garch

Syntax

garch(ds, endogColName, order, [maxIter=50])

Arguments

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.

Details

Use the generalized autoregressive conditional heteroskedasticity (GARCH) model to model the conditional volatility of univariate time series.

Return value: 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.

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]
*/