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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 ...

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14 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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60 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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213 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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99 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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176 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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77 views

How to fit Threshold Garch (TGARCH) with R and interpret the summary output?

Can somebody please provide an example of fitting a Threshold GARCH (TGARCH) model to stock log returns data with R and interpreting the summary output in terms of finding the best fit TGARCH model ...
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27 views

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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46 views

How to fit and test VaR in R

I have estimated the below model with gjr-garch11 ...
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32 views

How to interpret the p-value for a GARCH process

The p-values for the omega and gamma parameters are quite small, but for the beta, it is at 0.56. Should I conclude that I can't fit a GARCH process to this time series? Also, does it make sense to ...
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2answers
55 views

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
51 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
47 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
48 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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78 views

White noise process common in daily return series

When I fit an ARMA-GARCH in some financial time series, I often observe through the ACF/PACF that the daily return series shows a white noise process at once, especially in Forex time series. In ...
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2answers
73 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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78 views

Are ACF and PACF plots of squared returns useful in determining the lag-order when testing GARCH class of models?

I am trying to fit GARCH class of volatility models to the log return series of Bitcoin. ACF and PACF plots of the square of this return series are shown below. I need to know whether inferences can ...
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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
42 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
41 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
55 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
30 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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122 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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38 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
227 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
91 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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50 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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47 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
135 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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111 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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24 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
269 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
75 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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123 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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158 views

GARCH(1,1) Forecasting

My goal: I want to do in-sample forecasts of 22 days volatility (sum of squared returns) using a GARCH (1,1) model (rugarch package). I want to do this by forecasting daily volatility $n$ steps ahead (...
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28 views

How do I apply Fuzzy-GARCH to forecast real data?

I am currently working on fuzzy-GARCH to forecast. I would like to know how this can be done starting from scratch using an example (including obtaining consequent parameters). Next, how do I get two ...
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1answer
130 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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98 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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51 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
195 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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79 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
59 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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95 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 ...
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101 views

ARMA-GARCH Forecasting [closed]

I want to forecast a differenced time series of an Index using the combined ARMA-GARCH model (because I want to forecast the mean and not the variance). My model is a ARMA(2,2)-GARCH(1,1) model. So ...
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1answer
374 views

VaR : Student-t GARCH

I have a question on the VaR estimation via the student t GARCH model. Under this framework, the one day ahead VaR estimate is calculated by the following formula: $$VaR_{p}=\mu_{t+1}+\sigma_{t+1}\...
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0answers
49 views

Deduce GARCH(1,1) to the stochastic variance model

Here is the proof that the limit of GARCH(1,1) $$\sigma_n^2 = \gamma V_L + \alpha u_{n-1}^2 + \beta\sigma_{n-1}^2$$ is equivalent to stochastic process of variance $$d V = \alpha(V_L - V) dt + \xi VdW....
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133 views

Unconditional variance of an E-GARCH model

I am attempting to calculate the unconditional variance of an E-GARCH model: $$\log(h_{t+1}) = \beta_{0} + \beta_{1}\log(h_{t}) + \beta_{2}\left[|\varepsilon_{t} - \lambda| + \gamma(\varepsilon_{t} - \...
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1answer
68 views

VaR estimation when returns are not independent, e.g. ARCH

Time series of returns, $r_t$, in finance are often modeled with some type of conditional heteroskedasticity model, e.g. ARCH(1): $$r_t = \sigma_t z_t$$ $$\sigma_t^2 = a_0 +a_1 r_{t-1}^2$$ where, ...
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269 views

GARCH Option Pricing Model (Duan 1995)

I am trying to replicate Duan's results from his 1995 Paper, "The GARCH Option Pricing Model". I have written this code in Python myself, and using his parameters I consistently seem to obtain results ...
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1answer
90 views

I am trying to fit an GARCH(p,q) model to FX volatility. Should I be interested in the t-value of GARCH parameters?

So what I am trying to do is to model the volatility for different currencies by fitting a GARCH(p, q) model. I am selecting the values of (p, q) by iteratively going through p & q such that max(p,...
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2answers
2k views

Can I forecast stock returns using GARCH?

I know this is a rookie question, but I have seen some comments about using GARCH to forecast stock returns. Is it something people do? Wasn't GARCH just for volatility? Also, can you suggest any (...