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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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What kind of ARMA-GARCH model is that?

My question is what kind of ARMA-GARCH model is the following equation and how to specify it in rugarch R module: $$r_{t+1}- r_t = \alpha_0 + \alpha_1r_t+\...
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17 views

Gluing the error terms to a VAR model

I am trying to simulate a VAR model with heterokskedastic errors. I have no problem simulating a VAR model, And I have no problem simulating heteroskedastic errors. My problem is trying to do ...
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28 views

Does the variance-covariance matrix indicate GARCH errors?

I am trying to simulate VAR models with ARCH/GARCH errors, I am wondering the best way to do this? Can I insert a covariance matrix that will lead to heteroskedasticity? Any readings are suggestions ...
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23 views

monthly conditional volatility using EGARCH model

I need the conditional volatility values using the egarch model in eviews. The result of the estimation that I get is a table where there are coefficients, p values....My question is that how could I ...
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36 views

Rolling forecast using GARCH model

EDIT This is not a duplicate of my original question linked, since I have since overcome that problem and have posted an answer. Since solving the previous problem, I have run into the problem ...
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42 views

GARCH Parameters Standard Errors

How do you compute the standard errors of a GARCH model estimated with MLE ? This paper references a method by Bollerslev-Wooldridge: [...] and computed standard errors using the robust method of ...
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25 views

Can you use GARCH-MIDAS for intraday data?

I'm working on a project to forecast volatility and I'm using intraday data (1 min). I want to include exogenous variables to the model that have daily frequency. I was wondering if GARCH-MIDAS can be ...
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32 views

Log likelihood function, GARCH(1,1) with asymmetric term

I am modelling a GARCH(1,1) and a GARCH(1,1) with an asymmetric term. $$h(t)=\omega+\alpha\varepsilon(t-1)^2+\beta\sigma(t-1)^2$$ and $$h(t)=\omega+\alpha u(t-1)^2+\beta\sigma(t-1)^2 + \gamma (u(...
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41 views

Estimating an GARCH(1,1) model? Long hand method

I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
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1answer
73 views

Is this the correct way to forecast stock price volatility using GARCH

I am attempting to make a forecast of a stock's volatility some time into the future (say 90 days). It seems that GARCH is a traditionally used model for this. I have implemented this below using ...
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36 views

VaR of ARCH model

Consider the following: $r_t = \theta r_{t-1}+u_t$ $u_t=\sigma_t\epsilon_t$ $\sigma^2_t=\omega+\alpha u^2_{t-1}$ $-1<\theta<1,\omega>0,\alpha \in(0,1)$ What is the 99% 2-day VaR of a ...
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68 views

Poor results forecasting stock price volatility using Python's GARCH model

As far as I understand, forecasting stock price volatility should be more achievable than forecasting absolute prices or returns. It seems as though GARCH models are the traditional and most widely ...
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218 views

RiskMetrics VAR calculations and conditional distribution of sum of log returns

According to Tsay's book in Chapter 7, for the Risk Metrics model: A nice property of such a special random-walk IGARCH model is that the conditional distribution of a multiperiod return is ...
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1answer
42 views

When modelling ARCH/GARCH effects, do we use excess returns?

When modelling ARCH/GARCH effects, do we use excess returns? Is it common in the literature to use excess returns when modelling volatility as opposed to raw return data?
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1answer
142 views

Fractionally Integrated GARCH

I am currently working on a project to compare different GARCH(1,1) models on a financial data set. I use the rugarch package in R, and everthing seemed fine at first. However, now that I have started ...
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35 views

GARCH(1,1) and Value at Risk: Rolling window or non-overlapping samples

Currently studying on financial risk management. I want to test different methods of VaR estimation. I want to model volatility using a GARCH(1,1) model. My question is what should the size of the ...
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78 views

Time series analysis for stock prices

I am using GARCH model to simulate price of an index for 7 years. For input I am using difference of Log of prices (log of return). GARCH(1,1) has the lowest AIC, and I found parameters for the ...
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2answers
525 views

Predicting stock returns with GARCH in Python

I have seen this post: Correctly applying GARCH in Python which shows how to correctly apply GARCH models in Python using the arch library. Now I am wondering how I ...
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2answers
117 views

Volatility clustering and Behavioral Finance, possible explanation

Currently studying about time series modelling of financial data and faced the known GARCH$(p,q)$ model for modelling volatility. We observe that big changes are followed by large changes and vice ...
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1answer
191 views

Kurtosis in GARCH

In a GARCH(1,1) model $$ x_t = \sigma_tz_t$$ $$\sigma_{t+1}^2=a_0 + a_1x_t^2 + b_1\sigma_t^2$$ the kurtosis (when it exists) can be shown to be equal to $$ \kappa_x = \kappa_z \frac{1-(a_1+b_1)^2}...
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Unconditional correlation in CCC GARCH

What is the unconditional correlation (covariance) in CCC GARCH model $$\mathbf{x}_{t+1} = \mathbf{H}_{t+1}^{1/2} \mathbf{z}_{t+1}$$ $$\mathbf{H}_{t+1} = \mathbf{D}_{t+1}^{1/2} \mathbf{R} \mathbf{D}_{...
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GARCH fit: “failure to achieve convergence”… a problem?

Sometimes when one is trying to fit a GARCH model may happen that in the estimation summary (whatever software is) there is written "failure to achieve convergence after n iteration" or similar things....
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1answer
52 views

Negative signs in GARCH equation

When one try to fit a GARCH on a time series it may happen that one or more coefficients in the estimation output have negative sign. In these cases: all the negative coefficients (and relative ...
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1answer
49 views

Double sign for the error term in an ARMA-GARCH model

Why in an ARMA-GARCH model for a stationary series $r$ (without $c$ for simplicity) is $r_{forecast} = ARMA + \sqrt{GARCH} \cdot inn$ and not $r_{forecast} = ARMA \pm \sqrt{GARCH} \cdot inn$? The ...
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1answer
51 views

What's the correct graphical comparison in a GARCH fit?

Suppose that the stationary series $r_t$ is well fitted by an $ARMA(p,q)+c$ and $GARCH(r,s)$ model, where $GARCH(r,s) = \sigma_t ^2$ If in the testing sample I have to graphically compare the ...
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2answers
87 views

Error distribution assumption in a simple ARIMA model

why in an ARIMA-GARCH structure I have to assume an error distribution to run the estimation while in a simple ARIMA model it is not required? Thank you
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29 views

Finding the distribution and moments of returns with GARCH models (in R if possible)

I understand the GARCH type models and I know how to fit a model to a time series. But, there is a paper which calculates the moments of the distribution of returns (Variance, Skewness, and Kurtosis) ...
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1answer
48 views

Can GARCH volatility simulations generally be applied to return-modelling models?

This may be a naive question, but I still hope some discussion can elucidate a (so far) totally nebulous point for me. I've recently learned that GARCH models can give one simulations of ...
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1answer
49 views

EWMA Volatility vs Volatility of EWMA

Is taking the standard deviation of a EWMA smoothed series equivalent to getting the EWMA volatility for that series?
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1answer
61 views

ARCH Model: Which part does AR refer to?

My background is signal processing and I am fairly new to (financial) time series analysis. I was reading the article about autoregressive conditional heteroskedasticity (ARCH) models on Wikipedia. ...
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1answer
33 views

Drop weekend data Vs fill weekend data for GARCH-type modelling

I have a dilemma for an analysis I'm currently on. I doing some GARCH modelling of bitcoin and a fiat currency. There are some null values with the fiat datasets in comparison with bitcoin data as ...
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150 views

How to understand the forecasted output values of GARCH model in python?

arch_model in python produces the following output values in its forecast method: mean - forecast conditional mean variance - forecast conditional variance Query 1. I would like to know what do ...
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40 views

ARMA/GARCH forecasting prices?

i am dealing with brent crude oil price data and i am trying to forecast prices via ARMA/GARCH. I first convert prices into returns (return=diff(ln(P(t)-lnP(t-1))*100) and i obtained a stationnary ...
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1answer
320 views

Hedging with variance swaps: how to calculate the notional

Returns on an asset are negatively correlated with own variance, and I would like to set up a hedge with a variance swap (no options are traded). I need to decide on the notional of the swap: any ...
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1answer
92 views

Asset class dynamics differences

If we compare daily return dynamics of the main asset class time series (e.g. Stock indexes, bonds, precious commodities, etc) do we observe quantifiable differences? Are there some reference paper on ...
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61 views

GARCH-BEKK Model STATA

I was wondering can a GARCH-BEKK model be implemented on STATA? I've gone through a couple of forums that says it is not feasible, thought the posts dates from 2010-2015. Anyone can advise please? ...
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1answer
49 views

ARIMA vs ARIMA + GARCH [closed]

If an ARIMA model converges quickly, would using GARCH improve the forecast performance? By improve I mean provide longer time periods for forecasts. Basically trying to forecast returns.
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1answer
172 views

Accuracy for GARCH models

How does one calculate the accuracy of forecasts given by GARCH models considering GARCH is run on returns. Assuming GARCH is a derivative of a regression based prediction model, would regular ...
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159 views

GARCH-ARCH relating conditional volatility to unconditional volatility

After comparing the inferred conditional volatilities from GARCH models (using Matlab) with the unconditional volatilities from the actual training set, I noticed that although the general trends ...
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26 views

Chances a forecasting model exceeds/deceeds a specified threshold

I am interested in determining the confidence of a forecasting model with applications to quantitative finance. I have the following multivariate data $X$: \begin{align} X(t) \sim F_{X}(t) \end{...
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2answers
357 views

GARCH modeling - sliding or expanding window?

In practice, when modeling volatility do people tend to use expanding or sliding windows to fit GARCH models? For example see rolling forecast generation vs recursive forecast generation in the ...
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0answers
79 views

Explanation and Application of Quantile Regression of Value-At-Risk

Self-learner here. Please, excuse me if I am asking a Question already answered, but the explanations that I find online, just seem to be a bit hard for me. I am currently trying to apply the Basel ...
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158 views

Using the n-ahead function in R?

I am trying to use the one-step ahead forecasting method using my time series data (Called difflog.BC in my code). I have the following model which i am able to plot: ...
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1answer
158 views

Criticise GARCH relative to Realized Volatility

I would like to have your opinion about a simple question. While GARCH would be useful to calculate the conditional volatility, and the RV being in some sense the "historical" volatility, what would ...
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104 views

Measure how different forecasted volatility is from realized volatility

Hi Quantitative Finance Stack Exchange, I'm looking for an opinion on a simple question. Suppose I use a Garch(1,1) model to make a volatility forecast. At time $t$, I have realized volatility $\...
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55 views

Determine GARCH(1,1) from a mean reverting time series recursion

Let $(v_t)$ be a discrete time series of variance obeying a mean-reverting variance process $v_t$, which is actually the discrete version of the Heston model in finance. \begin{align} x_t &= \sqrt{...
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1answer
257 views

How to add controls (regressors) to GARCH model in R?

How can I estimate a GARCH(1,1) model with control variables like this: $$Y_t=a_0+a_1X_t+e_t$$ where$$ e_t\sim N(0,h_t)$$ $$h_t=b_0+b_1e_{t-1}^2+b_3h_{t-1}+b_3Z_t$$ I've checked some packages but can'...
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101 views

How to generate variance impulse response function as in Hafner and Herwantz (2006)?

I am trying to generate variance impulse response functions as described by Hafner and Herwantz (2006) and in Walter Enders' book "Applied Econometric Time Series". Is there a command in R for this? ...
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1answer
68 views

Typical SPX variance GARCH(1,1) coefficients

Can someone provide a typical numerical values of GARCH(1,1) coefficients $(\omega,\alpha,\beta)$ for estimating SPX index variance? I will appreciate it if some references could be provided.
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115 views

Garch(1,1) in R [closed]

I'm evaluating the impact of two variables on stock returns. For this I am using a Garch(1,1)-model in RStudio. This is the result I am getting. Why is the garch model not a valid choice? The external ...