# Tag Info

### How to calculate the conditional variance of a time series?

Let’s take a simple example to answer a broad but interesting question: Imagine that we have a daily return serie denoted $r_{t}$ ( which is assumed to be stationary) and let's take a little time to ...

### Why is GARCH(1,1) so popular, especially in academia?

Let me start with a disclaimer that I have no interest in promoting GARCH models. However, I am aware of their history, their capabilities and some practical aspects of using them. That helps me come ...
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### Kurtosis in GARCH

You've found parameterizations where fantastically long samples are required for sample 4th moments to converge on population 4th moments. Quick evidence of imprecise estimation Let $k_i$ denote ...
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### Realized Variance (realized volatility)

The TLDR; to your question: How can one use realized volatility as a volatility model to do out-of-sample prediction? You extend known models to incorporate additional information procured from high-...

### What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?

The best answer to your question is probably given by the Nobel prize committee itself in "The Prize in Economic Sciences 2003 - Advanced Information" document. You should read it in full. Below is an ...
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### Is there a HAR that deals with the leverage effect?

There exists a modification of the HAR model that accounts for leverage effect (á la GJR-GARCH) in a high-frequency setting. The semi-variance HAR model, termed the SHAR model of Patton and Sheppard (...

### What is the preferred GARCH method in practice?

I personally use the simple Garch(1,1) for volatility filtering in the risk management area. In fact in most cases I don't even estimate the parameters, I stick 0.94 for mean reversion, 0.04 for the ...
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### Does the unconditional variance implied by a GARCH equal the sample variance?

In this context, unconditional variance refers to the stationary variance level predicted by your GARCH model. This quantity need not coincide with the sample variance of the data on which the latter ...
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### GARCH on returns or on log-returns?

What is usually used in practice to forecast volatility? I believe it is log-returns. Is it more appropriate, in general, to fit a GARCH on returns or on log-returns to estimate volatility? The ...

### Filtering out AR(1) effects before using stochastic volatility model

Even though it's a straightforward extension, it took me a while (a year? yikes!); but now you can easily incorporate Bayesian ar(1) (or more generally, Bayesian regression) in joint estimation by ...
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### Density forecast of a GARCH model

EDIT : I read more about it and I get some help with someone else, here is the correct answer : The density forecast is the predictive likelihood value of the process estimated at the realized ...

### 2-step estimation of DCC GARCH model in Python

If $\log{(|R_t|)}$ is your first term, I'm not sure why this is a matrix. Modulus (determinant herein) applied to a matrix $R_t$ gives a scalar. If your implementation in python produces a matrix, ...
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### GARCH variance vs standard deviation for volatility

If your question is: "Given all the information available up to time $t$, if I compute the 1 period ahead forecast $r_{t+1}$, is the conditional volatility over $[t,t+1[$ given by $\sqrt{r_{t+1}}$?", ...
This is a partial answer to your 2. statement. The main points are, the conditional (on information up to time $t-1$) variance of the price $P_t$ is the same as the conditional variance of the "...