<p>It depends on the specific GARCH model you want to estimate. Traditional GARCH takes in squared % returns (C) assuming no mean equation. But there are other GARCH formulations that take in different values, such as the absolute value of % returns (like EGARCH).</p>

CC BY-SA 4.0
2022-02-10T10:43:26.887Z
This is incorrect. Squared returns are not used as inputs in GARCH or ARCH models.
Richard Hardy
CC BY-SA 4.0
2022-02-10T22:34:05.607Z
Assuming there is no mean equation, the residual/error is the return. And in standard arch/garch models, the squared error is the input (which again is equal to the squared return when there is no mean equation). Every standard text on arch/garch shows this. It’s also available on wikipedia.
RA334
CC BY-SA 4.0
2022-02-11T06:42:19.777Z
Sorry, but this is wrong. To see that in practice, consider simulating data from a GARCH model and then estimating the model's parameters on the simulated data. If your understanding were correct, you would get parameter estimates that are close to the true values. Since it is not correct, you will likely get something else. Then try what I am suggesting, and you will get something close to the truth (unless your estimation sample is quite short). That should be at least somewhat convincing.
Richard Hardy
CC BY-SA 4.0
2022-02-12T00:33:43.650Z
I understand what you’re saying but that’s technically not correct. Your exercise simulates *returns* from a process that specifies a GARCH variance (and can specify an equation for the mean too, like AR or ARMA or not). The GARCH variance equation has squared residuals - taken from the first stage - enter as inputs. Refer to any of the open access online resources on this stuff. Also you can go straight to the source Bollerslev (1986), just look at Eq. 2. Good luck.
RA334
CC BY-SA 4.0
2022-02-12T07:07:45.467Z
What I am saying is exactly correct. Moreover, the OP writes *we are trying to feed time-series data to a GARCH or ARCH model*, not *to the conditional variance equation of a GARCH or ARCH model*, and they are right in their choice. GARCH or ARCH model an entire conditional distribution of the random variable of interest, not just its conditional variance. You never feed squared returns, you feed raw returns. You cannot fit a GARCH or ARCH model for a time series $x_t$ using $x_t^2$ as inputs; rather, you use $x_t$ as inputs.
Richard Hardy
CC BY-SA 4.0
2022-02-06T19:16:27.747Z
2022-02-06T19:16:27.747Z
RA334
<p><strong>B</strong>: % of the difference between daily prices over-time.</p>
<p>This, or rather the closely related logarithmic returns, is what is typically used as inputs to GARCH and ARCH models. GARCH and ARCH model the conditional distribution of the inputs using a particular form of the conditional variance equation. Thus even if this answer alternative (B) is not perfect, it is very close to the truth. None of the other alternatives may work due to technical reasons (see definitions of GARCH and ARCH models).</p>

CC BY-SA 4.0
2022-02-10T10:42:30.197Z
2022-02-10T10:42:30.197Z
Richard Hardy
<p>When we are trying to feed time-series data to a GARCH or ARCH model, what kind of data should we give the model?</p>
<ul>
<li><strong>A:</strong> Absolute difference between daily prices over-time</li>
<li><strong>B:</strong> % of the difference between daily prices over-time</li>
<li><strong>C:</strong> B but squared (to take out the negative values)</li>
<li><strong>D:</strong> module of B (to take out the negative values)</li>
</ul>

CC BY-SA 4.0
2022-02-10T10:43:44.083Z
RA334's answer that you have accepted is incorrect. You may browse [Cross Validated](https://stats.stackexchange.com/questions/tagged/garch) and [Quantitative Finance Stack Exchange](https://quant.stackexchange.com/questions/tagged/garch) that have hundreds of threads on (G)ARCH models.
Richard Hardy
<econometrics><stock-market><applied-econometrics><time-series><autoregressive>
What type of data we use to predict volatility of an asset with GARCH or ARCH models?
Tiago
# What type of data we use to predict volatility of an asset with GARCH or ARCH models?

(Asked by: username_0 on 2022-02-06)

When we are trying to feed time-series data to a GARCH or ARCH model, what kind of data should we give the model?

* **A:** Absolute difference between daily prices over-time
* **B:** % of the difference between daily prices over-time
* **C:** B but squared (to take out the negative values)
* **D:** module of B (to take out the negative values)

**Tags:** econometrics, stock-market, applied-econometrics, time-series, autoregressive

> **Comments:**
> **username_1**: username_2's answer that you have accepted is incorrect. You may browse [Cross Validated](https://stats.stackexchange.com/questions/tagged/garch) and [Quantitative Finance Stack Exchange](https://quant.stackexchange.com/questions/tagged/garch) that have hundreds of threads on (G)ARCH models.  

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## 2 answers

### Answer by username_2 on 2022-02-06. Score: 1 | Accepted answer

It depends on the specific GARCH model you want to estimate. Traditional GARCH takes in squared % returns (C) assuming no mean equation. But there are other GARCH formulations that take in different values, such as the absolute value of % returns (like EGARCH).

> **Comments:**
> **username_1**: This is incorrect. Squared returns are not used as inputs in GARCH or ARCH models.  
> **username_2**: Assuming there is no mean equation, the residual/error is the return. And in standard arch/garch models, the squared error is the input (which again is equal to the squared return when there is no mean equation). Every standard text on arch/garch shows this. It’s also available on wikipedia.  
> **username_1**: Sorry, but this is wrong. To see that in practice, consider simulating data from a GARCH model and then estimating the model's parameters on the simulated data. If your understanding were correct, you would get parameter estimates that are close to the true values. Since it is not correct, you will likely get something else. Then try what I am suggesting, and you will get something close to the truth (unless your estimation sample is quite short). That should be at least somewhat convincing.  
> **username_2**: I understand what you’re saying but that’s technically not correct. Your exercise simulates *returns* from a process that specifies a GARCH variance (and can specify an equation for the mean too, like AR or ARMA or not). The GARCH variance equation has squared residuals - taken from the first stage - enter as inputs. Refer to any of the open access online resources on this stuff. Also you can go straight to the source Bollerslev (1986), just look at Eq. 2. Good luck.  
> **username_1**: What I am saying is exactly correct. Moreover, the OP writes *we are trying to feed time-series data to a GARCH or ARCH model*, not *to the conditional variance equation of a GARCH or ARCH model*, and they are right in their choice. GARCH or ARCH model an entire conditional distribution of the random variable of interest, not just its conditional variance. You never feed squared returns, you feed raw returns. You cannot fit a GARCH or ARCH model for a time series $x_t$ using $x_t^2$ as inputs; rather, you use $x_t$ as inputs.  

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### Answer by username_1 on 2022-02-10. Score: 1

**B**: % of the difference between daily prices over-time.

This, or rather the closely related logarithmic returns, is what is typically used as inputs to GARCH and ARCH models. GARCH and ARCH model the conditional distribution of the inputs using a particular form of the conditional variance equation. Thus even if this answer alternative (B) is not perfect, it is very close to the truth. None of the other alternatives may work due to technical reasons (see definitions of GARCH and ARCH models).


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