Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [volatility]

A statistical measure of the dispersion of a (financial) time series, e.g. its (annualized or regular) standard deviation

Volatility is the degree of variation of a time series such as an asset price or a market index, usually measured by the standard deviation of logarithmic returns. For any fund that evolves randomly with time, volatility is defined as the standard deviation of a sequence of random variables, each of which is the return of the fund over some corresponding sequence of (equally sized) times.

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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 stationarity before applying an ARMA-GARCH model? Further on…
Jen Bohold
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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(1,1) model on 3,000 data points and forecasted 1…
Vladimir Belik
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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 into a 93% probability of making money in any given year.…
shenflow
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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 observation can be a S in the first month, a B in the…
Rafael Martinez
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What is the entropy of a riskless random variable?

Variance and standard deviation are often used as proxies for risk and volatility. I make the analogy to information theory as follows, correct if it's wrong: a random variable $x\in \mathbb{R}$ that has no uncertainty is one that has zero…
develarist
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The best way to compute the PRESS statistic

I would like to forecast the return volatility in a financial market. I am using symbolic regression/genetic programming to generate models with a good in-sample fit. I would like to compute predictive R Squared for each model to enable me to…
BillB
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GARCH forecast of series (in R) seems too high

I am wondering why the mean of my model is so high leading to a high forecast of the time series data. I included a linear regression in the external regressors as there is a clear downward trend. I think I may have specified the linear regression…
user553480
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conditional volatility plot in R - GARCH

When I build a GARCH(1,1) with a skewed generalised error dist to model the innovations, with a linear trend using the fGarch library I get the following: mod = lm(Jobs ~ Month, df) library(fGarch) fit1 = garchFit(~garch(1,1), cond.dist="sged", …
user553480
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ARSV model estimation with (constrained) generalized method of moments in R

I am trying to perform the estimation of the following Autoregressive Stochastic Volatility model $$ y_t=\sigma_t u_t = exp(w_t/2)u_t \\ w_t = \omega + \phi w_{t-1} + \eta_t $$ in R via the function gmm of the homonymous package. The following lines…
Mr Frog
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Standard Deviation shows that a price series is riskier but annualized volatility computed with the log of returns shows the opposite

I apologize if this is not a smart question, but it seems contradictory that the standard deviations of two price series show that series A is riskier, but when I plot the annualized volatilities (using the log returns), series B seems riskier. Is…
Narjems
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A Markov Regime-Switching GARCH with Time-Varying Transition Matrix Package in R

Does anyone know if there exists any Markov regime-switching GARCH with time-varying transition matrix package or tutorial in R? I know of the "MSGARCH" package by D. Ardia et al. but the transition matrix is constant. Thanks in advance!
Blg Khalil
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Realized GARCH estimation problem

I'm trying to produce one-day ahead volatility forecasts for Bitcoin with Realized GARCH(1,1) using the rugarch package in R. The realized variance(data$rv5) is aggregated based on a 5 minute frequency, and the returns(data.xts$ret) are…
Crib
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The Nonlinear Asymmetric GARCH Model

I'm reading about the Nonlinear Asymmetric GARCH (NAGARCH) model. If NAGARCH(1, 1) is given by: $${\displaystyle ~\sigma _{t}^{2}=~\omega +~\alpha (~\epsilon _{t-1}-~\theta ~\sigma _{t-1})^{2}+~\beta ~\sigma _{t-1}^{2}},$$ where ${\displaystyle…
Blg Khalil
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ARCH: How is Volatility Formulation rewritten as Residuals Formulation

I am trying to understand the concept of ARCH(1) model from this tutorial video. From 4:15, it's explained that, the variance of residuals (1) can be formulated as (2). ( = residual at t, =variance of residual(volatility) at t, w=white noise) (1) …
koyamashinji
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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 models. However, as far as I understand, such models…
shenflow
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