Questions tagged [garch]

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

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3answers
261 views

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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0answers
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What is the “Generalized Error Distribution”?

In Nelson (1991), which develops the Exponential GARCH model, he refers (p. 352) to the "Generalized Error Distribution (GED)" and provides this density function: $$f(z; \nu) = \frac{\nu\...
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Where can I find an example of calculating a GARCH model without packages?

Every example I've come across uses predefined packages like 'import arch_model'. I can't determine the method given these black boxes. Thank you.
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1answer
27 views

Innovations/Residuals/Errors in statistics or GARCH

I'm pretty new to Statistics (my technical background is slightly different) so apologies if this question seems dull. I got thrown head first into an applied math based project. What is the ...
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24 views

ARCH coefficient in GARCH models

Is anyone knows to interpret ARCH Coefficient in GARCH Models ? I tried to find what is ARCH Coefficient means. Some says it's for detecting Spillover effect, Some says Volatility Clustering or ...
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1answer
12 views

Partially left truncated data in bivariate time series, one series is missing data what to do?

I have two time series of futures Settlement Prices where I am to model the systematic volatility of the settlement prices for these two time series. My plan is to: Calculate the logged returns. Fit ...
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0answers
30 views

GARCH estimation for subsamples

I would like to apply a GARCH(1,1) model for subsamples at time intervals length $k\delta$ on a stock return time series $\big(r(i\delta,(i+1)\delta)\big)_{i=0}^{kq-1}$ each element of which is the ...
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1answer
13 views

Forecasting two part ARIMA-GARCH model

I am conducting the ARIMA-GARCH model in two stages. First, I assess the ARIMA model and then apply GARCH model on the residuals from the ARIMA model. My model looks like this: ...
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1answer
19 views

Are distributions of innovations standardized in GARCH models in `rugarch` package in R

I estimates FIGARCH model using rugarch package. While model specification by the function ugarchspec, one of its argument is ...
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0answers
13 views

How to “de-mean” a series so it can be used in MSGARCH R package?

0 I would like to use MSGARCH package to fit a Markov switching GARCH model. I know that there is a useful MSGARCH package in R but it does not allow to add a conditional mean equation like in rugarch ...
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Does Volatility() method in MSGARCH package return standard deviation or variance?

Simple question but I struggle to find an answer. Does Volatility() method in MSGARCH package in R return standard deviation or variance?I am asking this question because I get strangely low estimates ...
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Mean reversion check on a DCC GARCH model

I have built up a DCC sGARCH(1,1) model. After the forecast I wanted to check visually if correlation and covariance forecast for a long period ahead like 10 year was mean reverting towards the mean ...
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choose GARCH Models to fit with data

So I'm trying to find a model that fit for my data. this confused me. I tried GARCH(1,1) and GJR-GARCH btw ... the one with GJR-GARCH has AIC and BIC higher than GARCH but in the Variance Equation, I ...
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R uGarchRoll Value at Risk calculation

I am using ugarchroll method to calculate VaR but I want your help to understand the calculation behind the function for a GARCH(1,1) model. Assuming I use the following code (zero mean - GARCH(1,1)) ...
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0answers
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R ugarchfit: statistical tests

I am building an ARMA + GARCH model to forecast the volatility of EURUSD exchange rate. I have been trying several combinations of p and q, but I cannot get a complete good model. This is the output ...
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0answers
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Is standard deviation of residuals of Markov switching GARCH model regime specific?

The MSGARCH package in R implements Markov switching GARCH model specified in the paper "A New Approach to Markov-Switching GARCH Models" (2004) by Haas et al. By the code ...
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0answers
24 views

Is it sound practice if I use min-max normalization to transform my data in GARCH modelling?

I am attempting to model inflation volatility of countries that have experienced hyperinflation. When using GARCH models (rugarch) in R, the parameters fail to converge. However, when I transform the ...
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0answers
54 views

how to interpret the results of a GARCH model fit R/python

I have got the following output from a gjrGARCH model, and I need help to interpret it in order to decide whether it is already a good model and proceed with the forecast. ...
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“Best” ARMIA model changes with introduction of ARCH/GARCH errors?

When one introduces ARCH or GARCH errors into an ARIMA models, sometimes the "best" (lowest IC) will change using automated software (e.g. "auto.arima"). In a theoretical sense I ...
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1answer
29 views

Interpret GARCH

is anyone know how to interpret GARCH model? I mean, maybe giving me some recommendations for books or research papers that contain an interpretation of GARCH in it? Thank You
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Volatility based Markow Switching GARCH model

I am trying to model returns using ARMA-GARCH process and noticed that returns series behave differently under the periods of high volatility when compared to periods with low volatility. Therefore, I ...
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2answers
59 views

Why do we fit (G)ARCH model?

The ARCH model is: $$\left\{ \begin{align*}& X_t=\sigma_t Z_t, \ \{Z_t\} \sim IIDN(0,1) \\ & \sigma_t ^2 =\alpha _0 +\alpha _1X_{t-1}^2+\ldots+\alpha _p X_{t-p}^2 \end{align*} \right. $$ ...
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What is conditional likelihood?

In my course book in time series I read that we usually use conditional likelihood to fit an ARCH model because the likelihood function is usually rather complicated. What is conditional likelihood?
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Choosing the best fitting model with AIC and p-value

I have a financial time series, exchange rates. Between ARCH(10) and GARCH(1,1) I would like to see which model fits best my TS. For ARCH I have a p-value smaller than 0.05 and for GARCH p-value is ...
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1answer
50 views

GARCH diagnostics: autocorrelation in standardised residuals and poor results of Goodness-of-Fit Test

I am trying to fit best ARMA - GARCH model using rugarch in Python on financial data 5 min returns series. I am using last 10k observations for this purpose. The goal is to predict next return and its ...
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1answer
31 views

GARCH(1,1) residuals are not homoskedastic

Given the following simulated GARCH(1, 1) process: ...
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0answers
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What are some sound multivariate GARCH models with proven mathematical/statistical properties?

Some popular multivariate GARCH models such as BEKK and DCC have been criticized for the nonexistence of the corresponding stochastic processes and (if I interpret that correctly) the following ...
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Bootstrap the estimated GARCH volatility…for the two stage estimation

GARCH(1,1) model is represented as \begin{aligned} x_t &= \sigma_t z_t, \\ \sigma_t^2 &= \omega+\alpha x_{t-1}^2+\beta\sigma_{t-1}^2, \\ z_t &\sim i.i.d (0,1). \end{aligned} If I want to ...
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1answer
25 views

Comparing different specifications of GARCH models with different distributional assumptions [closed]

For purely educational reasons I'm currently trying to fit different types of GARCH models, varying on the order parameters as well as flavor (standard, eGARCH, iGARCH, GJR-GARCH) and different ...
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1answer
27 views

Simulate GARCH volatility conditional on return series

Is it possible to simulate GARCH volatility series conditional on observed return series? What I want is that my simulated GARCH volatility will incorporate uncertainty of the estimated parameters but ...
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1answer
26 views

How to compare GARCH model outcomes from two equal time series

I'm writing my thesis and will sketch the scenario I try to research: I have data for my GARCH model from two periods. The input is the same, as is the length (1y). I want to compare both the outcome ...
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1answer
69 views

ARIMA + GARCH modelling in Python

I am trying to implement ARIMA(4,0,4) - GARCH (P,Q) model in Python (the ARIMA orders were selected based on best AIC/BIC). Multiple sources suggest fitting ARIMA and GARCH simultaneously rather than ...
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1answer
40 views

Multivariate GARCH, DCC(1,1) - Autoregressive order

About my question: it is a mix between the assumptions of the model and the implementation. I implemented a DCC(1,1) model for two retrun series (bivariate correlation), with the autoregressive order: ...
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1answer
24 views

Second-order moments of a White Noise process

One of my textbooks on time-series analysis claims that Dependency in the second moments of the residuals contradicts the assumption of a constant, time-invariant variance. Thus [the residual] is not ...
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0answers
53 views

IGARCH in Python

How can I simulate an IGARCH series in Python using arch library? I have already tried these two ways: used function GARCH.simulate with fixed parameters where ...
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1answer
39 views

GARCH forecast of series (in R) seems too high

I am wondering why the mean of my model is so high leading to a high forecast of the time series data. I included a linear regression in the external regressors as there is a clear downward trend. I ...
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1answer
49 views

Difference between heteroscedasticity and ARCH effects?

What is the difference between heteroscedasticity and ARCH effects? For example in R you can do a Breusch-Pagan Test to test for heteroscedasticity, and a Lagrange Multiplier (LM) test for ...
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0answers
49 views

Generate and estimate models like IGARCH, FIGARCH or HYGARCH

My issue is that I'm trying to simulate modifications of GARCH model like IGARCH, FIGARCH, or HYGARCH. I have already found that some of them are possible to generate in R (rugarch or (no more ...
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1answer
40 views

Standardized GARCH-residuals, distributions and AIC

So, I have been wondering about an interesting observation. My data contains 1006 log-returns of the SP500-index and I've estimated a GARCH(1,1)-process with Gaussian quasi-maximum likelihood - ...
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0answers
34 views

“rugarch”-package: Inconsistent output of p-values and t-values

I am using the "rugarch"-package to estimate the impact of two exegonous variables on a commodity price. Now I found that the p-values and t-values seem to be very unrealistic in some cases. For ...
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1answer
63 views

conditional volatility plot in R - GARCH

When I build a GARCH(1,1) with a skewed generalised error dist to model the innovations, with a linear trend using the fGarch library I get the following: ...
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2answers
22 views

Value-at-Risk formula with GARCH-model

I'm totally aware of that if we look at some loss process $L_t$, then $\text{VaR}(\alpha)$ is a quantile of the loss distribution. If we assume that $L_t=-X_t$ is the negative returns and they follow ...
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1answer
30 views

add linear trend back into time series prediction (in R)

I have the following GARCH(1,1) model ...
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1answer
31 views

How is modeling the time series error/variance, e.g. ARCH or GARCH models, different from modeling time varying forecast intervals?

I'm having a hard time understanding the intuitive difference between modeling the volatility or variance of a time series as it is done in ARCH and GARCH models: $$Y_t = c+\epsilon_t+\phi_1Y_{t-1}+....
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0answers
27 views

GARCH parameter estimation with only observed volatility

I would like to estimate the parameters of a GARCH process: \begin{equation} \begin{aligned} &r_t = \sigma_t\epsilon_t,\\ &\sigma_t^2 = \mu + \sum_{i=1}^m \alpha_ir_{t-i}^2 + \sum_{j=1}^n \...
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2answers
90 views

Are time series models limited in real life application and are primarily used to model the residuals of another model?

I"m trying to see the big picture and where time series fits in to statistical inference. I'm trying to understand when we would use a time-series model like ARIMA, GARCH, and others. From the ...
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1answer
33 views

How to simulate correlated GARCH using rmgarch package in R [closed]

I'd like to simulate a couple of simulated and correlated GARCH(1,1) using the R package rmgarch. I tried to do: ...
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0answers
22 views

Testing similarity of time series

I am looking for a metric and the associated statistical test to compare two time series or to determine whether a short series has the same parameters as the long one. The series are likely modeled ...
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0answers
56 views

Heteroskedasticity tests: heavy-tailedness of squared estimated errors

I have a time series model and obtain the following distribution of estimated errors: I suspect that the errors are heteroscedastic in the sense that their variance depends on the level of one or ...
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1answer
24 views

ARCH nested in GARCH

I have a quick question. I found this notion of "ARCH nested in GARCH" in one of the papers I'm reading right now, and I can't quite understand what it means. if anyone can help, I will be grateful.

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