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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24
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1answer
6k views

Algorithm to fit AR(1)/GARCH(1,1) model of log-returns

I am fitting numerically an AR(1)/GARCH(1,1) process to index and stock log-returns, $r_t=\log(P_t/P_{t-1})$, where $P_t$ is the price at time $t$, and thus far am not clear on where the observed log ...
2
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1answer
953 views

Does the unconditional variance implied by a GARCH equal the sample variance?

In the MATLAB default settings for GARCH estimation they say "presample conditional variance is the sample average of the squared disturbances of the offset-adjusted response data y". Am I right in ...
8
votes
1answer
588 views

Why is the GARCH intercept supposed to be strictly positive?

Maybe it's a simple question but I don't really understand why it is theoretically required. Let's take the standard GARCH(1,1) $$\sigma^2_{t+1}=\omega+\alpha\epsilon^2_{t}+\beta\sigma^2_{t}$$ In most ...
11
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2answers
17k views

GARCH model and prediction

I have a question about the prediction of volatility and returns of a time series. Basically it is a question about predict in the ...
18
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1answer
2k views

So many volatility models. Any comparisons of them?

Are there any papers that make an explicit contrast/comparison of the following (or other) vol models in terms of the suitability for addressing some empirical problem? Wavelet multiresolution ...
17
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1answer
19k views

Forecasting using rugarch package

I want to do one step ahead in-sample forecasts. My data can be found here. This is just a data frame with the date as the rownames. I specify my model and do the fit and show the plots with ...
10
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1answer
13k views

How to calculate the conditional variance of a time series?

I am reading a paper where the term conditional variance is mentioned, but I am not really sure what is meant by this and how this can be calculated: Fig. 2 shows the conditional variances of the ...
27
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1answer
17k views

Correctly applying GARCH in Python

Problem: Correct usage of GARCH(1,1) Aim of research: Forecasting volatility/variance. Tools used: Python Instrument: SPX (specifically adjusted close prices) Reference material: On Estimation of ...
21
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3answers
12k views

Why is GARCH(1,1) so popular, especially in academia?

What makes GARCH(1,1) so prevalent in modeling volatility, especially in academia? What does this model offer that makes it significantly better than the others?
14
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2answers
425 views

Is a linear combination of GARCH processes also a GARCH process?

If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
5
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2answers
5k views

GJR-GARCH Model In R

Any idea how to estimate GJR-GARCH models in R? Is there any particular library like fGarch that supports such models?
8
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2answers
477 views

Does GARCH derived variance explain the autocorrelation in a time series?

Given a time series $u_i$ of returns (where $i=1,\dotsc,t$), $\sigma_i$ is calculated from GARCH(1,1) as $$ \sigma_i^2=\omega+\alpha u_{i-1}^2 +\beta \sigma_{i-1}^2. $$ What is the mathematical ...
7
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2answers
7k views

How GARCH/ARCH models are useful to check the volatility?

Below a R code wrote by the moderator @richardh (whom I want to thank again) about ARCH/GARCH models. ...
4
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2answers
1k views

ruGarch - Interpret test results

I'm working on a R project, trying to calibrate a GARCH (so far, (1,1) ) model to the yields of the STOXX50 index over the last 2 years. I've tried the garch function of the tseries package, but it ...
3
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1answer
655 views

Correct procedure for modelling GARCH for forecasting volatility of stock Index returns

I will be using Eviews and am looking to forecast volatility of stock index returns using ARCH/GARCH models. I've generated the logarithmic returns and done the unit root tests. I then proceeded to ...
2
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1answer
262 views

distribution of AR, MA coefficients estimation in ARMA-GARCH models

could anyone give me an information about distributions of AR and MA coefficients via estimation? So, for example, I have ARMA(1,1)-GARCH(1,1) model with the same AR(1) and MA(1) parameters ...
1
vote
1answer
361 views

Constant decreasing volatility, GARCH forecasting

I am trying to forecast the volatility using GARCH modelling in R. I fit an ARMA(1,1)-GARCH(1,1) model, but my sigma predictions are constantly decreasing. Anybody know why? ...
0
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0answers
255 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 ...
3
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1answer
3k views

2-step estimation of DCC GARCH model in Python

Embedded in this thread are multiple questions. I'm currently im the process of implementing a DCC GARCH forecast model on quantopian (a python-powered trading platform). The two step consists of ...
1
vote
1answer
280 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 ...
1
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2answers
1k views

garchOxFit in R

Could someone please help me with trying to get the Ox interface to work in R. I followed the steps outlined in this paper (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1752095), but I get the ...
0
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1answer
598 views

Can I do a GARCH model to forecast a time series?

I read this paper https://research.aston.ac.uk/portal/files/240393/AURA_2_unmarked_Energy_demand_and_price_forecasting_using_wavelet_transform_and_adaptive_forecasting_models.pdf the two authors ...
-1
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1answer
273 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 ...