Autoregressive Conditional Heteroskedasticity (ARCH) models are used for time series in which the residual variance changes over time. The variance of the error term is assumed to follow an autoregressive (AR) process. Compare GARCH.
Questions tagged [arch]
44 questions
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Has anybody ever found data where ARCH and GARCH models work?
I'm an analyst in financial and insurance fields and whenever I try to fit volatility models I obtain awful results: residuals are often non-stationary (in the unit root sense) and heteroskedastic (so the model doesn't explain volatility).
Do…
Stefano R.
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What does one mean by ARCH effect?
What does one mean by ARCH effect?
I am a little bit confused... I understand the mathematical terms and so on. But I cant explain the ARCH effect in words.
Can someone explain the ARCH effect for me in words?
(ARCH effect for time series.)
Leah
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Computing VaR with AR-GARCH
I have the following AR(1)-GARCH(1,1) model for the daily returns $r_t$
$$r_t=\theta r_{t-1}+u_t\;\;\;u_t=\sigma_t\epsilon_t\;\;\;\sigma_t^2=\omega+\alpha u_{t-1}^2+\beta \sigma_{t-1}^2 $$
where $-1<\theta<1$, $\theta \neq0$, $\omega>0$,…
Wintermute
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VaR in case of ARMA-GARCH?
How do I calculate the VaR in case of using an ARMA-GARCH approach? I am not good at time series, so I am more or less confused with the different possible notations of an ARMA-GARCH process. I hope the notation I use is correct.
Suppose I use the…
evogonz
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Conditional heteroscedasticity vs iid hypothesis - McLeod-Li test
I am using the function McLeod.Li.test in the TSA package. According to the help file in R, this function “Performs the McLeod-Li test for conditional heteroscedasticity (ARCH).”
However, it has been mentioned on page 50 of the book “Introduction to…
Stat
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Lag length selection in ARCH-LM test
How to determine the lag length $q$ in the ARCH-LM test?
If I set $q=1$, the result is homoscedastic (failed to reject H0).
But if I set $q=4$ for example, the result is heteroskedastic (reject H0).
Which one should I use?
Fatma
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Unconditional mean of an ARCH (1) model
In demonstrating that the unconditional mean of $a_t=\sigma_t \epsilon_t$ is $0$, my professor uses the tower property of conditional expectation:
$\mathbb E [a_t] = \mathbb E\mathbb E[a_t|F_{t-1}]=\mathbb E[ \sigma_t\mathbb E(\epsilon_t) ]=0$
From…
Twilight Sparkle
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Error term/Innovation process in ARCH/GARCH processes?
I am wondering about the distribution of the error term/innovation process in a ARCH/GARCH process and its implementation, I am not sure about some points. The basic assumption is
$r_t=\sigma_t*\epsilon_t$
where the $\sigma_t$ is the volatility,…
Stat Tistician
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Is AR(1)-ARCH(1) covariance stationary?
Say I have the following model:
$$
y_t = c+\phi y_{t-1} +\epsilon_t \,, \epsilon_t|\Omega_{t-1} \tilde{} WN(0,\sigma_t^2 )
$$
$$
\sigma_t^2=\alpha_0+\alpha_1\epsilon_{t-1}^2
$$
$$
|\phi|<1 \,, \alpha_0 \geqslant 0, \ 0<\alpha_1<1 \,.
$$
I know that…
A_Jo
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How should I test for multivariate ARCH effects in R?
I want to test for conditional heteroskedasticity in the form of ARCH effects in a multivariate time series. In the univariate setting, an ARCH-LM test can be used. A natural extension for the multivariate setting would be a multivariate ARCH-LM…
Richard Hardy
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Simple asymmetric ARCH vs asymmetric ARCH
I am working with GARCH models. As I try to familiarize myself with Stata's options I have run into a number of questions I am having problems answering.
What is the difference between SAARCH and AARCH?
If EGARCH and AARCH are both tools to deal…
Clayton
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Forecasting in ARCH(1) models
I read this definition of an ARCH(1) model:
$$r_{ŧ}=\sigma_{t|t-1}\epsilon_{t}$$
$$\sigma^{2}_{t|t-1} = \omega + \alpha r_{t-1}^{2}$$
However, when it comes to forecasting the h-step-ahead variance, I don't understand why is defined in this way.…
Robert Smith
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Interpreting the coefficients of ARCH Lagrange Multiplier Test
I am new to econometrics and I am building my first econometric model. I ran the LM test on a univariate time series data of 12000 observations and got the following stats:
Chi-squared = 458.5313, df = 12, p-value < 2.2e-16
Can I reject the null?…
Piscean
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how to test heteroskedasticity of a time series in R?
How can I test heteroskedasticity of a time series in R? I have heard of two tests McLeod.Li.test and bptest (Breusch-Pagan test). Can I use these two tests? and what are the differences and assumptions of these tests if I can use them?
Thanks
Fred
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Interpretation of McLeod-Li test for ARCH effect
I want to know if I need to use ARCH/GARCH model for my time series. How can I use McLeod.Li.test in R to do that and how should I interpret the result? the description in R help was not clear for me because in the example of the R help they used…
Fred
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