garch
Syntax
garch(ds, endogColName, order, [maxIter=50])
Details
Use the generalized autoregressive conditional heteroskedasticity (GARCH) model to model the conditional volatility of univariate time series.
Parameters
ds is an in-memory table or a vector consisting of DataSource objects, containing the multivariate time series to be analyzed. ds cannot be empty.
endogColName is a string indicating the column names of the endogenous variables in ds.
order is a positive integral vector of length 2 indicating the orders. For example, order=[1,2] means p=1, q=2 for a GARCH model, where p is the order of the GARCH terms and q is the order of the ARCH terms.
maxIter (optional) is a positive integer indicating the maximum iterations. The default value is 50.
Returns
Return a dictionary with the following keys:
- volConstant: A floating-point scalar, representing the Vol Constant obtained through optimization.
- returnsConstant: A floating-point scalar, representing the Returns Constant obtained through optimization.
- archTerm: A floating-point vector, representing the ARCH Term obtained through optimization.
- garchTerm: A floating-point vector, representing the GARCH Term obtained through optimization.
- iterations: An integer representing the number of iterations.
- aic: A floating-point scalar, representing the value of the AIC criterion.
- bic: A floating-point scalar, representing the value of the BIC criterion.
- nobs: An integer representing the number of observations in the time series, i.e., the amount of data used for fitting.
- model: A dictionary containing the basic information of the fitted model, with
the following members:
- order: A vector with 2 positive integers, representing the order of the model.
- endog: A floating-point matrix, representing the observed data converted from ds.
- coefficients: A floating-point vector, representing the values of the exogenous variables after fitting.
- predict: The prediction function of the model. It can be called using
model.predict(x), where:- model: A dictionary indicating the output of
garch. - x: A positive integer representing the prediction step.
- model: A dictionary indicating the output of
Examples
Analyze the data in the macrodata.csv file with garch model:
data = loadText("macrodata.csv");
model = garch(data, "realgdp", [1,1]);
print(model)
/* output:
volConstant->0.000005999433551
returnsConstant->0.008474617943101
archTerm->[0.70725452294378]
garchTerm->[0.248859733003604]
aic->-1353.789403416915774
bic->-1340.576183784679415
nobs->201
iterations->38
predict->garchPredict
state->order->[1,1]
endog->#0
------------------
0.024942130816387
-0.001192952110668
0.003494532654372
...
start->[-12.023845501294935,-1.104702991485461,0.882087052766567,0.008474617943101]
*/