<p>Well I havent read the paper but this is what it looks like to me:</p>

<ol>
<li>Compute <span class="math-container">$R_t$</span> - the rolling average for month t.</li>
<li><span class="math-container">$R_t &gt; 0 \Rightarrow  R_{t+} = R_t \wedge R_{t-} = 0$</span> and<span class="math-container">$R_t &lt; 0 \Rightarrow  R_{t-} = R_t \wedge R_{t+} = 0$</span></li>
</ol>

CC BY-SA 4.0
2024-09-05T05:32:57.613Z
Yes it means that they model the effect of changes in returns differently depending on whether the returns are negative or positive. It is a well known empirical tendency that a lot of financial instruments respond asymmetrically to good and bad "news". The effect is asymmetric when beta values are different and usually you would expect the reaction to change in negative returns to be larger.
Jesper Hybel
CC BY-SA 4.0
2019-09-01T18:49:13.427Z
2019-09-01T18:49:13.427Z
Grada Gukovic
<p>I'm currently analyzing the relationship between stock, bonds, and real estate returns in Germany. I've gathered my data and am planning on estimating this equation:</p>

<p><span class="math-container">$\sigma_t = \beta_0 + \beta_1 R_{t+} + \beta_2 R_{t-} + y_t$</span></p>

<p>through a GARCH model. In the article where I found equation 1 (Chan and Chang, 2014), they
    have delineted the parameters as so: <span class="math-container">$R_{t+}= \max [0, R_t]$</span>, <span class="math-container">$R_{t–} = \min
[0, R_t]$</span>, and <span class="math-container">$R_t$</span> is the monthly return of stock, bond, or real
    estate. We use a three-month rolling return to calculate the
    standard deviation of the return." Does this mean they use the Max
    and Min of the series as parameters or the Max and Min of each
    rolling average across the series?</p>

CC BY-SA 4.0
2019-08-26T14:07:18.273Z
This questions seem quite distinct: please post separate questions in separate posts.
Giskard
CC BY-SA 4.0
2022-01-19T17:07:21.410Z
FYI: looking at the number of threads concerning GARCH, you will see that there is much more activity on [Cross Validated](https://stats.stackexchange.com/questions/tagged/garch) and [Quantitative Finance Stack Exchange](https://quant.stackexchange.com/questions/tagged/garch).
Richard Hardy
CC BY-SA 4.0
2024-09-05T05:37:31.813Z
It is simply a recoding of the return series splitting up positive and negative values. If you are familiar with regression and dummy interaction note the max(0,r)=1(r>0)r so equal to 0 if r is non-positive otherwise simply r.
Jesper Hybel
<econometrics><finance><time-series>
Data analysis with GARCH modeling
Peter V
# Data analysis with GARCH modeling

(Asked by: username_0 on 2019-08-26)

I'm currently analyzing the relationship between stock, bonds, and real estate returns in Germany. I've gathered my data and am planning on estimating this equation:

$\sigma\_t = \beta\_0 + \beta\_1 R\_{t+} + \beta\_2 R\_{t-} + y\_t$

through a GARCH model. In the article where I found equation 1 (Chan and Chang, 2014), they
have delineted the parameters as so: $R\_{t+}= \max [0, R\_t]$, $R\_{t–} = \min
[0, R\_t]$, and $R\_t$ is the monthly return of stock, bond, or real
estate. We use a three-month rolling return to calculate the
standard deviation of the return." Does this mean they use the Max
and Min of the series as parameters or the Max and Min of each
rolling average across the series?

**Tags:** econometrics, finance, time-series

> **Comments:**
> **username_1**: This questions seem quite distinct: please post separate questions in separate posts.  
> **username_2**: FYI: looking at the number of threads concerning GARCH, you will see that there is much more activity on [Cross Validated](https://stats.stackexchange.com/questions/tagged/garch) and [Quantitative Finance Stack Exchange](https://quant.stackexchange.com/questions/tagged/garch).  
> **username_3**: It is simply a recoding of the return series splitting up positive and negative values. If you are familiar with regression and dummy interaction note the max(0,r)=1(r>0)r so equal to 0 if r is non-positive otherwise simply r.  

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## 1 answers

### Answer by username_4 on 2019-09-01. Score: 0

Well I havent read the paper but this is what it looks like to me:

1. Compute $R\_t$ - the rolling average for month t.
2. $R\_t > 0 \Rightarrow R\_{t+} = R\_t \wedge R\_{t-} = 0$ and$R\_t < 0 \Rightarrow R\_{t-} = R\_t \wedge R\_{t+} = 0$

> **Comments:**
> **username_3**: Yes it means that they model the effect of changes in returns differently depending on whether the returns are negative or positive. It is a well known empirical tendency that a lot of financial instruments respond asymmetrically to good and bad "news". The effect is asymmetric when beta values are different and usually you would expect the reaction to change in negative returns to be larger.  

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