Questions tagged [garch]

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

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How can I use R to calculate and plot the volatility of Tether (USDT) and compare that to Bitcoin (BTC)? [closed]

for Tether (USDT), how can I calculate and plot the volatility using the GARCH model in R and then compare that to the volatility of Bitcoin (BTC) or even S&P500? Thanks in advance!
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Understanding GARCH

I am new to finance and volatility forecasting and am trying to understand how garch model works. Even though there are many tutorials on how to use arch_model from Python, none of them gives ...
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Why are the standardised residuals of a GARCH process a white noise process

Suppose I have a GARCH process: $$X_t = \mu_t+\varepsilon_t$$ $$\varepsilon_t=\sigma_tz_t$$ where $z_t$ is some iid zero mean, unit variance random variable, and: $$\sigma_t^2=α_1 \varepsilon_{t−1}^2 +...
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What are parametric conditions?

My dissertation supervisor asked me to explain further the following question for a GARCH model: "what are the alpha's and the beta's and what are their parametric conditions, and what do the ...
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Theoretical properties of joint maximum likelihood estimator on returns and options when fitting an option pricing model

Suppose we have a simple GARCH option pricing model $$ R_t = \sqrt{h(t)} z(t)$$ $$ h(t) = \omega + \alpha z(t-1) + \beta h(t-1)$$ where $R_t$ is the daily log return, $h(t)$ is the conditional ...
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Fitting ARMA-GARCH sequentially vs simultaneously

I am interested in fitting an ARMA-GARCH model to my data. After reading a few pages online I did so sequentially by first applying ARMA and then feeding the residuals into GARCH. I then took the ...
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What is the intuition of a GARCH model without fitting ARMA for the conditional mean?

I wanted to ask, as I've seen this used a couple of times before, about the logic of fitting a GARCH model in absence of estimating ARMA for a series that is clearly an ARMA process (Fitting a GARCH ...
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normal mean variance mixture garch with OBSERVED mixing variable

I need to estimate this univariate garch model with the following discription My model (regression): Yt=mu + gamma * Gt + et Gt is GIVEN Where the crucial part is that: et= sqrt(Gt) * sqrt(ht) * Zt ...
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Are there any key reasons as to why people would choose between apARCH, gjrGARCH and E-GARCH?

I’ve been doing a lot of R coding with GARCH for my dissertation, I'm coming to the end of my writeup now but have hit a bit of a wall. Obviously, gjrGARCH, apARCH and E-GARCH all allow for asymmetric ...
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Searching papers that compare different GARCH models

Like the title says, I'm searching for papers that compare the performance of different GARCH models (mainly the standard GARCH, EGARCH and GJR-GARCH). I'm sure there are some standard papers that ...
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Structural break time series

Knowing that tests for structural breaks deal with breaks in trend only, under what assumptions do you think it is reasonable to ignore these breaks when modeling the ARMA process? Can they can ...
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In a GJR model, is there any interpretation attributed to half of the asymmetry parameter?

I'm reading this paper by Abosedra et. al (2006), where they study the volatility of US natural gas prices. They report the estimation from a AR(1)-GARCH(1,1) model and a AR(1)-GJR-GARCH(1,1) model as ...
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Rolling fixed window scheme for GARCH forecasting

I'm working on my bachelors thesis which mainly revolves around this paper: https://www.mdpi.com/2225-1146/4/1/3/htm Shortly after describing the dataset in 3.1 the authors mention that they use a ...
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How to add both long-term and short-term interest rates as variables for a GARCH model?

I was facing some difficulties with a model of mine. I want to look up how the portfolio reacts to interest rate changes and I would like to use a GARCH model. However, both the short-term and long-...
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How does R calculate joint significance parameters DCCA1 and DCCB1 when conducting a DCC GARCH analysis?

I have conducted my DCCGARCH analysis using the RMGARCH package. Printing the function dccfit provides each of the parameters for the univariate models, but also joint signifiance parameters dcca1 and ...
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Implementing Breusch-Godfrey test in R

I am trying to perform the Breusch-Godfrey test (with lags=20) for autocorrelation among standardized residuals for ...
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Modelling the Conditional Variance in a Panel Setting

I am familiar with ARCH-type models to estimate the conditional volatility of some variable of interest in a univariate setting. I know that there also exists the concept of multivariate ARCH-type ...
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Showing that a GARCH(1, 1) model is an ARMA(1, 1) process for squared errors

Consider a GARCH(1, 1) model: $$ \sigma_t^2 = \alpha_0 + \alpha_1 u_{t-1}^2 + \beta \sigma_{t-1}^2 $$ Where $ \sigma_t $ is the conditional variance at time $ t $, $ u_{t}^2 $ is the error term in ...
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Ljung-box test of ARIMA-GARCH model for time-series analysis

I am using Python to model my time-series using ARIMA-GARCH model. I follow the given steps (with the assumption that fitting ARIMA first will give me sub-optimal solution): The time series trained ...
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Understanding the standardized residuals in time-series analysis

I am recently learning about time-series analysis and the model diagnostics. I am facing difficulties in understanding the following points: Mathematically, I understand that standardizing the ...
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(G)ARCH: Squared Residuals vs Absolute Residuals

I estimated a GARCH model to forecast the variance of a variable conditional on past information. I evaluated the forecast by comparing the squared forecast error, i.e. the squared value by which the ...
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Interpretation of the weighted portmanteau Li-Mak test for ARCH effects

From the literature I do not understand the null hypothesis of this test. I used it's implementation in R to confirm my multivariate model captures the ARCH effects present in the data. I use this ...
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fit suitable AR-GARCH models to returns in MATLAB

I fit AR(1)-GARCH(1,1) models to 100 shares return, but at almost all of them the fitted AR(1) model is not stationary (AR{1}=0.99). How I can find a suitable same model? (for example by using the AIC ...
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How can we select the best GARCH model by carrying out likelihood ratio test?

I have carried out the likelihood ratios of different GARCH models. GARCH(1,1) and GARCH(1,0)- Rejected null hypothesis so I chose GARCH(1,1) to do more sophistication. GARCH(3,1) and GARCH(1,1)- ...
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How to spot restricted and unrestricted GARCH models and identify the number of restrictions

Between GARCH(4,1) and GARCH(3,4), what will be the number of restrictions, and which model will be restricted and unrestricted?
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Should I include AR, MA, or ARMA in my DCC(1,1)GARCH(1,1) approach?

I know an AR, MA or generally speaking an ARMA term is included for the mean. I however can not find how to determine this for my specific application. Is there any information that can be derived ...
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Duan 1995 GARCH option pricing model (and R)

I added similar question to Stackoverflow, but I am not sure if it's more of a code related or model specification question. I want to replicate the below model of option pricing, from Duan's paper (...
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Strict stationarity and existence of moments ARCH(1)

Can a strictly stationary time series not have the fourth moment? For example the ARCH(1) process with the a(1) coefficient $ > \frac{1}{3}$ doesn't have the fourth moment. Can it be strictly ...
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Prove that $E[\log(\alpha X_t^2)] < 0 $ implies $\alpha < 3.5622$ with $X_t \sim N(0,1)$

I am trying to prove this statement: If $X_t \sim N(0,1)$ then $$E[\log(\alpha X_t^2)] < 0 \implies \alpha < 3.5622$$ which is a a necessary condition often found in textbooks for strict ...
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ARIMA vs ARFIMA (in R)

I got a bit confused for the mathematical definitions of ARIMA and ARFIMA when used them for asset price time series analysis in R. When using the function Arima (e.g. ARIMA(1,1,0)) of the forecast ...
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R: Density Forecasts using rugarch

I would like to construct a density forecast using a GARCH model. Is it possible to use rugarch in R to construct these? For example, using a ARMA(1,1)-GARCH(1,1) ...
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Out of sample ARCH forecast

I have estimated a conditional mean model for a time series: $ x_t = x_{t-1} + \epsilon_t$. Say I have estimated it using periods 1 to 10. I can do an out of sample conditional mean forecast by ...
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How to find fitting ARMA-GARCH model? Financial data

I'm using financial data - logarithmic rates of return of WIG-Banks index, 2000 observations. I'm supposed to find ARMA-GARCH type of model, the most fitting one. Relying on ACF and PACF i estimated ...
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Expected Value of an ARMA-GARCH Model

An ARMA(p,q) model is given by $ \qquad \qquad Y_t = c + \sum\limits_{i=1}^{p}\varphi_iY_{t-i}+\sum\limits_{i=1}^{q}\theta_i\varepsilon_{t-i} + \varepsilon$ with $\varepsilon_t \sim N(0,\sigma^2)$. ...
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simulation of mixture GARCH models

I want to simulate data that follow a mixture - GARCH specification. The conditional density of the return series $r_t $, based on information up to time t is given by $ f_{t-1}(r_t;\theta) = \sum_{i=...
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Fitting GARCH model with external regressors in R

I am trying to fit a GARCH model with external regressors. My goal is to see if the Covid-19 new cases and deaths have an effect on the volatility of daily stock returns. For this I used the ...
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Modelling the AR(1) process in a DCC-GARCH approach for hedging / safe haven aspects

I'm doing an analysis on an asset to find out whether it can be function as a hedge or safe haven for another asset. I got the sample to match the time frame in which I hypothesize it could function ...
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How should I interpret the output of CGARCH Model in Eviews? C3, C4, C5, C6 and C7

I am trying to understand how I should interpret the coefficients of CGARCH model. My topic is related to stock market volatility
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Propose a model for this time series

I'm analyzing the time series DAX (I call Z) from the dataset EuStockMarket. Could you ...
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ARMA/GARCH statistical significance of estimated parameters

My question is general and is concerned with ARMA-GARCH modeling. When performing the joint estimation of the ARMA and GARCH parts, some works tend to not be concerned with the statistical ...
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How to impute missing values at the beginning of a time series using GARCH model?

I want to use a GARCH(1,1) model to impute the missing data at the beginning of a time series, but GARCH model is normally used for predicting future data, is there a way to modify GARCH(1,1) so that ...
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Model specification for seasonal ARMA-GARCH model using rugarch

TL;DR: I'm trying to find an adequate model for time series data that exhibits multiplicative seasonality and volatility clustering by identifying an ARMA-GARCH-model with Fourier terms using ...
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Why aren’t GARCH and VAR models used as frequently as GEE or Mixed effects in modeling clinical trial data?

Why are VAR models and GARCH models used in forecasting for economics and stocks but not in analyzing clinical trial data? The most common for clinical trial is mixed effects or GEE. Are they bad for ...
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forecast for gjrmodel and egarch model

I do forecast on the model with rugarch package, i'm using ugarchforecast for prediction, but have only result on sigma, i do other for complete prediction?
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Reference request for t-distribution GARCH maximum-likelihood estimation

This video's second half formulates the GARCH autoregressive model combined with the heavy-tailed t-distribution (t-GARCH) and implies its log-likelihood function based on the first half's derivation ...
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Questions regarding ARCH models

A simple ARCH(1) model for the residuals of some model is defined as follows: $\epsilon_t = \sigma_t u_t$, with $\sigma_t^2 = \alpha_0 + \alpha_1 \epsilon_{t-1}^2$, and $u \sim i.i.d(0,1)$. I have ...
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Time ordering and the `garch` function in `tseries` package in R

I have fitted a garch function using the tseries package in R, and I have observed that the series of residuals produced by the ...
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Accounting for multiplicative seasonality by including external regressors in ARIMA-GARCH model using R?

At the moment, I'm trying to model a time series in preparation for a multivariate analysis. The time series comprises tweets per hour for a period of nine weeks. As you can see, and as is to be ...
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How to determine the inputs for the MA terms when forecasting with an ARIMA-GARCH model?

I am having difficulty determining how to forecast values for an ARIMA-GARCH model manually (by hand). I understand that for an ARIMA model, the inputs for the MA terms are the residuals (i.e. the ...
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ARCH(2) Process Stationarity

Lets say that we have an ARCH(2) process such that: $$ y_t = \epsilon_t \sigma_t$$ where $\epsilon_t \textit{~} MDS(0,1)$ $$ \sigma_t^2 = w + \alpha_1 y_{t-1}^2 + \alpha_2 y_{t-2}^2 $$ I am trying ...

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