Questions tagged [garch]

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is used for time series in which the conditional variance is time-varying and autocorrelated. The conditional variance is a linear combination of lagged conditional variances and lagged squared errors. The conditional variance equation in GARCH models is deterministic, in contrast to Stochastic Volatility (SV) models.

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744 views

How to obtain one-step ahead forecast in Python based on GARCH?

I am trying to produce one-step ahead forecast using GARCH in Python using a fixed windows method. I ultimately want to put the code below in a for loop, but this code snippet does not perform as I ...
0 votes
1 answer
228 views

Interpretation conditional volatility plot

I have plotten the log differences of exchange rates and in the same plot, I show the conditional volatility $\sigma_t^2$. The conditional volatility follows approximately the same path, but is much ...
0 votes
0 answers
104 views

Forecasting VIX with GARCH(1,1)

Aim: Forecast VIX using GARCH(1,1) Reason: I want to be able to forecast VIX on several horizons, in order to be able to forecast the SP500 index through linear regression. Tools used: Python, ...
2 votes
1 answer
83 views

Optimal Hedging Ratio using Copula Models

Let $r_{s, t}$ and $r_{f, t}$ be the return rates of the spot and futures of a commodity at time $t$. The hedging ratio based on variance minimization is calculated by finding the minimum of the ...
3 votes
1 answer
670 views

Realized Variance (realized volatility)

I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
0 votes
1 answer
95 views

Can one estimate rather than forecast volatility using the GARCH model?

Can one use the GARCH model to estimate the realized variance/volatility, such as done in this paper, rather than forecast the volatility, from (high frequency) price/tick data?
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0 answers
65 views

Long-run volatility forecast of a GARCH(1,1)

Can I assume that "the long run volatility forecast of a GARCH(1,1) is higher in periods of high volatility than in periods of low volatility?
2 votes
1 answer
257 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
1 vote
1 answer
136 views

Looking for a good introduction to modelling ARCH-type models

I am starting to think about my dissertation topic for my undergraduate degree. I am interested in comparing volatility of stock indices during COVID-19 to the years leading up to the pandemic. I have ...
1 vote
1 answer
582 views

Manually calculating and backtesting VaR and CVaR from DCC-GARCH R

I estimated a GARCH fit to the log returns of three series (CAC 40, a french real estate index and french T10 bond yield series) using rugarch. I then manually ...
3 votes
1 answer
335 views

GARCH(1,1)-M MLE optimization with fmincon in R

I've searched thru dozens of papers and did not find in any of them satisfying and enough theoretical answers to my concerns. So I've combined everything what I found below. Please indicate if my ...
1 vote
2 answers
151 views

$n$-day ahead forecast for asymmetric DCC-GARCH model

I am working on forecasting covariances with the use of MGARCH models. I was wondering if anyone knows how to implement a n-day ahead forecast of the aDCC (asymmetric DCC) model in R. The ...
3 votes
1 answer
458 views

VAR-aDCC full ARCH and GARCH parameter matrices in R

I am working with the rmgarch package in R and I estimated a VAR-aDCC model. Is there any way to extract the extended version of estimates (allowing for volatility ...
3 votes
2 answers
341 views

When the two time series with different length, how could we analysis them with a bivariate GARCH model?

At this moment, i need to do the analysis of rouble/us dollars exchange rate and the stock market index in Russia, I prefer to do that in a multivariate GARCH model. However, I have a question about ...
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0 answers
81 views

GARCH option pricing

I have been trying to implement GARCH(1,1) model for pricing call options. Suppose I have calibrated Garch(1,1) model for modelling the conditional volatility using the historical data of an equity ...
1 vote
2 answers
248 views

2-day ahead prediction of value at risk with GARCH(1,1) in R

Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2: ...
1 vote
1 answer
137 views

Variance of the price from returns variance

Let's say that we have the variance of the daily return at $t_0$: $$\sigma_{r_{t_0}}^2=\text{Var}[r_{t_0}]=\text{Var}[\frac{S_{t_0}-S_{t_0-1}}{S_{t_0-1}}]$$ for price process $S_t$. Is there a way to ...
4 votes
1 answer
276 views

evaluating garch models

I used ugarchroll to backtest my garch model on S&P returns this is my code ...
3 votes
1 answer
196 views

Is there a HAR that deals with the leverage effect?

The EGARCH is a special GARCH model that treats the leverage effect of the volatility. The HARV does not make a distinction between negative and positive returns. Is there a special HARV that deals ...
0 votes
1 answer
173 views

Conditional Value at Risk using GARCH models

In this paper: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjSlIHYnMj1AhWqNOwKHZfHDhkQFnoECAkQAQ&url=https%3A%2F%2Fwww.mdpi.com%2F2076-3387%2F9%...
1 vote
1 answer
237 views

How to deal with negative intercept terms on GJR-GARCH(1,1) model?

Recently, I have been studying the relationship between COVID-19 and stock returns using a GJR form of threshold ARCH model. However, I got some unusual estimation results I can't figure out whether ...
0 votes
1 answer
98 views

Why in ARCH/GARCH model we don't add residual?

The most simple ARCH is given by: $$\sigma^2_t=E{\epsilon_t^2|I_{t-1}}=\alpha_0+\alpha_1\epsilon^2_{t-1}$$ Why in this model we do not have residual as well? Example: $$\sigma^2_t=E{\epsilon_t^2|I_{t-...
1 vote
1 answer
73 views

What implies "conditional heteroskedasticity" in (G)ARCH? [closed]

I have trouble to understand what implies "conditional heteroskedasticity" term in (G)ARCH models. The residual $\epsilon$ is stationary, hence homoskedastic (unconditional variance is ...
0 votes
0 answers
76 views

how should i interpret the gjr-garch output where the gamma coefficient comes positives but insignificant?

i run gjrgarch model on russia stock market where the gamma coefficient in gjrgarch(1,1) model output is insignificant but positive. "gamma1 -0.026240 0.033785 -0.77669 0.437340" how ...
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0 answers
91 views

Any reproducible r code for week day effect in garch?

I am looking for an r code to run a GARCH model with a day of week effect. Is there any package or code I can use for this?
2 votes
2 answers
5k views

How to fit a SARIMA + GARCH in R?

I'd like to fit a non stationary time series using a SARIMA + GARCH model. I have not found any package that allow me to fit this model. I'm using rugarch: ...
0 votes
0 answers
132 views

I am getting an $\alpha=0$ in the GARCH(1,1) model. Is this normal and how must I interpret it?

I am running a GARCH(1,1) on return data. For some data sets, I am getting an $\alpha=0$ and a $\beta$ of 0.999. Is this normal? If so how should I interpret it? Here is my code, here j are daily ...
4 votes
1 answer
588 views

Simulation of a DCC-GARCH

I want to simulate some exchange rates with a DCC GARCH. I know the package rmgarch but I want to code the simulation my self. The following are the main equations ...
1 vote
1 answer
489 views

How to interpret Sign bias test in GARCH (1,1) and in GJR-GARCH?

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3 votes
0 answers
73 views

What is the relationship between the estimated GARCH(1,1) conditional volatility and the true conditional volatility

Suppose that the data has been generated by a GARCH(1,1) model, i.e. \begin{align} y_t &= h_t \epsilon_t, \; \epsilon_t \sim N(0,1) \\ h_t &= \alpha_0 + \alpha_1 \epsilon_{t-1}^2 + \...
2 votes
0 answers
72 views

Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility

Realized volatility is a long-memory process and so I fitted an ARFIMA(0,d,0) to log(RV15) where RV15 is realized volatility calculated from 15-min bars. I proceeded to examine how changing the bar ...
0 votes
1 answer
325 views

How to use conditional volatility under GARCH model to forecast price?

I have come across videos on youtube about GARCH model in stimulating and forecasting stock price, however, it is programmed in R language. Is there any tutorials teach the similar as the videos shown ...
0 votes
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51 views

Covariance of ARCH(2) model

I am having problems solving the following exercise: The solution is the following: I understand we are calculating E(r^2t) and E(r^2tr^2t-1) because they are part of the covariance formula, and ...
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0 answers
61 views

Any way to identify optimal lag length for garch model using Python

Is there any python library that automatically calculate p and q for the GARCH model? (for example: auto_arima in pmdarima) since that for both statsmodels and arch library in python needs to manually ...
1 vote
2 answers
211 views

GARCH(1,1) parameter estimation optimization method

In estimating a GARCH(1,1) model, $$\sigma_{t+1}^2 = \omega+\alpha \epsilon_t^2+\beta\sigma_t^2$$ Usually the parameter tuple $(\omega,\alpha,\beta)$ is estimated by the quasi-maximal likelihood. ...
0 votes
1 answer
100 views

GARCH parameter estimation by linear regression?

In estimating a GARCH(1,1) model, $$\sigma_{t+1}^2 = \omega+\alpha \epsilon_t^2+\beta\sigma_t^2$$ Usually the parameter tuple $(\omega,\alpha,\beta)$ is estimated by the quasi-maximal likelihood$. Can ...
2 votes
1 answer
136 views

GARCH calibration with overlapping time intervals

In constructing a GARCH(1,1) model over a time length $\delta$, I am considering the following procedure. The purpose of this procedure is to give more training (calibrating) samples than non-...
0 votes
0 answers
132 views

Realized Volatility + GARCH - can I use hourly realized volatility?

I hav minute bar FX data and I am trying to fit a realized variance GARCH model using rugarch. This normally works by providing daily returns and daily realized volatility to the model. Realized ...
2 votes
0 answers
105 views

Fitting GARCH(1,1) to log returns instead of residuals - centering crucial?

For a project I need to fit a GARCH(1,1) model to the log returns of an index. When using the residuals of an ARMA or ARIMA model it is clear that the (conditional) mean is 0. When using the log ...
0 votes
1 answer
91 views

How to include heteroscedasticity in copula modelling

I have a dataset of 9 variables and I want to fit a t-copula to them in order to construct a multivariate and after that resample from it. I am using Matlab. ...
3 votes
1 answer
1k views

How to fit exogenous + GARCH Model In Python?

I am studying a textbook of statistics / econometrics, using Python for my computational needs. I have encountered GARCH models and my understanding is that this is a commonly used model. In an ...
1 vote
0 answers
55 views

HNGARCHFIT in R (No standard deviations or P values printed)

When I estimate an HN-GARCH model using the hngarchfit() from the fOptions package in R, only the coefficient estimates are printed. There are no standard deviations or P-values printed. Does anyone ...
0 votes
0 answers
36 views

Perfect in-sample size for out-sampling volatility prediction (EGARCH(1,1)

I have a few questions regarding in-sample size for volatility forecasting in EGARCH(1,1). I'm currently sitting with a dataset consisting of 1387 trading days of the S&P-500 index. I would like ...
1 vote
0 answers
35 views

How to estimate lambda from NAGARCH submodel in R

I am trying to estimate the model="fGARCH", submodel="NAGARCH" from the rugarch package in R. However, when I am estimating the parameters, only omega, alpha, beta and gamma are ...
2 votes
0 answers
127 views

GARCH Option Pricing in R

I am trying to code a GARCH option pricing model in R. I am still new to R so this does seem a bit complicated. I want to estimate an asymmetric GARCH model as well as an EGARCH model. This I have ...
2 votes
0 answers
38 views

Empircal data analysis delta hedge error of Black-Scholes by Mark Davis

Regarding Mark Davis derivation of the delta-hedging error occuring in the black-scholes as a result of difference in realized volatility and implied volatily. The formula reads as follows: $$ Z_t = \...
2 votes
2 answers
100 views

Deciding (p,q) in garch and model test on empirical data

I'm currently working on a dataset containing data from the 29 January till the 29 July 2009. In the dataset I have prices of the S&P 500 index for all days. Furthermore, I have the implied ...
2 votes
0 answers
122 views

HNGARCH Option Pricing in R (How to loop)

I am having difficulties when using the HNGOption program in R. The program will only run for 1 specific option price, meaning that I would have to manually insert strike price etc. and this would ...
1 vote
0 answers
36 views

Calculating E^2[σ^2] where σ is a GARCH(1,1) Proces

Given that α =0,113079 β = 0,873884 ω = 0,0000081 Need the calculate a call price using garch volatility I alsa calculated the kurtosis = 235 enter image description here: https://www.researchgate.net/...
3 votes
1 answer
188 views

EGARCH(1,1) mean

I'm trying to model an EGARCH(1,1). However, I dont understand why the mean from the general to (1,1) becomes $\sqrt{(\frac{2}{\pi})}$. The following I am refering to is:

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