This demo version of PcGive is limited only by the data sets it allows.
In addition to PcGive, STAMP and PcGets tutorial data files:
| PcGive | data.in7 |
| PcGive | MulTut1.in7 |
| PcGive | exch_debp.in7 |
| PcGive | finney.in7 |
| PcGive | grunfeld.xls |
| PcGets | DHSY.in7 |
| PcGets | M1UK.in7 |
| STAMP | energy.in7 |
| STAMP | spirit.in7 |
| X12arima | Airline.xls |
this version can handle two of the data sets accompanying
|
Market Models: A Guide to Financial Data Analysis Carol Alexander ISBN: 0-471-89975-5 Published November 2001 by Wiley |
This tutorial explains how the results in chapter 4 (GARCH models) have been obtained. It is based on the US stocks data that are used in that chapter. PcGive also has sophisticated time series modelling capabilities, suitable for all the models that are described in part 3 of the book, including cointegration analysis. So that the reader may see this for themselves, this demo version may be used with the equity index data that are used in chapters 11 and 12.
The two additional data sets from Market Models: A Guide to Financial Data Analysis that may be used with this demo are:
| indices.csv | 1207 daily observations on 4 equity indices (AEX, CAC, DAX, FTSE100) from 1996-01-03 to 2000-10-02 | USStocks_close.xls | 1200 daily observations on 20 US stocks from 1996-01-02 to 2000-10-06 |
Please begin by reading the Getting Started chapter in the online help (available on the internet at www.pcgive.com).
First start GiveWinDemo, then PcGive can be started from the Modules menu of GiveWinDemo or, more conveniently, from the Modules group in the workspace window on the left-hand side of GiveWinDemo. Access the File menu in GiveWinDemo and locate USStocks_close.xls. You can find a subset of the data in GiveWin2Demo\PcGive\USStocks_close1.xls, or the full data set on the CD accompanying Market Models. The screen captures below use the full data set.
The next step is to create the returns data. This involves taking the logarithms of the prices, and then the first differences. This can be achieved in one step using the dlog function. Activate the calculator, and select the stock prices in the window on the right-hand side (here only 3 are selected):
Then press the dlog button, and press the = button. Confirm the default names (which uses the DL prefix).
The interest is in the volatility, so also create the squared returns, either using the calculator, or with the following Algebra code:
sqrDLaig = DLaig ^ 2;
sqrDLaol = DLaol ^ 2;
sqrDLaxp = DLaxp ^ 2;
The following figure illustrates for the first three stocks, American International Group, American Express and America Online:
To create this graph, click on Graphics (either on the toolbar or from the Tools menu), select the series in the database window on the right, press the << button to make this the selection, then press the button as shown:
and cancel the dialog.
To create the sample autocorrelation functions (ACF), select the first variable, then press Next: choose graph, and select Time series: ACF etc. as shown and then Finish:
Repeat this for the remainder, to see:
Start PcGive from the GiveWinDemo workspace window, and select Descriptive Statistics from the PcGive Package menu. Select DLaig, DLaol and DLaxp:
click on OK, and select Normality Tests:
The output is:
Descriptive statistics for 2 (1) to 1200 (1) Normality test for DLaig Observations 1199 Mean 0.0012317 Std.Devn. 0.019626 Skewness 0.28092 Excess Kurtosis 1.8233 Minimum -0.078282 Maximum 0.10460 Asymptotic test: Chi^2(2) = 181.86 [0.0000]** Normality test: Chi^2(2) = 99.920 [0.0000]** Normality test for DLaol Observations 1199 Mean 0.0025546 Std.Devn. 0.041083 Skewness 0.19038 Excess Kurtosis 1.5012 Minimum -0.18739 Maximum 0.16508 Asymptotic test: Chi^2(2) = 119.83 [0.0000]** Normality test: Chi^2(2) = 76.956 [0.0000]** Normality test for DLaxp Observations 1199 Mean 0.0012802 Std.Devn. 0.023069 Skewness 0.067819 Excess Kurtosis 1.9412 Minimum -0.11493 Maximum 0.12017 Asymptotic test: Chi^2(2) = 189.17 [0.0000]** Normality test: Chi^2(2) = 121.70 [0.0000]**
Next, select the squared variables, and select Correlogram with lag 4:
sqrDLaig : Sample correlogram (ACF) from lag 1 to 4:
0.14656 0.11293 0.14190 0.13505
Portmanteau statistic for 4 lags and 1199 observations: 467.82
sqrDLaol : Sample correlogram (ACF) from lag 1 to 4:
0.11353 0.068872 0.069970 0.056654
Portmanteau statistic for 4 lags and 1199 observations: 380.455
sqrDLaxp : Sample correlogram (ACF) from lag 1 to 4:
0.23413 0.18664 0.17414 0.14635
Portmanteau statistic for 4 lags and 1199 observations: 592.169
The first term is the first autocorrelation coefficient of the squares.
To compute ARCH-LM tests, regress the returns on a constant. Ensure that the Package menu is set to Econometric Modelling (PcGive). Activate Single Equation Modelling from the Model menu, and select DLaig (if DLaig_1, the first lag of DLaig, is added as regressor, delete that from the model):
Next, select the default of OLS in Model Settings, and accept the default sample. Following successful estimation, choose Test/Test... and select ARCH with order 1:
This prints the ARCH coefficient, which is very close to the first ACF. The first order ARCH-LM test is printed as an F-test
ARCH coefficients:
Lag Coefficient Std.Error
1 0.14672 0.0286
RSS = 0.000665393 sigma = 0.000745888
Testing for error ARCH from lags 1 to 1
ARCH 1-1 test: F(1,1196)= 26.315 [0.0000]**
An alternative way to compute this statistic is to regress sqrDLaig on a constant and sqrDLaig_1:
EQ( 3) Modelling sqrDLaig by OLS (using USStocks_close.xls)
The estimation sample is: 3 to 1200
Coefficient Std.Error t-value t-prob Part.R^2
sqrDLaig_1 0.146582 0.02860 5.12 0.000 0.0215
Constant 0.000330273 2.444e-005 13.5 0.000 0.1324
sigma 0.000754279 RSS 0.00068044842
R^2 0.0214872 F(1,1196) = 26.26 [0.000]**
log-likelihood 6914.43 DW 2.03
no. of observations 1198 no. of parameters 2
mean(sqrDLaig) 0.000386992 var(sqrDLaig) 5.80459e-007
The Chi2 statistic is T.R2 = 1198 * 0.0214872 = 25.74.
(Note: when additional regressors are involved, the test
is based on the R2 from a regression of the squared residuals
on lagged squared residuals, see PcGive Volume 1. )
The asymmetric version of the test can be computed in a similar fashion, by regressing sqrDLaig on a constant and DLaig_1.
The ARCH(1) test for many return series at once can be computed using Multiple-equation Dynamic modelling: all the returns are marked as endogenous (Y variables), only a Constant as regressor. Then using the Test/Test option:
DLaig : ARCH 1-1 test: F(1,1196)= 26.315 [0.0000]** DLaol : ARCH 1-1 test: F(1,1196)= 17.462 [0.0000]** DLaxp : ARCH 1-1 test: F(1,1196)= 72.608 [0.0000]**
Select Volatility Models (GARCH) from the PcGive Package menu. Then formulate a model of DLaig on a Constant:
In the next dialog, accept the default of GARCH(1,1):
Estimation is nearly instantaneous:
VOL( 1) Modelling DLaig by restricted GARCH(1,1) (USStocks_close.xls)
The estimation sample is: 2 to 1200
Coefficient Std.Error robust-SE t-value t-prob
Constant X 0.00145641 0.0004866 0.0004985 2.92 0.004
alpha_0 H 2.63324e-006 1.367e-006 1.511e-006 1.74 0.082
alpha_1 H 0.0465619 0.01041 0.01255 3.71 0.000
beta_1 H 0.946750 0.01150 0.01304 72.6 0.000
log-likelihood 3101.55668 HMSE 2.6653
mean(h_t) 0.000388262 var(h_t) 5.49639e-008
no. of observations 1199 no. of parameters 4
AIC.T -6195.11335 AIC -5.16690021
mean(DLaig) 0.0012317 var(DLaig) 0.00038519
alpha(1)+beta(1) 0.993312 alpha_i+beta_i>=0, alpha(1)+beta(1)<1
Initial terms of alpha(L)/[1-beta(L)]:
0.046562 0.044082 0.041735 0.039513 0.037409 0.035417
0.033531 0.031745 0.030055 0.028454 0.026939 0.025505
Used sample mean of squared residuals to start recursion
Robust-SE based on analytical Information matrix and analytical OPG matrix
BFGS using analytical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence
Used starting values:
0.0012317 1.9259e-005 0.56555 0.38445
Graphic analysis, selecting Conditional standard deviation and residual correlogram of squares:
shows that the autocorrelation in the squares has been removed by the GARCH(1,1) model:
Note that GARCH(1,1) models for Ford (f), BankOne (one) and Rockwell (rok) returns do converge in PcGive. The first two have insignificant alpha_1, DLrok has insignificant beta_1. The GARCH(1,1) model for Unicom (ucm) does not converge, although ARCH(1) (so p=0, q=1) converges.
Asymmetric GARCH models can also be estimated with PcGive. In the Model Settings dialog, expand GARCH variations, and select Asymmetric GARCH:
Estimation for Cisco Systems gives:
VOL(15) Modelling DLcsco by restricted AGARCH(1,1) (USStocks_close.xls)
The estimation sample is: 2 to 1200
Coefficient Std.Error robust-SE t-value t-prob
Constant X 0.00159877 0.0007653 0.0007636 2.09 0.036
alpha_0 H 1.58551e-005 2.035e-005 2.170e-005 0.731 0.465
alpha_1 H 0.0860131 0.02105 0.02392 3.60 0.000
beta_1 H 0.828972 0.03603 0.04477 18.5 0.000
asymmetry H 0.0259116 0.006273 0.006440 4.02 0.000
log-likelihood 2602.44627 HMSE 2.3408
mean(h_t) 0.00084481 var(h_t) 2.05857e-007
no. of observations 1199 no. of parameters 5
AIC.T -5194.89253 AIC -4.33268768
mean(DLcsco) 0.0021406 var(DLcsco) 0.000861546
alpha(1)+beta(1) 0.914985 alpha_i+beta_i>=0, alpha(1)+beta(1)<1