (ARCH) Test ============================================================================== Ho: Homoscedasticity - Ha: Heteroscedasticity ------------------------------------------------------------------------------ - Engle LM ARCH Test AR(1) E2=E2_1-E2_1= 1.4900 P-Value > Chi2(1) 0.2222 - Engle LM ARCH Test AR(2) E2=E2_1-E2_2= 1.7011 P-Value > Chi2(2) 0.4272 - Engle LM ARCH Test AR(3) E2=E2_1-E2_3= 3.1166 P-Value > Chi2(3) 0.3740 - Engle LM ARCH Test AR(4) E2=E2_1-E2_4= 4.1508 P-Value > Chi2(4) 0.3860 ------------------------------------------------------------------------------
+---------+ ----+ Authors +----------------------------------------------------------
- Emad Abd Elmessih Shehata Professor (PhD Economics) Agricultural Research Center - Agricultural Economics Research Institute - Eg > ypt Email: emadstat@hotmail.com WebPage: http://emadstat.110mb.com/stata.htm WebPage at IDEAS: http://ideas.repec.org/f/psh494.html WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm
- Sahra Khaleel A. Mickaiel Professor (PhD Economics) Cairo University - Faculty of Agriculture - Department of Economics - Egypt Email: sahra_atta@hotmail.com WebPage: http://sahraecon.110mb.com/stata.htm WebPage at IDEAS: http://ideas.repec.org/f/pmi520.html WebPage at EconPapers: http://econpapers.repec.org/RAS/pmi520.htm
+------------------+ ----+ LMHARCH Citation +-------------------------------------------------
Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2012) LMHARCH: "OLS Heteroscedasticity Engle (ARCH) Test"
Online Help:
* Heteroscedasticity Tests:
* (1) (OLS) * Ordinary Least Squares Tests: lmhreg OLS Heteroscedasticity Tests lmharch OLS Heteroscedasticity Engle (ARCH) Test lmhcw OLS Heteroscedasticity Cook-Weisberg Test lmhgl OLS Heteroscedasticity Glejser Test lmhharv OLS Heteroscedasticity Harvey Test lmhhp OLS Heteroscedasticity Hall-Pagan Test lmhmss OLS Heteroscedasticity Machado-Santos-Silva Test lmhwald OLS Heteroscedasticity Wald Test lmhwhite OLS Heteroscedasticity White Test --------------------------------------------------------------------------- * (2) (NLS) * Non Linear Least Squares Tests: lmhnls Non Linear Least Squares Heteroscedasticity Tests lmharchnl NLS Heteroscedasticity Engle (ARCH) Test lmhcwnl NLS Heteroscedasticity Cook-Weisberg Test lmhglnl NLS Heteroscedasticity Glejser Test lmhharvnl NLS Heteroscedasticity Harvey Test lmhhpnl NLS Heteroscedasticity Hall-Pagan Test lmhmssnl NLS Heteroscedasticity Machado-Santos-Silva Test lmhwaldnl NLS Heteroscedasticity Wald Test lmhwhitenl NLS Heteroscedasticity White Test --------------------------------------------------------------------------- * (3) (MLE) * Maximum Likelihood Estimation Tests: lmhmle MLE Heteroscedasticity Tests lmharchml MLE Heteroscedasticity Engle (ARCH) Test lmhcwml MLE Heteroscedasticity Cook-Weisberg Test lmhglml MLE Heteroscedasticity Glejser Test lmhharvml MLE Heteroscedasticity Harvey Test lmhhpml MLE Heteroscedasticity Hall-Pagan Test lmhmssml MLE Heteroscedasticity Machado-Santos-Silva Test lmhwaldml MLE Heteroscedasticity Wald Test lmhwhiteml MLE Heteroscedasticity White Test --------------------------------------------------------------------------- * (4) (2SLS-IV) * Two-Stage Least Squares & Instrumental Variables Tests: lmhreg2 2SLS-IV Heteroscedasticity Tests lmharch2 2SLS-IV Heteroscedasticity Engle (ARCH) Test lmhcw2 2SLS-IV Heteroscedasticity Cook-Weisberg Test lmhgl2 2SLS-IV Heteroscedasticity Glejser Test lmhharv2 2SLS-IV Heteroscedasticity Harvey Test lmhhp2 2SLS-IV Heteroscedasticity Hall-Pagan Test lmhmss2 2SLS-IV Heteroscedasticity Machado-Santos-Silva Test lmhwald2 2SLS-IV Heteroscedasticity Wald Test lmhwhite2 2SLS-IV Heteroscedasticity White Test --------------------------------------------------------------------------- * (5) Panel Data Tests: lmhxt Panel Data Heteroscedasticity Tests lmhgwxt Panel Data Groupwise Heteroscedasticity Tests ghxt Panel Groupwise Heteroscedasticity Tests lmhlmxt Panel Data Groupwise Heteroscedasticity Breusch-Pagan LM Test lmhlrxt Panel Data Groupwise Heteroscedasticity Greene LR Test lmharchxt Panel Data Heteroscedasticity Engle (ARCH) Test lmhcwxt Panel Data Heteroscedasticity Cook-Weisberg Test lmhglxt Panel Data Heteroscedasticity Glejser Test lmhharvxt Panel Data Heteroscedasticity Harvey Test lmhhpxt Panel Data Heteroscedasticity Hall-Pagan Test lmhmssxt Panel Data Heteroscedasticity Machado-Santos-Silva Test lmhwaldxt Panel Data Heteroscedasticity Wald Test lmhwhitext Panel Data Heteroscedasticity White Test --------------------------------------------------------------------------- * (6) (3SLS-SUR) * Simultaneous Equations Tests: lmareg3 (3SLS-SUR) Overall System Autocorrelation Tests lmhreg3 (3SLS-SUR) Overall System Heteroscedasticity Tests lmnreg3 (3SLS-SUR) Overall System Non Normality Tests lmcovreg3 (3SLS-SUR) Breusch-Pagan Diagonal Covariance Matrix r2reg3 (3SLS-SUR) Overall System R2, F-Test, and Chi2-Test diagreg3 (3SLS-SUR) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- * (7) (SEM-FIML) * Structural Equation Modeling Tests: lmasem (SEM-FIML) Overall System Autocorrelation Tests lmhsem (SEM-FIML) Overall System Heteroscedasticity Tests lmnsem (SEM-FIML) Overall System Non Normality Tests lmcovsem (SEM-FIML) Breusch-Pagan Diagonal Covariance Matrix Test r2sem (SEM-FIML) Overall System R2, F-Test, and Chi2-Test diagsem (SEM-FIML) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- * (8) (NL-SUR) * Non Linear Seemingly Unrelated Regression Tests: lmanlsur (NL-SUR) Overall System Autocorrelation Tests lmhnlsur (NL-SUR) Overall System Heteroscedasticity Tests lmnnlsur (NL-SUR) Overall System Non Normality Tests lmcovnlsur (NL-SUR) Breusch-Pagan Diagonal Covariance Matrix Test r2nlsur (NL-SUR) Overall System R2, F-Test, and Chi2-Test diagnlsur (NL-SUR) Overall System ModeL Selection Diagnostic Criteria --------------------------------------------------------------------------- * (9) (VAR) * Vector Autoregressive Model Tests: lmavar (VAR) Overall System Autocorrelation Tests lmhvar (VAR) Overall System Heteroscedasticity Tests lmnvar (VAR) Overall System Non Normality Tests lmcovvar (VAR) Breusch-Pagan Diagonal Covariance Matrix Test r2var (VAR) Overall System R2, F-Test, and Chi2-Test diagvar (VAR) Overall System ModeL Selection Diagnostic Criteria ---------------------------------------------------------------------------