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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28
votes
1answer
18k 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 ...
24
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1answer
7k 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 ...
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?
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
20k 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 ...
14
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2answers
427 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?
12
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2answers
822 views

GARCH model, expectation of volatility?

Consider a time series $\{r_t\}$ following a standard GARCH(1,1) model, i.e., $$ r_t = \sigma_t \epsilon_t,$$ where $\epsilon_t \sim N(0,1)$ and are i.i.d, and $$\sigma_t^2 = \omega + \alpha_1 r_{t-1}^...
12
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1answer
901 views

rugarch: Joint estimation leads to different results

I want to fit an ARMA-GARCH model to my data using rugarch package in R. First of all, I look at the acf and pacf: ...
12
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2answers
592 views

How to estimate the following model?

Suppose I have the following model: $$r_t=\sigma_t * \epsilon_t$$ where $r_t$ is the return at time t, $\sigma_t$ is the volatility, the model used to model this volatility is an exponentially ...
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 ...
10
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2answers
8k views

How do I evaluate the suitability of a GARCH model?

Suppose I downloaded the closing price of a company, say Google or whatever, I want to use GARCH model to model and forecast the volatility of the return. To simplify, I only have two questions. As ...
10
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1answer
14k 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 ...
10
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1answer
2k views

ARMA+GARCH prediction with package rugarch (R)

I am analyzing FTSE 100 series, from 2007-01-01 to 2010-12-31 (university exam homework). I have to use the data 'til 2010-11-30 as sample, and the remaining (23) observations as in-sample forecast (...
8
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4answers
4k views

Stock Price Behavior and GARCH

In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book I'm currently reading, the discrete-time version of this ...
8
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2answers
19k views

GARCH(1,1) good fit found, how to predict one day volatility ahead?

I used SPY data to fit GARCH(1,1) in my model. My data starts from Jan, 2000 until Dec, 2013. I compared the volatility using runSD on the 21 rolling window and GARCH(1,1). It looks a pretty good fit ...
8
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1answer
807 views

Improving GARCH modeling approach

Modeling Exchange Rate Using GARCH Let's consider the following exchange rate : USD/JPY For each sequence, we consider changes in the daily difference between the highest price and the open price of ...
8
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1answer
623 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 ...
8
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1answer
1k views

Markov-Switching E-GARCH with R

I am looking for a R library for modeling a Markov-Switching E-GARCH process. In other questions at StackExchange related to GARCH models, the package rugarch is often mentionned. Do you recommend it ...
8
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1answer
855 views

Density forecast of a GARCH model

I am currently working on developing a series of density forecasts and I am encountering some problems. I am working on weekly S&P 500 returns and the returns process is described as $r_{t} = \...
8
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2answers
485 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 ...
8
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1answer
2k views

Problems with dealing with GARCH models and intra-day data

A Short question would be "Which type of model from GARCH family is most suitable for modeling 5-minute data returns ?" but I've added some story to it. A Long time ago I was preparing my thesis, one ...
8
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1answer
5k views

Conditional or unconditional volatility?

I am reading a paper (reference below) that states "The conditional volatility for each underlying security (or for a market index) can be estimated using the standard deviation of the stock’s ...
8
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2answers
924 views

Fitting Copula and Simulation

I would greatly appreciate any insights into the problem described below, regarding using the data obtained from applying the functions of the rugarch package ...
7
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2answers
449 views

What is the preferred GARCH method in practice?

My advance apologies, if this question is too naive or basic. Please be patient with my first experiences with SE; ask for clarification, if needed. I recognize there are many (often-criticized) ...
7
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1answer
2k views

Difference between GARCH and Heston Volatility model

I know that the difference between the GARCH and the Heston model is volatility vs variance in the stochastic part of the volatility sde. However,from my solutions, there is only ever a 2 - 10 cent ...
7
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2answers
4k views

Garch modelling on Stata

I would like to ask "how to do GARCH modelling on stata". Basically I want to estimate stock market volatility using daily data. I have one variable as return series, $r_t=\ln(\frac{P_t}{P_{t-1}})$. ...
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. ...
7
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2answers
579 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 ...
7
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2answers
474 views

The use of GARCH

I have a conceptual question that I haven't managed to grasp yet and is most likely a econometrics 101 question by here it goes: If we estimate a GARCH model for a time series, how do we then use ...
7
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1answer
373 views

Filtering out AR(1) effects before using stochastic volatility model

I wonder if I first filter out AR(1) (autoregressive model with lag 1) effects from univariate time series and then fit stochastic volatility model does above procedure introduce any bias at first or ...
7
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1answer
636 views

How can I compare 30 day implied volatility forecasts with GARCH forecasts?

I'm trying to understand whether there is a good way to compare forecasts for volatility from different sources i.e., implied volatility and GARCH. I'll outline a few statements that I believe and if ...
7
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2answers
1k views

Is it too important that my residuals be normal? I am Using an ARMA/GARCH model

I am trying to fit an ARMA/GARCH model to a time series. I found that the best candidate is an ARMA(1,0) + GARCH(1,1) with gaussian white noise It has coefficients with p-values near cero and the ...
7
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0answers
374 views

Why are my GARCH forecasts biased?

I've run an ARMA(1, 1)-GARCH(1, 1) model with normal density on log returns for twelve stocks. I computed the one-step-ahead out of sample forecast for daily volatility on a rolling windows for 500 ...
6
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2answers
770 views

What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?

In a ARCH(m) model we have $$ \sigma_n^2=\sum_{i=1}^{m} \alpha_i u_{n-i}^2 $$ where $u_i$ is defined as the continuously compounded return during day $i$ (between the end of day $i-1$ and the end of ...
6
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1answer
2k views

GARCH volatility modeling, squared returns, and convergence

After reading some more of Volatility Trading, I decided to try to make a simple volatility model using daily log returns of an ETF I follow. It turns out "simple" is sort of relative. Unfortunately, ...
6
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3answers
3k views

How to trade volatility?

I am analyzing the volatility of financial stock returns and let's say I have a pretty good model to forecast tomorrows volatility of the stock returns. So let's say for simplicity reasons I have a ...
6
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1answer
80 views

Error message when backtesting GARCH in R

I am trying to backtest my ARCH model using ugarchroll from rugarch package in R, but I am getting this warning message ...
6
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0answers
120 views

What kind of errors arise when I fit ARMA(1,1) to data generated from ARMA(1,1)-GARCH(1,1) process?

As far as I know estimates of parameters of ARMA(1,1) are asymptotically optimal when fitted to data from ARMA(1,1)-GARCH(1,1) process, and only their variance increase, so when we assume large ...
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?
5
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4answers
2k views

Is there any way to easily estimate and forecast seasonal ARIMA-GARCH model in any software?

I use R to estimate a seasonal ARIMA(8,0,0)(5,0,1)[7] model for the seasonal differences of logs of daily electricity prices: ...
5
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2answers
563 views

Intuition behind interest rate models

I am modelling the 3M yield of US Treasuries using an ARMA/ GARCH approach. Most interest rate models (e.g. Vasicek) describe the process as follows: $r_{t}-r_{t-1} = some ARMA+ \epsilon_t $ ...
5
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2answers
2k views

How to compare volatility models?

What are the most popular ways to compare volatility models? Suppose I wanted to compare the forecasting accuracy of a GARCH(1,1) model with the historic 30 day volatility. What method should I use?
5
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1answer
577 views

DCC GARCH: specifying ARCH and GARCH parameter matrices in STATA

The command in STATA to estimate the DCC model of two variables is: mgarch dcc ( x1 x2=, noconstant) , arch(1) garch(1) distribution(t) $$ \begin{bmatrix} h_1{...
5
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1answer
487 views

Cross validation of a garch model

Suppose I divide a time series into 10 sequential time windows, where each window contains 1000 data points. I want to do test 5 different garch models using cross validation. So for each model, I ...
5
votes
2answers
243 views

Regression coefficient and basic trading strategy

This question might be very basic but still I couldn't really find a satisfying answer anywhere. I want to analyse the effect of a repeated event (data release) on the price of a specific asset (I ...
5
votes
0answers
130 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 $\...
5
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0answers
963 views

Fitting Student t-distributions to log-returns

It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without ...
4
votes
1answer
215 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}...
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 ...
4
votes
2answers
231 views

Understanding the conditioning in a GARCH process

In a GARCH model like the following $$y_t=\sigma_tz_t,\\ \sigma_t^2=\omega(1-\alpha-\beta)+\alpha y_{t-1}^2+\beta \sigma_{t-1}^2$$ where $z_t$ is assumed to be iidN(0,1), we say that conditional on ...