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# Questions tagged [garch]

A model for time series in which the conditional variance is time-varying and autocorrelated.

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26 views

### Interpreting test results for ARCH effects in ARIMA model

I would like to ask you, how to correctly interpret different results for different number of lags in arch.test (R)? We reject the null hypothesis (homoscedasticity)...
11 views

### How to implement Girardi & Ergun's (2013) three-step multivariate GARCH estimation of CoVaR in R?

I'm trying to calculate multivariate GARCH estimation of conditional value-at-risk, by adopting a three-step model from Girardi & Ergun (2013) paper entitled "Systemic risk measurement: ...
1 vote
10 views

### GARCH (sGARCH) with ARFIMA (ARIMA) model in Rugarch equation formula output

Could you please help to write down the exact equation? It is clear for Garch part but not clear how to add ARFIMA (1,0,1) or here just ARMA(1,1) in model equation specification. Should we also type ...
10 views

### GARCH fit to the residuals of AR/ARMA mean equation previously fitted

Suppose I have an ARMA (p,q) (let it be ARMA (2,2)) fitted to my original returns series and have the residuals of said ARMA model extracted. Next, it is my understanding that I need to fit a GARCH ...
1 vote
22 views

### gradient of the conditioned log-likelihood from GJR-GARCH model

given the following GJR-GARCH(1,1) $y_t = \sqrt{h_t} \epsilon_t$ where = $h_t= \alpha_0+(\alpha_1+\bar{\alpha_1}\mathbb{I}(y_{t-1}<0))y_t^2+\beta_1h_t$ and $\alpha_0>0$ $\alpha_1,\beta_1>0$ , ...
20 views

### Estimating and fitting a GARCH model

By far I've become really familiar with the concept of GARCH but I'm still confused on how to go on with the implementation especially that I've seen multiple sources using different approaches: ...
17 views

### How to compare the performance of a volatility forecast like GARCH (1,1) with exogenous variables (MSE?)

I want to investigate, weather financial news have an influence on the volatility prediction of asset returns (daily data) when including them into the variance model/mean model. I have fit a GARCH/...
36 views

1 vote
60 views

### GARCH CCC/DCC : empirical correlation coefficient different than the one in input CCC matrix

I implement a GARCH-DCC model in Python, for number of asset = 2. My implementation is the following : ...
61 views

### Implementing DCC GARCH Model with External Regressors in R

I am trying to estimate a DCC GARCH model with an external regressor in the DCC equation. However, the external regressor option in the rmgarch package is for the ...
32 views

### Implementing GARCH(2,2) QMLE: where does the data (squared returns) come into play?

I am trying to implement a QMLE estimation of GARCH(2,2) model as a side project. We can represent GARCH(2,2) as follows: \begin{aligned} r_{t} &= \mu_{t} + \epsilon_{t}, \\ \mu_{t} &= 0, \\ \...
26 views

### rugarch: Forecast result does not show any AR structure

I am currently working with the rugarch package to forecast the EU-ETS price. While I get reasonable results for the in-sample volatility, the forecast of the of the time series does not look correct ...
74 views

### Evaluating goodness-of-fit for GARCH models in R with QQ-plots (rugarch package)

I'm currently working with multivariate GARCH representations of time-series for financial data using the rmgarch R package. This package in turn uses the well-...
89 views

### Autocorrelation in residuals of mean model to be used in a GARCH model

My question is related to the autocorrelation present in the mean-model (which is an ARMA process), which will be used in a GARCH model. Is it ok to have autocorrelations in the residuals of the mean-...
1 vote
15 views

### Log-likelihood function for GARCHs parameters

I am writing a bachelor thesis on the evaluation of value-at-risk using GARCH models. To estimate the parameters for the GARCH models, I explained that we can do it with maximum likelihood as shown in ...
47 views

### Accelerate the fitting of an ECM-GARCH model by computing MLE gradient numerically?

I'm trying to fit an ECM model with variance following a GARCH-DCC model (GARCH with dynamic cross correlation). It has 16 parameters for 2 assets (ECM : 4 gammas, 2 lambda, GARCH: 2 alphas, 2 beta, 2 ...
1 vote
93 views

### Forecasting the conditional variance of AR(p)-GARCH(1,1) model

How can I derive forecasting formula for the conditional variance $h_{t+k}$, $k\geq1$ for AR(p)-GARCH(1,1)?
21 views

### Autocorrelation function of AR(1)-GARCH(1,1) [duplicate]

How can I derive the Autocorrelation function of AR(1)-GARCH(1,1) process which is the combination of AR(1) with GARCH(1,1) process?
88 views

### Initial guess of a GARCH-DCC model?

I’m trying to fit an ECM-GARCH-DCC model for 2 time series, the whole 3 in the same time using log-likelihood estimation. It has 14 parameters to estimate: ECM has 2 gammas and 1 lambda per time ...
46 views

### External regressor rugarch

Consider a ARMA$(p,q)$ model of $y$ with $m$ external regressors $x_1, ..., x_m$. Do I understand the documentation of the R package rugarch correct, that the considered model is of the form y(t):=\...
113 views

### $k$-th order autocorrelation of a squared ARCH(1) process

I want to derive that in ARCH(1) model, $\operatorname{Corr}(y_t^2,y_{t-k}^2)=\alpha^k$. Could you please take a look at to the photo attached and help me on how to proceed:
23 views

### Is a generalized linear model (GLM) an appropriate model where ARCH effects are found in the dependent variable?

The dependent and independent variables are all time series variables. The dependent variable is found to have ARCH effects. Is a GLM an appropriate model for modeling the relationship between the ...
70 views

### Likelihood function of GARCH with exogeneous variables in the variance model

I can see the R package rugarch allows the estimation of GARCH models with exogenous variables in the specification of the ...
32 views

1 vote
78 views

### Autocovariance of ARMA-GARCH vs. that of pure ARMA

Is the autocovariance of an ARMA-GARCH process the same as that of the ARMA part of that process? If this is too difficult/cumbersome to show, analysis of a special case like MA(1)-GARCH(1,1) or AR(1)-...
46 views

### What is the autocovariance of a GARCH process with a constant mean?

What is the autocovariance of a GARCH process with a constant mean?
I have estimated an ARCH(1) model using a skew-$t$ distribution. The results summary is: I am wondering how to get an estimate for the autocovariance given the parameters. Assuming mean zero, I am ...