# Tag Info

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

A conditional volatility model such as the GARCH model is defined by the mean equation $$r_t = \mu + \sigma_t z_t = \mu + \varepsilon_t$$ and the GARCH equation (this is ...
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### 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 ...
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### 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 ...
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### R and Time Series Analysis; Suggestions for forecasting a series with a shock

This is not a time series question. ARIMA or GARCH are completely irrelevant. There is exactly one question you need to consider, and we can't tell you the answer: what happened at the end of the ...
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### 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, ...
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### 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 ...
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### 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 $f(x_i|\theta) < 1$ ...
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### Modeling timeseries with strong seasonality

Please look at the $y$ axes of your decomposition plots, which are on vastly different scales. Your data is almost perfectly nonseasonal. Compare this answer. As to what I would do: I would use R's <...
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### Testing if the volatility of single stocks and/or indices have risen in the past

You don't need a model to show that volatilities are changing. Simply show the time series of squared returns, you'll be able to spot the clusters of high and low volatilities easily. If you want to ...
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### 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 &...
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### How to forecast from GARCH-copula model?

How to fit a copula GARCH model? For each series (margins): (a) fit a univariate GARCH model (e.g. using ugarchspec followed by ...
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### White's test interpretation

I wouldn't base my choice of model on a test for heteroscedasticity. And I'm not the only one. Here is a quote from the great George Box: To make the preliminary test on variances is rather like ...
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### For intuition, what are some real life examples of uncorrelated but dependent random variables?

I found the following figure from wiki is very useful for intuition. In particular, the bottom row show examples of uncorrelated but dependent distributions. Caption of the above plot in wiki: ...
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