I am investigating the time varying dependence between financial return series using copula theory.
For each marginal time series I have fitted a GJR GARCH model with t-distributed innovations and extracted the standardized residuals.
These residuals I use as input for my copula models.
Now, with the estimated copula models I have simulated 1000 standardized residuals for each point t.
I have already transformed these simulated uniformly distributed residuals back to their t-distribution.
I am wondering how I can transform these simulated t-distributed residuals back to returns with the GJR GARCH model for each point in time.
Thank you in advance!
Related
I'm working on Magnetic Resonance Imaging data, on Matlab R2020a. In particular, i have to characterize the background noise of the image and i know it has a noncentral chi distribution. Now, i'm trying the mle method whitout results:
[phat,pci] = mle(data,'pdf',#(data,v,d)ncx2pdf(data,v,d),'start',[1 1]);
data is a row vector (1024,1), v are the dof of the distribution and d the noncentrality parameter (the two parameters that i have to find).
The problem lies in the fact that the distribution strongly depends on the value of the mean, and the order of magnitude of my data is 10^-6.
histogram of the data:
Does anyone know a method to fit the data to a noncentral chi distribution? I already tried the 0-1 and 0-255 normalization, but they produces unreliable mean values. Any suggestions are welcome.
data.mat
I have two covariances of size 6*6, one is supposed be the true covariance and the other is the Maximum likelihood estimate for my covariance. Is there any way I could validate my estimated covariance?
I don't know how exactly you determined your covariance matrix, but generally it is a good first step to check the confidence intervals of your estimators.
Heuristically speaking a wide confidence interval suggests that your estimator has a lot of uncertainty.
Take a look at the Matlab function corrcoef, which also gives lower and upper bounds for the estimated correlation coefficients,
cf. https://uk.mathworks.com/help/matlab/ref/corrcoef.html#bunkanr .
Maybe using this function on your data gives you a good starting point. If you use your own function to estimate the ML estimators, you will have to add the confidence intervals yourself.
I'm confused that lolimot approximate data by sum of linear models or by some of gaussian models? I see here on page 184 that lolimot is a model for dividing space into linear sub-spaces, but structure of lolimot is sum ofweighted gaussian models. Actually I mean data in every subspace have linear distribution or gaussian distribution?
Thanks
I'm calculating displacement from the motion of an accelerometer and using a Kalman filter to improve the displacement accuracy. Please note that I am aware of ineffectiveness of using acceleration to obtain displacement in real scenarios, but in my case displacement is pretty small (like 10 cm over 2–3 seconds).
I am following this paper (PDF). In the paper there are two matrices, Q and R, for noise modeling and they are set such that displacement error is minimized. The authors tested the above with synthetic acceleration data of a known covariance to use the same in matrices Q and R.
I decided to vary the particular covariance and find its corresponding minimum error in displacement. But in my case there is no change in displacement at any value of covariance. Any help?
let us assume,
I have a vector t with the times in seconds of my samples. (These samples are not equally distributed on the time domain.
Also I have a vector data containing the samplevalues at the time t.
t and data have the same length.
If I plot the graph some sort of periodical signal is obtained.
now I could perform: abs(fft(data)) to get my spectrum, which is then plotted over the amount of data points on the x-axis.
How can I obtain my spectrum regarding the times in vector t and plot it?
I want to see which frequencies in 1/s or which period in s my signal contains.
Thanks for your help.
[Not the OP's intention]: FFT will give you the spectrum (global) for any number of input data points. You cannot have a specific data point (in time) associated with parts (or the full) spectrum.
What you can do instead is use spectrogram and obtain the Short-Time Fourier Transform (STFT). This will give you a NxM discrete grid of time-frequency FT values (N: FT frequency bins, M: signal time-windows).
By localizing the (overlapping) STFT windows on your data samples of interest you will get N frequency magnitude values, thus the distribution of short-term spectrum estimates as the signal changes in time.
See also the possibly relevant answer here: https://stackoverflow.com/a/12085728/651951
EDIT/UPDATE:
For unevenly spaced data you need to consider the Non-Uniform DFT (and Non-uniform FFT implementations). See the relevant question/answer here https://scicomp.stackexchange.com/q/593
The primary approaches for NFFT or NUFFT, are based on creating a uniform grid through local convolutions/interpolation, running FFT on this and undoing the convolutional effect of the interpolation filter.
You can read more:
A. Dutt and V. Rokhlin, Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14, 1993.
L. Greengard and J.-Y. Lee, Accelerating the Nonuniform Fast Fourier Transform, SIAM Review, 46 (3), 2004.
Pippig, M. und Potts, D., Particle Simulation Based on Nonequispaced Fast Fourier Transforms, in: Fast Methods for Long-Range Interactions in Complex Systems, 2011.
For an implementation (with an interface to MATLAB) try NFFT and possibly its parallelized version PNFFT. You may find a nice walk-through on how to set-up and use here.
You can resample or interpolate your sample points to get another set of sample points that are equally spaced in t. The chosen spacing or sample rate of the second set of equally spaced sample points will allow you to infer frequencies to the result of an FFT of that second set.
The results may be noisy or include aliasing unless the initial data set is bandlimited to a sufficiently low frequency to allow interpolation. If bandlimited, then you might try something like cubic splines as an interpolation method.
Although it may look like one can get a high FFT bin frequency resolution by resampling to a larger number of data points, the actual useful resolution accuracy will be more related to the original number of samples.