# Questions tagged [garch]

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

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19 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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### Equivalence between ARIMA and HMM

The question is about the equivalence between ARIMA models and hidden Markov models in the context of time series analysis/prediction. Specifically: Can any ARIMA(p,d,q) model bet represented by an ...
11 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. ...
19 views

### “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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### 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 ...
47 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. ...
26 views

### 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 ...
33 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 ...
26 views

### GARCH(1,1) residuals are not homoskedastic

Given the following simulated GARCH(1, 1) process: ...
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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 ...
26 views

### 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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### 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 ...
24 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 ...
23 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 ...
40 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 ...
29 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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### 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 ...
33 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 ...
38 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 ...
35 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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### 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 ...
35 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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### “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 ...
36 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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### 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 ...
28 views

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

I have the following GARCH(1,1) model ...
24 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}+....
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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### 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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### 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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### 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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### 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 ...
22 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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### ruGARCH newsimpact curve different from theoretical value

When calculating the NIC https://www.nber.org/papers/w3681 I get a different value from the ones calculated by ruGARCH. To get the same data (not optimized, just an example): ...
67 views

### Interpretation of Ljung-Box tests for GARCH models from the 'rugarch' package in R

I have used the 'rugarch' R package to fit a GARCH model, as: ...
21 views

### Comparison of daily fitted volatility and observed absolute daily return

I am trying to estimate daily volatility of stock's return. I have the below daily stock return data for 400 days: ...
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### Does the method of reruning GARCH models every day (to update parameter values and improve out-of-sample forecasting performance) have a name?

It is my understanding that normally GARCH models make forecasts for say T-K days ahead. Instead of doing that I would like to use the data for days 1, 2, ...,k in my dataset to fit a GARCH model to ...
49 views

### What are the differences between GARCH/ARCH and LSTM for time series prediction? [closed]

Can somebody explain in-detailed differences between the GARCH/ARCH model and LSTM for time-series prediction and how the model works under the hood?
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### How does GARCH compute the realized daily volatility to be compared to the output of the model, to compute in-sample MSE?

How do GARCH and GJR-GARCH models (as implemented in rugarch or in EViews) calculate the in-sample MSE if they use the time series of daily returns as the input and don't use a time series of daily ...
19 views

### volatility and conditional correlation O-GARCH

Doing an assignment i have to compare the volatility and conditional correlation of two type of O-GARCH: in the first one is standard O-GARCH while the second is an O-GARCH with principal component ...
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### Is it possible to fit GJR-GARCH using BOTH daily variances and daily returns?

I have to fit a GJR-GARCH to daily variances (computed using the 5-minute stock price data for that day) in addition to using the daily returns (computed using the daily stock price data) as the input....
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### Autocorrelation in the squared residuals of Multivariate GARCH models

Most papers use the Hosking (1980) to detect whether the multivariate GARCH model used captures all heteroskedasticity effects. However, Bauwens (2006)(p.101-102) do state shortcomings of it, when ...
25 views

### Check leverage phenomenon on ARCH-GARCH models in R

I estimated an ARCH(10) and a GARCH(1,1) models on R. I have to verify the presence of leverage phenomenon, graphically or descriptive evidence. Leverage effect: volatility reacts asymmetrically to ...
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### What is the “standardized residuals” in GARCH(1,1) model with Student-$t$ innovations?

I'm using the dataset daxreturns, with the description of the data like: "This data set contains transformed standardized residuals of daily log returns of 15 ...
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### Which GARCH model to choose if both are showing same AIC/BIC and log-likelihood?

I am doing a GARCH model for returns under different error distributions using the R rugarch package. However, two models, under the generalised error distribution and the skewed generalised error ...
16 views

### Should I standardize forecasted and actual values for Mincer Zarnowitz test?

I have some out-of-sample forecasted values of variance through some GARCH model, and now I am trying to perform a Mincer-Zarnowitz test for validity of my predictions. I first standardized both ...