ARMA-GARCH model and dummy variables MATLAB

I have an array of percentage returns that I want to run dummy variables on in order to extract certain values for certain dates of the month. I want to fit a ARMA-GARCH model to this. This is what I do:

    EstMdl = estimate(Mdl,Reg_var_SSE)

Reg_var_SSE is a 6260x21 matrix with returns in column 1 and intercept plus dummy variables in 2:21.

Looks like this:

I get the error message:

    Error using arima/estimate (line 224) Input response series data must be non-empty and a column vector.

Probably estimate() is not meant to be used this way, but this is want I want to do.

Answer 1

[Brendan Hamm]

The second input to the estimate function should be the "univariate time series", so we cannot pass a matrix as this argument. What are you trying to do with the dummy-variables here? Is it that you want to estimate the parameters of different GARCH models for each of these groups?

[Ali Akbar]

No I don't want to estimate the parameters of GARCH models.

I have a calendar with >6000 observations of index return values. I want to estimate the coefficient on different days of the month to evaluate if certain days give higher returns than other days. For this, I have created a large matrix with dummy variables that I want to regress on these returns that I have collected in an array. This is how it looks:

Notice the "1":s. Column 1 returns and the rest are dummies. 6260x21 matrix.

I can easily do this with fitlm() but I want to model the volatility with GARCH and fitlm() does not do that. How do I do this practically?

[Brendan Hamm]

In a GARCH model you would be regressing on the previous lags of the model, therefore auto-regressive. For this reason you would pass in only the first column (the returns) and we cannot use a dummy variable in this model.

[Ali Akbar]

Is what I am trying to do possible at all?

I want to capture the returns of specific days of the month with dummies and I want to model the volatility with GARCH.

[Brendan Hamm]

I cannot see what you think the model would be using dummy variables and it does not seem to make much sense to do this. In a GARCH model your returns would be regressed on by the previous values, so your predictor variables are the same as the response variables excepting they are lagged. This is not like a regression model with categorical predictors where the dummy variables consider grouping. So try and take a step back and ask yourself what this model would like like mathematically. You will likely find yourself either landing on using monthly lags to account for this (likely your only option) or trying a new approach entirely. I would only use monthly lags if there was evidence to support the seasonality in the data.