Questions tagged [volatility]
A statistical measure of the dispersion of a (financial) time series, e.g. its (annualized or regular) standard deviation
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Measure of volatility for time series data?
I would like to calculate some measure of volatility or noise for stationary time series data. This can be a measure for a single time series or a relative measure comparing multiple time series ...
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Why is volatility an important topic in financial econometrics?
I do not know if it is totally off-topic, but I thought it might be useful to have opinions and an aggregate answer about why volatility is an important topic in financial econometrics.
I think it ...
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Has anybody ever found data where ARCH and GARCH models work?
I'm an analyst in financial and insurance fields and whenever I try to fit volatility models I obtain awful results: residuals are often non-stationary (in the unit root sense) and heteroskedastic (so ...
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Persistence in GJR-GARCH (asymmetric GARCH)
Consider the standard GARCH model:
$$ \sigma^2_t = \omega + \alpha\varepsilon^2_{t-1} + \beta\sigma^2_{t-1}.$$
The so-called persistence parameter is defined as the sum $\alpha+\beta$.
Now consider ...
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Bootstrap sample with size greater than the original sample
I want to predict future returns over a 20 days horizon using an ARMA-GARCH model fitted to my data.
The goal is to estimate different risk measures like VaR or CVar.
In particular say I use AR(1) ...
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Does GARCH($p$,0) make sense at all?
I wonder if a GARCH model with only "autoregressive" terms and no lagged innovations makes sense. I have never seen examples of GARCH($p$,0) in the literature. Should the model be discarded altogether?...
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Interpreting QLIKE and MSE Loss function (Patton 2011)
In Patton (2011) the author finds that both the MSE and the QLIKE loss function are robust when used to compare rivalling volatility forecasting models, which means that using a proxy for volatility ...
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How Large a Difference Can Be Expected Between Standard GARCH and Asymmetric GARCH Volatility Forecasts?
I have been using various GARCH-based models to forecast volatility for various North American equities using historical daily data as inputs.
Asymmetric GARCH models are often cited as a ...
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Weak stationarity and ARMA-ARCH/GARCH models?
I am slightly irritated about weak stationarity in connection to ARCH/GARCH models. I do not know the answer and I am not sure about it:
The basic question is:
Do we have to test weak ...
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Why is GARCH offering no predictive value?
I am playing around with GARCH models for the first time (I have a stats background but basically no experience with GARCH), trying to forecast volatility in a financial time series.
I trained a GARCH(...
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Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term
I would like some help with a GARCH(1,1) volatility modeling.
I am working with the assumption the volatility is the weighted sum of three factors: Long run variance + $n-1$ squared return + $n-1$ ...
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Estimating the confidence interval for the volatility of a GARCH model
This question is a followup of my previous question
Forecasting with ARIMA and GARCH: does my plan look alright?
I have a times series $r_t$ and I am trying to estimate its volatility with a GARCH ...
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GARCH estimates differ in rugarch (R) vs. EViews
I modelled a stock's volatility using the "rugarch" package in R and Eviews.
The estimated model is GARCH(1,1).
Data is as below:
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On forecasting, the mean squared error and realized volatility
Say one has finished estimating a correctly specified GARCH(1,1) on a daily time series and now wants to evaluate the accuracy of the one step ahead forecasts what steps or tests could one do?
I ...
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Stochastic volatility: particle filter vs Metropolis-Hastings
In many of the papers on particle filter I've read (e.g. Douc, Moulines and Olsson, 2007), stochastic volatility is a common example to show that a newly-proposed filter is working. At the same time, ...
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Fitting a GARCH model and forecast using validation set approach In R
I have seperated the data into training and testing data. Then I fitted this simple garch model for training data as follows,(using rugarch package)
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Setting up a MCMC scheme for Multivariate Stochastic Volatility
I want to understand the survey of Lopes and Polson (2010) regarding MV stochastic volatility.
Assume the $p$-dimensional vector $y_t$ follows
$$y_t\sim N(\Theta,\Sigma_t).$$
In order to model the ...
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Probability on different time scales
I just finished reading "Fooled by Randomness" by Nassim Taleb. He, inter alia, gives the following example to prove one of his points:
A 15% return with 10% volatility per annum translates ...
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Diebold-Mariano in the context of volatility forecasting: What is the ultimate aim of this test?
Perhaps I'm missing a simple conceptual point here. But do the error statistics (RMSE, MAE) not tell which is the best forecast by presenting the lowest figures between the forecast and the actual ...
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Best way to deal with forecasting with noisy data?
I have a bunch of sales data. It is from distributors of 2000 different items, who service big companies and large distributors to a number of small independent stores. They sell some items which do ...
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How to interpret GARCH volatility forecast?
I am trying to model the volatility of gold using GARCH models and here is the forecast that I obtained.
The plot seems to indicate that the volatility decreases as time passes but I was expecting to ...
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Is there a mathematical model that distinguishes between volatility and trend?
Say we are studying Twitter hashtags over time. We monitor how popular they are day to day. Some hashtags may be volatile (i.e. "lunch", "Celtics", "Friday"). Their popularity rises and falls ...
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Volatility forecasting in presence vs. absence of ARCH effects
Suppose I have a time series $x_t$ with no autocorrelation (consider for example log return of stock prices). If $x_t^2$ is autocorrelated, we can model the series with a GARCH model and provide a ...
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Forecasting AR-ARCH/GARCH models
I have a simple theoretical question as I am a beginner in time series analysis.
The idea of modeling an AR-ARCH or GARCH is to model the mean and the variance. After modeling, I want to forecast the ...
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How to pick the daily volatility component in Multiplicative Components GARCH modelling?
Recently I've been drawn to the rather interesting Multiplicative Components GARCH model for intraday volatility modelling, a draft paper written on it can be found here: Chanda, Engle, Sokalska, 2005 ...
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Manual estimation of a GARCH(1,1) parameters using MLE vs rugarch package in R
I want to estimate parameters of a GARCH(1,1) model using rugarch package in R and manually(using maximum likelihood).
Firstly, I import and transfrom the data as below(Amazon return data)
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Testing if the volatility of single stocks and/or indices have risen in the past
I'm currently writing my bachelor thesis and the main goal of my paper is to test if the volatility of single stocks and indices have risen in the past. My data consists of all stocks of the SMI and ...
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Why is the periodogram of differenced white noise not flat?
I'm a final year undergrad who was doing a project that involved the implementation of a frequency-domain volatility estimator. I haven't a lot of stats background so not understanding a point that ...
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Why "modeling volatility" is not an oxymoron?
Firstly, I'm sorry, if my question will come across as simple or even naive, but I have no formal background in statistics and I'm trying my best to learn it as much as I can, among other areas.
My ...
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Normal vs leptokurtic distribution for financial returns
Financial returns have been shown to follow leptokutotic distributions, however volatility forecasting models like EWMA and DCC-GARCH assume conditionally (dependent on time) Normal distribution for ...
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Unbiased estimator of standard deviation
I'm reading "Properties of range-based volatility estimators" where the authors talk about using the range of a distribution ($h$ - $l$) to estimate its volatility. Specifically, they say,
Daily ...
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Expression for the unconditional variance in the EGARCH model
Given the EGARCH specification:
$\log(\sigma_t^2)=\omega + \alpha(|z_{t-1}| + E[|z_{t-1}|]) + \gamma z_{t-1} + \beta \log(\sigma_{t-1}^2)$
Is it possible to find a closed-form solution for the ...
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GARCH or TARCH model when assymetric volatility but GARCH(1,1) already performs well?
I have the following question: I am analyzing Brent Oil returns and I have found that there's a significant negative sign bias. So first, I have tried with a GARCH(1,1) and it turns out that completly ...
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Interpretation of DCC-GARCH output
I have done fitted a DCC-GARCH model using the dccfit function from the "rmgarch" package in R. The output is below:
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Stochastic Volatility Model
In Kim et al. (1998) stochastic volatility model is specified as:
$y_t=\beta\exp({\frac{h_t}{2}})\varepsilon_t,\quad t\geqslant1$
$h_{t+1}=\mu+\phi(h_t-\mu)+\sigma_\eta\eta_t$
$h_1\sim N(\mu,\frac{...
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Aggregating Multiperiod DCC-GARCH Forecast Covariance Matrices
Say I fit a $DCC$-$GARCH(1,1)$ model to a dataset of weekly returns for four assets.
I forecast the covariance matrix for the next month (so four weekly steps ahead). This gives me four $4 \times 4$ ...
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Conditional Volatility of GARCH squared residuals
Motivation
I want to wrap up my own GARCH implementation
to make sure I have understood the underlying model/assumption.
to leverage forecast::auto.arima to ...
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Density forecasting
I am having some troubles obtaining density forecasts of any returns series. As I couldn't find any numerical examples on the Internet, I would like to ask you guys for some help.
My goal is to ...
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A volatility score not sensitive to the overall scale of the variable
I want to measure volatility in my customer base using the last 5 years of activity. That is, a total of purchases summed by year over a 5 year period.
I plan to use this formula to calculate the ...
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Standard BEKK parameters
I am looking at a BEKK Multivariate GARCH model.
In a standard GARCH model, we generally expect,
$$h_t=\omega+\alpha u_{t-1}^2 +\beta\sigma_{t-1}^2$$
The alpha ($\alpha$) coefficient to be ...
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VaR from Bayesian GARCH / Quantile Estimation
I have fitted a Bayesian GARCH(1,1) model with Student $t$ innovations to some time series data, $X_1,...,X_n$ and now want to estimate Value-at-Risk (VaR) (i.e., 5% quantiles) at each times $t=1,,...,...
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Combining multiple stock time series to one data set for LSTM
I am trying to predict daily stock return volatility using an LSTM network. My data comprises price data of five different stocks, over the same time frame. My question, to which I have not found an ...
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How to measure volatility of a categorial variable?
I have a variable that is a rank of 6 categories though 12 months. The categories are S, A, B, C, D, and E. Where S is best and E is worst. The variable can change overtime, for example one ...
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GARCH(1,1) residuals are not homoskedastic
Given the following simulated GARCH(1, 1) process:
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What are some sound multivariate GARCH models with proven mathematical/statistical properties?
Some popular multivariate GARCH models such as BEKK and DCC have been criticized for the nonexistence of the corresponding stochastic processes and (if I interpret that correctly) the following ...
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How do I extract VaR estimation from DCC-GARCH model in R?
I have estimated a DCC-GARCH model in R and I need to extract the Value at Risk for an equally weighted portfolio from the estimated model.
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How to measure/predict volatility of a time series?
Here's the problem:
We have an entity, and entity can switch ownership. The data can be seen as a time series of events (i.e. ownership change). Of course, events are labeled with epoch time.
So ...
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Causality in variance with a BEKK model
I am using a BEKK model in the following form,
$$H_t=C^\ast{C^\ast}^\prime+\sum_{i=1}^{m}{A_i\varepsilon_{t-i}\varepsilon_{t-i}A_i^\prime+\sum_{j=1}^{s}{B_jH_{t-j}B_j^\prime}}$$
I first start with a ...
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Forecastability and Coefficient of Variation
I'm trying to get a sense check here. When determining "forecastability" for sales data, I tend to use the CV. However, this is highly susceptible to seasonality and outliers. As such, I was wondering:...
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Exponentially Weighing Moving Average (EWMA) for weekly data
I'm aware that the typical EWMA approach is applied over larger time periods (say for Volatility, where lambda = 94% and all weights add up to 100% for stock returns data from last 5 years). ...
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