# Questions tagged [garch]

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

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### Is chi-squared distribution almost surely bounded?

Let $$X_t=\eta_th_t, \eta_t\sim N(0,1), h_t=\omega+\alpha X_{t-1}+\beta h_{t-1}$$ be a GARCH(1,1)-Model with $0<\beta, \alpha<1, \omega>0$ Parameters. Let $l_t=log h_t+\frac{X^2}{h_t}$ be a ...
11 views

### ANOVA of Returns and Volatilities forecast

In my GARCH(1,1) model simulations, I generated (based on two different distribution assumptions) returns and conditional volatilities for 8 stocks across 3 scenarios over a 20-day forecasting period. ...
29 views

### How to predict residuals using ARCH model

I have been reading about the autoregressive conditional heteroskedasticity (ARCH) models and they seem amazing. I Understand that the model captures the volatile of the variance of residuals. However,...
35 views

### Calculate price forecasts from forecasted returns

I have a question which makes me so hurt. Let's have a price time series $y_{t}$ for the same asset (for example, daily S&P 500 values) $y_{t}$ It can be trendy (trend stationary or difference ...
12 views

### Normalization of Time Series for GARCH

It is generally observed that financial times series is not normally distributed. So I want to clear the following doubts: Is it necessary to normalize time series data especially before proceeding ...
1 vote
18 views

### Is it possible average an information criterion across models?

Is it possible to take the average of information criterion like the AIC? For my model comparison, I have 24 different models. I use 4 different GARCH models each with 6 different distributions for ...
1 vote
19 views

### Residuals in GARCH (1,1) is the same as the original data

I am trying to fit a GARCH(1,1) model using the rugarch package. When I use residuals to extract the residuals, I find the data ...
10 views

### MCMC predict volatility with GARCH

This is using MCMC (MH) algo to predict volatility from GARCH model: https://www.oreilly.com/library/view/machine-learning-for/9781492085249/ch04.html For simplication, consider (0,10)-GARCH (only ...
13 views

### BEKKS package in R. Are you supposed to feed residual of a mean equation model into the BEKK.fit or the return series?

I am trying to use the BEKKs Package in R. For context, my plan is to fit a VAR model of index prices to obtain the residuals. Then feed the residual into the BEKK.fit function. However, I am not sure ...
18 views

### Likelihood function of VAR-MGARCH-BEKK model?

I am doing my dissertation on the spillover effect between countries' markets and looking to use VAR-MGARCH model to do it. For example how would a change/shock of US market index affect Thailand ...
1 vote
26 views

### Fast algorithm of ARIMA-GARCH model selection

I use ARFIMA(p, x, q)-GARCH(P, Q) models for time series forecasting and when I calibrate models for selection the best via BIC criteria, I use "slow" approach when I calculate BIC for every ...
38 views

### How to Implement Newey-West covariance matrix properly for MDE estimation

I am trying to implement the MDE method for GARCH given by Baillie and Chung '01 (Estimation of GARCH Models from the Autocorrelations of the Squares of a Process, Jrl. of Time Series Analysis) but I ...
38 views

### using the GARCH model, the result of 10 forecasting values are (erroneously) equal. Any suggestion?

I am currently facing a problem with my GARCH model, specifically with the forecasted results. It appears that all the forecasted values are turning out to be identical, which leads me to suspect that ...
24 views

### Why the result of forecasting GARCH being constant?

I am new to researching modeling and forecasting using the GARCH model. So I am still confused about the result that I get. I forecast stock return volatility using Eviews. The best ARIMA model in my ...
36 views

### Bayesian variant of Ljung-Box test?

I am using Bayesian MCMC estimation methods for GARCH models and I want to check, if model residuals are uncorrelated. In classical frequentist approach, one would use standard Ljung-Box test to check ...
53 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)...
26 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
21 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 ...
13 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 ...
28 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: ...
33 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/...
89 views

1 vote
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### 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 : ...
100 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 ...
36 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, \\ \...
39 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 ...
120 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-...
124 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
20 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 ...
60 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
132 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)?
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### 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?
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):=\...