# Tag Info

20

First, Garch models stochastic volatility. Thus its use should be limited to estimating the volatility component. The difference in some of the volatility models is the assumption made of the random variance process components. I believe it has been popular because it is an extension of the ARCH family of models and it is relatively easy to setup and ...

6

Your question's title suggests the market prices are mean reverting. I strongly suggest verifying that assumption via one of the usual tests, such as the Augmented Dickey-Fuller test (implemented in the tseries package of R by the adf.test function, and in other R packages, too). If the market is truly mean reverting, a possible strategy is Detrend the ...

5

In terms of interpretation, an $MA$ model simply means that the time series is a function of the error from previous periods. You might find it informative to consider plotting simple $AR(1)$ models alongside various $ARMA(1,1)$ to develop a more intuitive understanding. For instance, the $AR(1)$ model (chosen as it is common for financial time series) ...

3

You want to compute the BIC (Bayessian Information Criterion) or the AIC (Akaike information criterion) for different (p,q) pairs. Here is a wikipedia article with information on how to interpret those criteria in practice. Here is a mathworks page with detailed instructions on how to perform this task within Matlab. Keep in mind that in practice and ...

3

I know only that Jurik's JMA is good causal filter, better than Kalman and Volterra filters, but I don't know for sure what algorithm inside - it's black box. Does anybody know better causal filter?

2

There is no guarantee that the optimization method always converges! In an introduction the author of the package recommends using the "hybrid" solver, which starts out with the "solnp" and goes through the other solvers, if it doesn't converge. According to him, this should at least guarantee convergence in 90 % of the cases. ...

2

Wavelets and Kalman filtering.

2

The issue with wavelets is that you'll have some boundary distortions so be careful when exploiting the results.

2

1.Is it correct, that the coefficients are now different to the coefficients of the arima output? It seems right that the ARMA coefficients are different. Indeed, in the second model, the GARCH component will capture fluctuations that the ARMA component will not have to capture, resulting in different ARMA parameter estimates. 2.This is the acf of ...

2

Use acf and pacf as to determine AR and MA parts. Use the position of last significant value for the two tests as the AR and MA terms respectively. or use autoarima if matlab has one with AIC or BIC coefficients. AIC returns a more general model (all possible values) while BIC results in a more constrained one (simpler).

2

Another possible solution is the EACF of Tsay and Tiao (1984) where the idea is that if the order of the AR process is known the MA can be inferred. The output is a table where the first left corner 0 is taken to be the order of the ARMA(p, q) model.

1

It is a classical misunderstanding, your model is right, you always have a acf equal to one at lag zero (and not one) since if there is no lag acf = covariance(x , x_lag 0) / variance x = variance x / variance x = 1. So you need to pay attention to the x axis , some software displays ACF starting at lag zero and some others from 1 (which make better ...

1

The Autocorrelation Function (ACF) $\rho_k=Corr(y_t,y_{t-k})$ expresses the strength of linear dependency between the $k$-lagged realizations and hence represents an important tool for identification of the lag orders of ARMA and GARCH processes: $$\rho_k:=Corr(y_t,y_{t-k})=\frac{\gamma_k}{\gamma_0},\,\,k\in\mathbb{Z}$$ where the Autocovariance $\gamma_k$ is ...

1

Some models do use ln(r_t), like Black–Derman–Toy and the Black–Karasinski models. Mainly to avoid negative interest rates in low rates / high volatility environments through the use of the log-normal distribution. Negative rates can wreak havoc in option premiums for example. They are interest rates indeed, that we call short rates, not yield on ...

1

These are not yield. They are instantaneous short rates which are not directly observable in the market.

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