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21

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

Even though it's a straightforward extension, it took me a while (a year? yikes!); but now you can easily incorporate Bayesian ar(1) (or more generally, Bayesian regression) in joint estimation by using designmatrix = "ar(1)" as an argument to svsample. It's not well documented yet (except in the help files), but I nevertheless hope easy to use. From the ...


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

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. ...


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

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

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 ...


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.


2

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 ...


2

It is just a problem of how you pass times series to yuima. Just one more thing, if you want to estimate a CARMA driven by a Brownian motion, it is better to work with log-prices instead of prices. Indeed, in the considered model, we have a non zero probability assigned to negative values of the process. Try the following code require(yuima) library(xts) ...


2

There is no particular issue with your polynomials. However if you really want them to both start with a 1, you can apply a change of variable by defining : \begin{equation}Y_t = -\frac{1}{4}X_t\end{equation} Then your polynomials $\Phi_y(B)$ and $\Theta(B)$ such that : \begin{equation}\Phi_y(B)Y_t=\Theta(B)Z_t\end{equation} will both start with a $1$. It ...


2

Normally distributed and that's why the two first moments are sufficient to infer their statistical significance. Proof are rather technical (and sometimes are not specific to time-series models) and mainly depends of: The estimation method employed ( QMLE, Least Squares, Moment, Whittle...) The parameter space Moment restrictions ... These proofs ...


1

The code is correct regarding your question (and only for an AR(1) ), you made a mistake because the last observation of the data set is $t-1$ and not $t$ since you are forecasting the point at time $t$. In the code : MF(i,1) is the current point forecast ($t$) and lag one observation ( MF(i-1,1) which is $t-1$ ) is correctly related to the AR part. ...


1

To improve your model I would recommend you to take into acount the intraday periodicity : ie the fluctuation of the exchange rate over the daily cycle. For instance we observe strong increase on the volatility around 07:00 GMT (opening of European Market.) The following image taken from Andersen, T. G., & Bollerslev, T. (1997) illustrates it. It ...


1

To get it out the way: you cannot ask 'what model is better' without a reference to what its use is. Do you want to test for the mean or the AR parameter to trade it? Do you want to calculate VaR? Do you want to forecast volatility over one period? Or over 1000 periods? Or higher moments? Do you want to simulate volatility over one period? Or longer? For ...


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

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



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