4 Maggio 2022 14:56

Markov-Switching E-GARCH con R

What is Markov switching GARCH?

A solution to this problem is to allow the parameters of the GARCH model to vary over time according to a latent discrete Markov process. This approach is called the Markov-switching GARCH (MSGARCH) model, which leads to volatility forecasts that can quickly adapt to variations in the unconditional volatility level.

How do you use GARCH in R?

Indeed considering a GARCH(p,q) model, we have 4 steps :

  1. Estimate the AR(q) model for the returns. …
  2. Construct the time series of the squared residuals, e[t]^2.
  3. Compute and plot the autocorrelation of the squared rediduals e[t]^2.

How do I choose the best GARCH model in R?

A Greedy ARMA/GARCH Model Selection

  1. Choose the one with higher returns.
  2. If returns are the same, choose the one with less parameters.
  3. If the number of parameter is the same, (3,5) and (5,3) for instance, choose the one with less AR parameters – (3,5) in the previous example.

What does a GARCH model do?

GARCH models describe financial markets in which volatility can change, becoming more volatile during periods of financial crises or world events and less volatile during periods of relative calm and steady economic growth.

What is Msgarch?

The R package MSGARCH implements a comprehensive set of functionalities for Markov-switching GARCH (Haas et al. 2004a) and Mixture of GARCH (Haas et al. 2004b) models, This includes fitting, filtering, forecasting, and simulating. Other functions related to Value-at-Risk and Expected- Shortfall are also available.

How do you write a GARCH model?

A generally accepted notation for a GARCH model is to specify the GARCH() function with the p and q parameters GARCH(p, q); for example GARCH(1, 1) would be a first order GARCH model. A GARCH model subsumes ARCH models, where a GARCH(0, q) is equivalent to an ARCH(q) model.

How do I choose a GARCH model?

(1) define a pool of candidate models, (2) estimate the models on part of the sample, (3) use the estimated models to predict the remainder of the sample, (4) pick the model that has the lowest prediction error.

What is multivariate GARCH model?

MGARCH stands for multivariate GARCH, or multivariate generalized autoregressive conditional heteroskedasticity. MGARCH allows the conditional-on-past-history covariance matrix of the dependent variables to follow a flexible dynamic structure.

When would you use a GARCH model?

GARCH models are used when the variance of the error term is not constant. That is, the error term is heteroskedastic. Heteroskedasticity describes the irregular pattern of variation of an error term, or variable, in a statistical model.

What does the AR mean in GARCH?

The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.

What is the difference between ARCH and GARCH model?

GARCH is an extension of the ARCH model that incorporates a moving average component together with the autoregressive component. GARCH is the “ARMA equivalent” of ARCH, which only has an autoregressive component. GARCH models permit a wider range of behavior more persistent volatility.

Is GARCH stationary?

The GARCH(1,1) process is stationary if the stationarity condition holds. ARCH model can be estimated by both OLS and ML method, whereas GARCH model has to be estimated by ML method.

What is a GARCH 1 1 model?

In GARCH(1,1) model, current volatility is influenced by past innovation to volatility. Multivariate GARCH is model for two or more time series. In this case, current volatility of one time series is influenced not only by its own past innovation, but also by past innovations to volatilities of other time series.

What are the uses of ARCH and GARCH models how these models are used in forecasting?

ARCH and GARCH models have become important tools in the analysis of time series data, particularly in financial applications. These models are especially useful when the goal of the study is to analyze and forecast volatility.

What is P and Q in GARCH?

Just like ARCH(p) is AR(p) applied to the variance of a time series, GARCH(p, q) is an ARMA(p,q) model applied to the variance of a time series. The AR(p) models the variance of the residuals (squared errors) or simply our time series squared. The MA(q) portion models the variance of the process.

Why do we use the letter H instead of Sigma when describing a GARCH model?

9)Why do we use the letter h instead of sigma when describing a GARCH model? It means variance is variablerather than parameter. It means variance is variable rather than parameter .

Which of the following statements are true concerning a comparison between ARCH Q and GARCH 1 1 models?

Which of the following statements are true concerning a comparison between ARCH(q) and GARCH(1,1) models? Correct! The GARCH(1,1) model uses only 3 parameters in the conditional variance equation, and is therefore highly parsimonious.

Is Gjr GARCH better than GARCH?

According to research (Laurent et al. and Brownlees et al.) the GJR models generally perform better than the GARCH specification. Thus, including a leverage effect leads to enhanced forecasting performance.

Which of the following is wrong statement about the maximum likelihood method step?

Which of the following is wrong statement about the maximum likelihood approach? Explanation: This method involve probability calculations to find a tree that best accounts for the variation in a set of sequences. All possible trees are considered. Hence, the method is only feasible for a small number of sequences.

Does MLE always exist?

If the interval included its boundary, then clearly the MLE would be θ = max[Xi]. But since this interval does not include its boundary, the MLE cannot be the maximum, and therefore an MLE does not exist.

Are MLE efficient?

It is easy to check that the MLE is an unbiased estimator (E[̂θMLE(y)] = θ). To determine the CRLB, we need to calculate the Fisher information of the model. Yk) = σ2 n . (6) So CRLB equality is achieved, thus the MLE is efficient.

Are MLE unique?

The maximum likelihood estimate is shown to exist and to be unique if a twice continuously differentiable likelihood function is constant on the boundary of the parameter space and if the Hessian matrix is negative definite whenever the gradient vector vanishes.

Is the MLE The MVUE?

The maximum likelihood estimator (MLE) is an alternative to the minimum variance unbiased estimator (MVUE). For many estimation problems, the MVUE does not exist.

Is MLE always UMVUE?

Most often the domination is strict thus the MLE is not even admissible. It was proven when p is Cauchy but I guess it’s a general fact. Thus MLE can’t be UMVU. Actually, for these families it’s known that, with mild conditions, there is never an UMVUE.

Can MLE be biased?

It is well known that maximum likelihood estimators are often biased, and it is of use to estimate the expected bias so that we can reduce the mean square errors of our parameter estimates.