Questions tagged [garch]
A model for time series in which the conditional variance is time-varying and autocorrelated.
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Is there any gold standard for modeling irregularly spaced time series?
In field of economics (I think) we have ARIMA and GARCH for regularly spaced time series and Poisson, Hawkes for modeling point processes, so how about attempts for modeling irregularly (unevenly) ...
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What is the difference between GARCH and ARMA?
I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?
Here is the (G)ARCH(p, q) process
$$\sigma_t^2 =
\underbrace{
\underbrace{
\...
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For intuition, what are some real life examples of uncorrelated but dependent random variables?
In explaining why uncorrelated does not imply independent, there are several examples that involve a bunch of random variables, but they all seem so abstract: 1 2 3 4.
This answer seems to make sense....
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How to interpret GARCH parameters?
I use a standard GARCH model:
\begin{align}
r_t&=\sigma_t\epsilon_t\\
\sigma^2_t&=\gamma_0 + \gamma_1 r_{t-1}^2 + \delta_1 \sigma^2_{t-1}
\end{align}
I have different estimates of the ...
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Implementation of CoVaR (a systemic risk measure) in R
I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this ...
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Does applying ARMA-GARCH require stationarity?
I am going to use the ARMA-GARCH model for financial time series and was wondering whether the series should be stationary before applying the said model.
I know to apply ARMA model the series should ...
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If $X_t^2$ is stationary, is $X_t$ necessarily stationary?
I came across a proof for one of the properties of the ARCH model which says that if $\mathbb{E}(X_t^2) < \infty$, then $\{X_t\}$ is stationary iff $\sum_{i=1}^pb_i < 1$ where the ARCH model is:
...
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Fit a GARCH (1,1) - model with covariates in R
I have some experiences with time series modelling, in the form of simple ARIMA models and so on. Now I have some data that exhibits volatility clustering, and I would like to try to start with ...
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Accuracy of Volatility Forecast
I understand the basic concept of ARCH/GARCH models and the basic mathics behind it. That is, one models the "volatility" of a time series, i.e. the residuals of a time series describing ...
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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 ...
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Using ARMA-GARCH models to simulate foreign exchange prices
I've fitted an ARIMA(1,1,1)-GARCH(1,1) model to the time series of AUD/USD exchange rate log prices sampled at one-minute intervals over the course of several years, giving me over two million data ...
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How to choose number of lags in ARCH models using ARCH LM test?
I would like to ask you, what is the correct number of Lags in ARCH LM Test? I am referring to ArchTest in FinTS package, but other ArchTest (such as the one in Eviews) provide same results. In many ...
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Is there an equivalent of ARMA for rank correlation?
I am looking at extremely non linear data for which the ARMA/ARIMA models do not work well. Though, I see some autocorrelation, and I suspect to have better results for non linear autocorrelation.
1/ ...
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Time series analysis: since volatility depends on time, why are returns stationary?
I run Dickey Fuller test in order to know if stock returns are stationary.
I get that no matter which stock I take, his return is stationary.
I don't know why I get this result since it is clear that ...
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Bootstrap sample with size greater than the original sample
I want to predict future returns over a 20 days horizon using an ARMA-GARCH model fitted to my data.
The goal is to estimate different risk measures like VaR or CVar.
In particular say I use AR(1) ...
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Forecasting time series using ARMA-GARCH in R
I'm using rugarch package to estimate and forecast my time series. First, I estimate an ARMA model:
...
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Which econometric models can be used to forecast security returns + ARIMA/GARCH questions
I'm trying to write an undergraduate thesis wherein I test the predictive power of a given econometric model on a given financial time series. I need some advice on how I should go about doing this. ...
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Persistence in GJR-GARCH (asymmetric GARCH)
Consider the standard GARCH model:
$$ \sigma^2_t = \omega + \alpha\varepsilon^2_{t-1} + \beta\sigma^2_{t-1}.$$
The so-called persistence parameter is defined as the sum $\alpha+\beta$.
Now consider ...
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Better understanding of GARCH and ARCH models [closed]
I want to make a function that does GARCH and ARCH in python for calculating variance. But I only have a general understanding of the model. Are there any good papers that can be recommend to give me ...
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Fitting a GARCH(1, 1) model
I am trying to fit my own GARCH(1,1) model using python. I have read numerous papers at this point looking for the log likelihood function of the parameters that I need to optimize. To further confuse ...
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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 ...
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What is fitted in a GARCH: residual or log-return?
Given a time-series of log-return of SP500, then to obtain the volatility process what should we do? Some people say that we need using the ARMA model to withdraw the residual series, then plug this ...
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What's the skewed-t distribution?
I have just learned GARCH model. One condition distribution of it is "sstd". One question of my coursework is to justify if the conditional distribution is skewed. I have seen another example sheet ...
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GARCH vs SV for Forecasting
I believe I am aware of how GARCH family and stochastic volatility models differ in their construction and assumptions on the volatility states, (i.e. GARCH family assumes deterministic volatility ...
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Automated parameter selection for a GARCH model, in a similar manner to the forecast package
I was wondering: is there are a package in R for automated GARCH model selection? I'm thinking of something like what the forecast package does for ARIMA models.
If I implement this myself, would it ...
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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&...
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How Large a Difference Can Be Expected Between Standard GARCH and Asymmetric GARCH Volatility Forecasts?
I have been using various GARCH-based models to forecast volatility for various North American equities using historical daily data as inputs.
Asymmetric GARCH models are often cited as a ...
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ARMA-GARCH model selection / fit evaluation
I'm trying to fit an ARMA-GARCH model to a data set of FTSE 100 log returns (which I've uploaded here). However, I'm not able to find a well-fitting model. Below are the ACF and PACF of the log return ...
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How to decide the p and q for GARCH model?
My question is simple. When shall I stop when trying the value for p and q?
I have got the loglikelihood from ARCH(1) to ARCH(10). It's increasing. And then I tried GARCH(1,1), GARCH(2,1) etc. The ...
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Weak stationarity and ARMA-ARCH/GARCH models?
I am slightly irritated about weak stationarity in connection to ARCH/GARCH models. I do not know the answer and I am not sure about it:
The basic question is:
Do we have to test weak ...
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Maximum likelihood in the GJR-GARCH(1,1) model
In the standard GARCH(1,1) model with normal innovations
$\sigma^2_t=\omega+\alpha\epsilon^2_{t-1}+\beta\sigma^2_{t-1} $
the likelihood of $m$ observations occurring in the order in which they are ...
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Why is GARCH offering no predictive value?
I am playing around with GARCH models for the first time (I have a stats background but basically no experience with GARCH), trying to forecast volatility in a financial time series.
I trained a GARCH(...
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Should log-likelihood values increase when the sample size of a simulation increases?
If one simulates a process (such as an ARMA-GARCH process) with sample size $n$ and log-likelihood $x$, should this log-likelihood increase when the sample size increases to $2n$ for example?
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Do parameters stay unchanged when GARCH is scaled?
Let's say we have a GARCH($1,1$) process specified as follows:
$y_t = \epsilon_t \sqrt h_t, \quad \epsilon_t \sim N(0,1) \quad \text{i.i.d.}$
$h_t = a_0 + a_1 y^2_{t-1} + b_1 h_{t-1}.$
If we were ...
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Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term
I would like some help with a GARCH(1,1) volatility modeling.
I am working with the assumption the volatility is the weighted sum of three factors: Long run variance + $n-1$ squared return + $n-1$ ...
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Selecting between ARMA, GARCH and ARMA-GARCH models
I am following this tutorial (mirror) on ARIMA and GARCH modeling and I wanted to make sure I am interpreting the results correctly.
ARMA model:
...
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Initial value of the conditional variance in the GARCH process
From what I know, the GARCH(p,q) model is estimated via MLE and through an iterative process. Let's say if i wanted to recreate a GARCH(1,1) parameter estimation with excel solver (through maximizing ...
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What to do if time series are non-stationary? [closed]
Data:
I have a time series data of 2528 daily observations for OMXS.30 (Stokholm) closing price.
The aim is to fit proper ARCH/GARCH models and use for forecast daily Value at Risk. Here is a plot of ...
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Applications of ARCH models
As self-study, I'm interested in learning about ARCH models and its extensions/variations, and I've been looking for journal-published articles about its possible real-life modeling and applications ...
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Interpreting QLIKE and MSE Loss function (Patton 2011)
In Patton (2011) the author finds that both the MSE and the QLIKE loss function are robust when used to compare rivalling volatility forecasting models, which means that using a proxy for volatility ...
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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 ...
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Why is a GARCH model useful?
As I understand it, one can model changing variance of a time series process with a GARCH model. What I don't understand is, how can one actually make predictions with this?
Since
$$
y_t = \sigma_t \...
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On forecasting, the mean squared error and realized volatility
Say one has finished estimating a correctly specified GARCH(1,1) on a daily time series and now wants to evaluate the accuracy of the one step ahead forecasts what steps or tests could one do?
I ...
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ARMA/GARCH estimation in sequence
I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with ...
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Procedure for fitting an ARMA/GARCH Model
I want to try fitting an ARMA/GARCH model but want a methodological approach rather than fitting different models and picking the best one. However, I'm not sure how to choose my AR and MA terms for ...
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What's the point of (G)ARCH when you can square the residual and use ARMA?
I'm taught that
$$
\begin{equation}
\begin{aligned}
X_t \sim \text{ARCH}(p) & \rightarrow X_t^2 \sim \text{AR}(p) \\
X_t \sim \text{GARCH}(p, q) & \rightarrow X_t^2 \sim \text{ARMA}(\max(p, q)...
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Why fit ARMA before GARCH if I am interested in variance of the data, not the residuals?
I have been working on a time series where after the first difference, I observe heteroskedasticity. To handle the situation, I found that ARCH/GARCH models are used typically.
When I read about the ...
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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).
...
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