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Questions tagged [garch]

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

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Coding a BEKK mutlivaraite GARCH model

I have the code, but I am struggling to determine which specific BEKK model it is for... Any advice would be appreciated, ...
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14 views

How to implement a SARIMA-GARCH model

I was reading this paper about electricity demand forecasting and I'm interested in reproducing the model they claim to use : SARIMA-GARCH and the Reg-SARIMA-GARCH. There is no code linked to the ...
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Using GARCH to model seasonal variance clustering

Question: is it a good idea to model variance clustering in a time series with GARCH when the clusters are seasonal? Details: Imagine that we are given a time series $(x_t)_{t\in \mathbb{N}}$ that ...
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1answer
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Writing a VAR(1) with ARCH(1) errors as a bilinear model?

I have been reading a paper and found this quote? "Note that a linear conditional mean model with ARCH disturbances can be described by a nonlinear specification without ARCH, i.e. the bilinear ...
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Correcting for ARCH effect in VAR and impulse response results

I find significant ARCH effect in my series when running a VAR analysis $Y_t=(y_{1,t};y_{2,t};y_{3,t};y_{4,t};y_{5,t})^\top$ I have two questions: Does the ARCH effect impact the impulse response ...
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241 views

Using ARMA-GARCH models to simulate foreign exchange prices

I've fitted an ARIMA(1,1,1)-GARCH(1,1) model to the time series of AUD/USD exchange rate log prices sampled at one-minute intervals over the course of several years, giving me over two million data ...
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21 views

Obtaining from scratch the volatility in GARCH model using R?

I'm trying to obtain the same vector of volatility by myself $\sqrt{h_{t|t-1}}$ of a Garch Model, that I obtained "automatically" using the function "ugarchfit" from the package "rugarch". So after ...
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1answer
25 views

Starting values in numerical algorithms?

I am estimating an ARCH(1) model, not to difficult apart from one small problems, which starting value should I use for the estimation. I am estimating it long hand, so understanding the minor details ...
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31 views

Should I use weekly or daily returns for modelling FX returns?

I am currently modelling Foreingn Exchange returns using a GARCH model. I am simulating returns 1-year forward. Would it be better to use weekly or daily data on Foreign Exchange returns? Weekly data ...
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13 views

How should I interpret a non significant intercept in a GARCH model? [duplicate]

I am currently building a model based on a GARCH process. You can find a quick description of how the variance is modelled below. $\sigma_t^2 = \alpha_0 + \sum\limits_{i=1}^{n} \alpha_i \epsilon_{t-...
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19 views

How can you test dependence for non-Gaussian standardised residuals?

Let's say you fit an ARMA-GARCH model to financial data and find that the standardised residuals are non-Gaussian through the Kolmogorov-Smirnov test. These residuals have mean -0.002 and standard ...
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12 views

Homoskedasticity of the residuals

When, I fit an ARMA model to data, I look at the standardized residuals plot to assess if they behaves like uncorrelated random variables with zero mean and costant variance (if the model is good). ...
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24 views

Strange rugarch error: $ operator invalid for atomic vectors? [closed]

So, I am trying to make a huge nested for loop (optimizations be left for later) to fit all of the GARCH models available from rugarch. This is my MLE that ...
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1answer
41 views

Principles behind time-series forecasting intervals

So, this is truly a bit of a general question, but I am not aware of the guiding principles (if there are any) behind forecasting intervals. For whatever time-series model one might be using, whether ...
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49 views

What's the variance of an AR(1)/ARCH(1)

The main question is: an AR(1)/ARCH(1) process has the variance of the ARCH(1)? I've tried to compute the unconditional variance of an AR(1)/ARCH(1) model, so an AR(1) in which the noise is modelled ...
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12 views

Does it make sense to run a SARIMA model and then a ARCH(0,0)-GARCH(1,1) model on residuals?

It was tough to write the question in a simple manner. A time series I am working with follows a seasonal ARIMA model. In my software I cannot jointly estimate a SARIMA and a GARCH(1,1) model. Is it ...
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39 views

Returns correlated, but squared returns not correlated [closed]

I'm trying to apply a GARCH model to a financial time series, and as usual I plotted the ACF and PACF of both returns and squared returns. In my time series the returns show serial correlation, but ...
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ARCH testing and Stationarity

I have a time series y and I need to build the "best" autoregressive model for it i.e. y(q*). What I do: 1. Start with y(1) and test for serial correlation in the errors until I find an AR lag -lets ...
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14 views

AR(1)-GARCH(1,1). A bad fit with log likelihood?

Consider these two DCC models: ...
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1answer
28 views

Books on Bayesian inferential analysis of GARCH models

Do you know books about Bayesian inferential analysis of GARCH models with the analysis of these models in R and JAGS? Here is a list of the books I already have: [Ardia] - Financial Risk Management ...
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16 views

Is a test of stationarity important before fitting GARCH?

Is it important (and if it is why?) to test for stationarity of a time series before fitting a GARCH model/ ARMA-GARCH to a financial time series?
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1answer
22 views

What prior distribution of parameters in the Bayesian estimation of a GARCH model?

In the case of the Bayesian estimation of GARCH(1, 1) model with Student–t or a Skewed distributions for innovations, is it more correct to assume a uniform distribution for the parameters or to ...
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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
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Should log-likelihood values increase when the sample size of a simulation increases?

If one simulates a process (such as an ARMA-GARCH process) with sample size $n$ and log-likelihood $x$, should this log-likelihood increase when the sample size increases to $2n$ for example?
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Proof that sequential GARCH fitting is not efficient?

I've read that authors like Tsay (as well as several other researchers) use a sequential method for fitting a ARCH-type model. This means first estimating the conditional mean model (ARMA-type) and ...
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43 views

Estimating a MS-ARMA(p,q)-GARCH(r,s) parameters via MCMC

I am currently working on a MS-ARMA-GARCH model proposed by Dhiman das on this paper, and trying to fit it on simulated data. So far I understand the model and its construction, but I'm having a hard ...
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14 views

Returns forecast back to closing price?

I'm working with log returns. I've selected an ARMA-GARCH for mean and volatility forecasting and I would like to get the forecasted confidence intervals and plot expressed in terms of the closing ...
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30 views

How does one estimate parameters in a GARCH-M(1,1) model?

Say you have a GARCH-M(1,1) model as follows: $y_t = \beta y_{t-1} + \delta h_t + \epsilon_t, \quad \epsilon_t \sim N(0, h_t) $ $h_t = a_0 + a_1 \epsilon^2_{t-1} + b_1 h_{t-1}.$ How exactly does ...
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1answer
32 views

Does $\delta$ parameter in GARCH-M stay unchanged when the process is scaled?

Assume we have a GARCH-M(1,1) process as follows: $y_t = \beta y_{t-1} + \delta h_t + \epsilon_t, \quad \epsilon_t \sim N(0, h_t) $ $h_t = a_0 + a_1 \epsilon^2_{t-1} + b_1 h_{t-1}.$ If we scale $...
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2answers
62 views

Do parameters stay unchanged when GARCH is scaled?

Let's say we have a GARCH($1,1$) process specified as follows: $y_t = \epsilon_t \sqrt h_t, \quad \epsilon_t \sim N(0,1) \quad \text{i.i.d.}$ $h_t = a_0 + a_1 y^2_{t-1} + b_1 h_{t-1}.$ If we were ...
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21 views

Stationary time series input to ARMA-GARCH

I’m thoroughly confused as I have been using ARMA-GARCH to model a conditional mean and conditional variance so I can effectively remove them by taking the residuals and be left with an i.i.d process. ...
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ARMA model residuals fed to GARCH process

I have seen a few people say you can produce an ARMA model and feed the residuals from this model directly into a GARCH model. This doesn't make sense to me however, I assume the GARCH model is ...
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30 views

Fitting an ARMA-GARCH using AIC

I am trying to fit an ARFIMA(p,d,q)-GARCH(1,1) model to an asset returns time series. I start with an ARFIMA(0,0,0)-GARCH(1,1). The diagnostics tests like persistence requirement, Ljung Box test for ...
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Nature of a stochastic process [closed]

I am a econometrics student, and I've to understand what type of process the one in the image below is. I am not able to go back to the main classic stochastic processes (AR, MA, ARMA, ARCH/GARCH). In ...
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Evaluate the conditional variance forecast from a GARCH model

I wanna evaluate a simple GARCH(1,1) model for the conditional variance. Firstly, I understand that the conditional variance is unobserved and that is really the crux of the issue. Out-of-sample, I ...
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Is stochastic GARCH-M a stochastic volatility model?

https://www.bankofengland.co.uk/-/media/boe/files/archive/discussion-paper/a-note-on-the-estimation-of-grach-m-models-using-the-kalman-filter defines a stochastic GARCH-M model for returns $r_t$ as ...
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Why the expression from “parse” function doesnot work to fix parameters of “ugarchfit” [closed]

I´m writing a automatic proceso of fitting any stock-index with Garch model which involves writing a function which refines the garch model by fixing those non-significant parameters to zero. First I ...
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0answers
13 views

What is the difference between GARCH, ARGARCH, and DCC-GARCH?

What is the difference between GARCH(1,1), AR(1)GARCH(1,1), and DCC-GARCH?
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How to deal if different univariate time series which has different AR and MA orders. Can multivariate model like DCC model be a fit in such scenario?

I am planning to run DCC model on some time series. The problem is that all time series have different AR and MA orders. Many articles have taken AR and MA (1,1) order without discussing the rationale ...
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0answers
60 views

Realized GARCH forecasting the realised measure of volatility (rugarch package)

A question regarding the Realized GARCH model in the rugarch package (or perhaps quite a general question). In the original paper by Hansen, Huang and Shek (2011), they mention the model can be used ...
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62 views

Unit root in time series of log return of s&p 500. What to do? [closed]

I have 9500 closing prices of s&p500. I took daily return of the prices dailyreturn and then log return of the prices logreturn=log(1+dailyreturn). Now I checked the data using augmented Dickey-...
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0answers
28 views

How to manually find ARMA-GARCH residuals in R? [closed]

Let's say the data input is called data, which is in the form of a financial time series that will be fitted into an ARMA-GARCH model. The GARCH(1,1) is used ...
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1answer
37 views

GARCH specification - why are $\sigma_t^2$ and $\epsilon_t^2$ not the same?

Often times people specify the GARCH model as follows: $$ \sigma _{t}^{2}=\omega +\alpha _{1}\epsilon _{t-1}^{2}+\cdots +\alpha _{q}\epsilon _{t-q}^{2}+\beta _{1}\sigma _{t-1}^{2}+\cdots +\beta _{p}\...
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42 views

What is the difference between Pearson correlation and dynamic correlation (DCC-GARCH)?

I often read dynamic correlation, which I believe related to DCC-GARCH. How is the dynamic correlation different comparing to the Pearson correlation?
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81 views

Diagnostic testing of DCC-GARCH: implementation in R and interpretation

I am modelling the volatility spillover between SP500 and the USD/CNY from 2008 to 2018 with a DCC-GARCH(1,1) model as follows: ...
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2answers
123 views

What to do if time series are non-stationary? [closed]

Data: I have a time series data of 2528 daily observations for OMXS.30 (Stokholm) closing price. The aim is to fit proper ARCH/GARCH models and use for forecast daily Value at Risk. Here is a plot of ...
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0answers
25 views

Stationarity restriction of a TGARCH process?

What is the stationarity/convergence restriction for a threshold GARCH model, TGARCH? I know that for a GARCH model: $\alpha+\beta<1$, but I'm guessing it's not that simple for a TGARCH model. ...
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0answers
16 views

Estimating a GARCH-M model with a mean-equation dummy

I'm trying to estimate a GARCH-M model with a dummy volatility variable on the mean equation, so the mean equation looks something like this: $$r_t = \mu + \lambda_1{\mkern 1mu} \sigma_t + \lambda_2 ...
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1answer
95 views

Obtaining point forecasts from a DCC-GARCH model in rmgarch in R [closed]

I am becoming more acquainted with GARCH models in R, but I am not sure my code is right for what I am trying to do, so I would appreciate any help. Based on an xts I create using data from a csv ...
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1answer
43 views

Mean and Correlation of a First-Order ARCH(1) Process

For a first-order ARCH(1) process $$ Y_t = \epsilon_t(\alpha_0 + \alpha_1Y_{t-1}^2)^{1/2} $$ $$ t \in \mathbb{Z} $$ $$ \alpha_0, \alpha_1 > 0 $$ $ \{\epsilon_t\}_{t \in \mathbb{Z}} $ and $Y_t$ is ...