# Tag Info

### What is the difference between GARCH and ARMA?

Edit: I realized the answer was lacking and have thus provided a more precise answer (see below -- or maybe above). I have edited this one for factual mistakes and am leaving it for the record. ...
Accepted

### For intuition, what are some real life examples of uncorrelated but dependent random variables?

In finance, GARCH (generalized autoregressive conditional heteroskedasticity) effects are widely cited here: stock returns $r_t:=(P_t-P_{t-1})/P_{t-1}$, with $P_t$ the price at time $t$, themselves ...

### What is the difference between GARCH and ARMA?

ARMA Consider $y_t$ that follows an ARMA($p,q$) process. Suppose for simplicity it has zero mean and constant variance. Conditionally on information $I_{t-1}$, $y_t$ can be partitioned into a known (...
Accepted

### Fit a GARCH (1,1) - model with covariates in R

Here is an example of implementation using the rugarch package and with to some fake data. The function ugarchfit allows for the ...
Accepted

### Time series analysis: since volatility depends on time, why are returns stationary?

I think your problem is that you confuse the UNconditional variance and the conditional variance. Indeed, you can have a time-varying conditional volatility but a constant unconditional variance. ...
Accepted

### Why is a GARCH model useful?

GARCH can be used for what you call predictions. The question is: predictions of what? Predictions of volatility. The reason why GARCH is useful is because it may better explain the volatility of ...
Accepted

### Accuracy of Volatility Forecast

The point of volatility forecasting is to forecast the full predictive density. For instance, you might assume a normal future density with mean zero, and forecast the one free parameter, which ...
Accepted

### Maximum likelihood in the GJR-GARCH(1,1) model

A conditional volatility model such as the GARCH model is defined by the mean equation \begin{equation} r_t = \mu + \sigma_t z_t = \mu + \varepsilon_t \end{equation} and the GARCH equation (this is ...

### Time series analysis: since volatility depends on time, why are returns stationary?

The augmented Dickey-Fuller test assesses whether the time series under inspection has a unit root or not. The test is designed specifically for that purpose. It either rejects the null of unit root ...
Accepted

### Fitting a GARCH(1, 1) model

I explain how to get the log-likelihood function for the GARCH(1,1) model in the answer to this question. The GARCH model is specified in a particular way, but notation may differ between papers and ...
Accepted

### Forecasting time series using ARMA-GARCH in R

Obtaining accurate point forecasts for financial time series is notoriously hard. That has to do with the nature of the financial markets; actors look for opportunities to exploit any predictability, ...
Accepted

### Should log-likelihood values increase when the sample size of a simulation increases?

It depends. More importantly though, it doesn't really matter. Remember, in an iid setting, the Likelihood is the product of PDFs (or PMFs) as a function of $\theta$. If each $f(x_i|\theta) < 1$ ...

### Accuracy of Volatility Forecast

Speaking about evaluating volatility forecasts in general (not GARCH in specific), I will mention an alternative to Stephan Kolassa's answer. One can also study proper scoring rules for statistics or &...

Accepted

Accepted

### ARMA GARCH estimation process in practice

I suggest you should determine both the ARMA and the GARCH parts simultaneously. If you determine the ARMA part first by temporarily ignoring GARCH, this will lead to inconsistent ARMA parameter ...
Accepted

### Which econometric models can be used to forecast security returns + ARIMA/GARCH questions

My goal is simply to ... find statistically significant predictive results. Also, is there a particular market you would look at (energy, rates, equities)? Most if not all the established and liquid ...