Any help with a AR-GARCH model issue on SAS system?

[dutran]

I am currently working on a large time series dataset. Due to the confidentiality issue, I can not post the dataset as well as the true nature of the case here, but let me make up an example:

We have a dataset which record daily transaction of gas from 1990 to 2000. Each observation contains price, quantity, revenue (price*quantity), weather statistics (temperature, windspeed, dew-point), and time statistics (weekdays or weekend, holiday or normal day, and months). Now suppose we have to run a regression with revenue being the dependent variable and the list of independent variables are weather statistics, time statistics and lag1 values of price and quantity.

1. Using autoreg procedure (SAS system), I proceed by testing for autocorrelation. Durbin-h test reveals that there is autocorrelation issue.

2. Using stepwise autoregression method, I can supposedly detect the order of autocorrelation. However, the output indicates that lag1 is dropped, but lag2 is not, and so on. A rule of thumb in this case is to specify an order larger than the order of any potential seasonality (n=5 for quarterly data, n=13 for monthly data). But this is a daily dataset. I tried up to n=366 and the output dropped around 290 lags and keep the remaining ones.

What can I do in this case? Should I use factored autoregressive models and use all the significant lag-orders in my regression?

3. The next step is testing for heteroskedasticity. I used Portmanteu Q - Test and ML test. The results suggest the presence of heteroskedasticity.

4. With both heteroskedasticity and autocorrelation issues. I tried to use AR(m)-GARCH(p,q) model for my regression. However, regardless of the parameters (m, p, q) I tried to use, the output window always return this:

ERROR: Likelihood function cannot be evaluated at initial point.

ERROR: Garch cannot be fit. Job will be terminated.

WARNING: OUTPUT data set will not be created since parameter estimates do not exist.

Since I am quite new to the SAS system and Time Series Analysis, I have no idea how to make it work. It seems that STATA allows users to supply some initial values when the system fails to do that. But I haven't found any similar suggestion for SAS system.

[dutran]

Guys, regarding the error in (4), I figured it out already, thanks any way.

[neomikeo]

Hi, you could use polynomial distributed lags PDL function with order of 2 or 3 in SAS and use Proc Model to estimate. PDL is good to capture very long lag structure.

[dutran]

Thanks bác Minh. Tôi sẽ thử xem sao. Bình thường tôi vẫn dùng proc autoreg khi deal with time series vì cái này có nhiều build-in functions để dùng deal with autocorrelation, heteroskedasticity và autoregressive conditional heteroskedasticity.