[R] ARCH modelling/MA process
Hi all ARCH modelling I have a problem now on how to proceed with further steps in my analysis. I did a linear OLS regression with my daily data of stock and index returns. There is now the problem of arch in my error terms. Thus I used the following r command: garch(resid_desn, order=c(0,2)) ## This ARCH(2) process seems to fit the best after trial and error. Consequently, I get there three a's. (resid_desn are the residuals of the ols regression of the company desn) The problem is now that I want to analyse the excess return for a given period. I don't know how I should include these a's in my linear regression to address this problem and get new alphas and betas... /(FOR INFORMATION: excess return without ammendements for ARCH effects is given as: êt=Ri,t-alpha(from regression)-beta(from regression)*Rm,t)/ There is a paper which does this in a simple manner (see page 12 and 13 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1100573 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1100573 ). It is described as follows: Ri=alpha(arch)+beta(arch)*Rm,i+et et=thetat*sqrt(h) h=lamda(0)+lamda(1)*e(t-1)^2 ##e are the residuals of the ols regression Thus my question is now: How can I regress this? Ri=alpha(arch)+beta(arch)*Rm,i+thetat*sqrt(h) ## This seems not to work as it calculates an additional errorterm. Also the parameter theta changes over time. Thus the problem is on how I should estimate this one I hope there is a solution for this problem or some hints on how I can use the output of the garch model for my linear regression and the estimation of new alphas and beta (with consideration of ARCH effects). MA Process: I have for example an MA(1) process. This mean that ut=et+theta*et-1 Thus the linear regression gets (also excess return on the left hand side): et=Ri,t-alpha-beta*Rm,i-theta*et-1 The problem is now that et depends on et-1. I want to start with et-1=0, thus I cant do this with one formula. And typing this in for 180 days is simply to time consuming. Any suggestions on that Problem? One solution would be to do this with excel. Thanks and kind regards Andi Kind regards Andi -- View this message in context: http://r.789695.n4.nabble.com/ARCH-modelling-MA-process-tp4632535.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] Problem with ARCH
Hi I have a problem on how to proceed with further steps in my analysis. I did a linear OLS regression (ri,t=alpha*beta*rm,t+et) with my daily data of stock and index returns. There is now the problem of arch in my error terms. Thus I used the following r command: /garch(resid_desn, order=c(0,2)) ## This ARCH(2) process seems to fit the best after trial and error. Consequently, I get there three a's. (resid_desn are the residuals of the ols regression of the company desn) / And now I am stuck. For further analysis I want to estimate new alphas and betas which do incorporate this ARCH effect (thus including all the a's in some way). There is a paper which does this in a simple manner (see page 12 and 13 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1100573). It is described as follows: /Ri=alpha(arch)+beta(arch)*Rm,i+et ## equation one et=ut*sqrt(h) h=lamda(0)+lamda(1)*e(t-1)^2+lamda(2)*e(t-2)^2 ##e are the residuals of the ols regression / I don't know how I should include these a's in my linear regression to address this problem and get new alphas and betas. I tried to substitute and rearrange (h can be calculated from the ols and garch output, then I substitute et in equation one with ut*sqrt(h) and divide the whole equation by sqrt(h)). After the regression procedure there is still significant ARCH effect in my model. I don't know if dividing is the right step but without this, r would incorporate another error term. My assumption is that ut is an error term. The purpose of this is to estimate excess returns after the estimation period. (FOR INFORMATION: excess return without ammendements for ARCH effects is given as: êt=Ri,t-alpha-beta*Rm,t) Thus my question is now: How can I regress this to get results without ARCH effect? I hope there is a solution for this problem or some hints on how I can use the output of the garch model for my linear regression and the estimation of new alphas and beta (with consideration of ARCH effects). *Help is really appreciated!!!* Kind regards Andi -- View this message in context: http://r.789695.n4.nabble.com/Problem-with-ARCH-tp4632778.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] looking for an add-in for daily data analysis
Hi all I am looking for an add-in. I am currently working on something and I use daily data of closing stock prices. As not all companies are traded daily (e.g. on monday, then on thursday etc) at the stock exchange, there is satistically a problem. There are some papers which explain the approach to handle infrequent trading of a stock or non synchronous data and beta estimation (Dimson, 1979; Scholes & Williams, 1977). I looked for add-ins which do address this topic, but i couldn't find any. I have to calculated daily returns from the daily colsing stock prices. Afterwards I want to estimate the alphas and betas of the market model for a given timeperiod. Then I calculate abnormal returns and CAR's and assess their significance (event study methodology with the market model). Does someone have any idea on how I should handle these problems or a link for an appropriate package? For implementing these statistics on my own, I knowledge in R is not sufficient. Kind Regards AM -- View this message in context: http://r.789695.n4.nabble.com/looking-for-an-add-in-for-daily-data-analysis-tp4589711p4589711.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] Problem with Autocorrelation and GLS Regression
Hi, I have a problem with a regression I try to run. I did an estimation of the market model with daily data. You can see to output below: /> summary(regression_resn) Time series regression with "ts" data: Start = -150, End = -26 Call: dynlm(formula = ror_resn ~ ror_spi_resn) Residuals: Min 1Q Median 3QMax -0.0255690 -0.0030378 0.0002787 0.0039887 0.0257857 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.0003084 0.0007220 -0.4270.670 ror_spi_resn 0.0363940 0.0706150 0.5150.607 Residual standard error: 0.008016 on 123 degrees of freedom Multiple R-squared: 0.002155, Adjusted R-squared: -0.005958 F-statistic: 0.2656 on 1 and 123 DF, p-value: 0.6072 / I did several tests for assessing the quality of the estimation (like breusch-pagan, breusch-godfrey, chow-breakpoint, arch lm tests). The model has now clearly a problem with autocorrelation as you can see in de images below: http://r.789695.n4.nabble.com/file/n4631336/resid_resn.png http://r.789695.n4.nabble.com/file/n4631336/pacf_resid_resn.png To take into account the problem of autocorrelation, I did a gls estimation with an AR(1) process and get the following output: /> summary(gls(ror_resn~ror_spi_resn, correlation=corARMA(p=1), method="ML")) Generalized least squares fit by maximum likelihood Model: ror_resn ~ ror_spi_resn Data: NULL AIC BIC logLik -859.0308 -847.7176 433.5154 Correlation Structure: AR(1) Formula: ~1 Parameter estimate(s): Phi -0.3182399 Coefficients: Value Std.Errort-value p-value (Intercept) -0.00034277 0.00052344 -0.6548430 0.5138 ror_spi_resn 0.04337265 0.06741179 0.6433986 0.5212 Correlation: (Intr) ror_spi_resn -0.159 Standardized residuals: Min Q1 Med Q3 Max -3.21202187 -0.38283220 0.03863226 0.50313857 3.24224614 Residual standard error: 0.007953852 Degrees of freedom: 125 total; 123 residual/ I plot acf and pacf again to assess the changes in autocorrelation. But interestingly, there is no change in the plots, they are equal to the images above... Can anyone give advice on how to handle this problem? There is the possibility that I am clearly on the wrong path. I am still a beginner in using R. Furthermore, I did the same procedure with EVIEWS (also implementing AR(1) process) and the model gives different results for the coefficients and error terms. Regards Andi /Output EVIEWS: Dependent Variable: ROR_RESN Method: Least Squares Date: 05/25/12 Time: 17:17 Sample (adjusted): 2 125 Included observations: 124 after adjustments Convergence achieved after 7 iterations VariableCoefficient Std. Error t-Statistic Prob. C -0.000409 0.000525-0.779074 0.4375 ROR_SPI_RESN0.0529960.0677940.7817160.4359 AR(1) -0.314260 0.085592-3.671586 0.0004 R-squared 0.104144Mean dependent var -0.000365 Adjusted R-squared 0.089337S.D. dependent var 0.007945 S.E. of regression 0.007581Akaike info criterion -6.902354 Sum squared resid 0.006955Schwarz criterion -6.834122 Log likelihood 430.9460Hannan-Quinn criter. -6.874637 F-statistic 7.033211Durbin-Watson stat 2.070520 Prob(F-statistic) 0.001289 Inverted AR Roots-.31 / -- View this message in context: http://r.789695.n4.nabble.com/Problem-with-Autocorrelation-and-GLS-Regression-tp4631336.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Problem with Autocorrelation and GLS Regression
For the analysis I follow the approach of Keown & Pinkerton ( http://e-m-h.org/KePi81.pdf http://e-m-h.org/KePi81.pdf ). They do also use daily data to compute alphas and betas of the market model. These estimated coefficients are then used to estimate abnormal returns for a given period. market model would be: Rjt=ajt+bjt*Rmt+ejt Rjt is the return of company j on day t Rmt is the return of the market on day t (Index) ejt is the unsystematic component of firm j's return after estimation I want to estimate abnormal returns: êjt=Rjt-(âj+bj*Rmt) aj and bj are the estimatet coefficients from the equation above. -- View this message in context: http://r.789695.n4.nabble.com/Problem-with-Autocorrelation-and-GLS-Regression-tp4631336p4631355.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] Arima model, breusch godfrey/breusch pagan test
Hi all I did an estimation of a simple regression model (ror_xxx~ror_spi_xxx) and assessed the quality of this estimation. After having detected that there are indications of autocorrelatio and an AR(1) process, I used an arima model: absi.arima=arima(ror_absi, order=c(1,0,0), xreg=ror_spi_absi) Output: > absi.arima Call: arima(x = ror_absi, order = c(1, 0, 0), xreg = ror_spi_absi) Coefficients: ar1 intercept ror_spi_absi -0.5377 -1e-04 -0.0060 s.e. 0.0752 3e-040.0215 sigma^2 estimated as 1.579e-05: log likelihood = 513.49, aic = -1018.97 This eliminated the arch effect in my model, but I want to check weather there is still any autocorrelation in my model (with breusch godfrey test, bgtest). My question is now on how to implement this in the bgtest function. As there has to be typed in the exact equation of the model or a fitted lm model, I do not have any idea on what to do now Is there a simple solution for my problem? Same question would be when using the breusch pagan test. Any suggestions are higly appreciated! Kind regards, Andi -- View this message in context: http://r.789695.n4.nabble.com/Arima-model-breusch-godfrey-breusch-pagan-test-tp4631617.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
