/ [root]
├── code
│ └── [matlab scripts]
│ Main.m
│ createsimulationset.m
│ MVAR_KF.m
│ MVAR_MKFA.m
│ MVAR_MKFA2.m
│ GA_MVAR_KF.m
│ GA_MVAR_MKFA.m
│ GA_MVAR_MKFA2.m
│ simulate_MVAR_KF.m
│ simulate_MVAR_MKFA.m
│ simulate_MVAR_MKFA2.m
│ smooth_MVAR_KF.m
│ smooth_MVAR_MKFA.m
│ smooth_MVAR_MKFA2.m
│ estimate_GARCH.m
│ estimate_MVARmeasures.m
│ MVAR_measures.m
│ plot_MVARmeasures.m
│ colorcet.m
│ TVcoef.mat
- code contains the following:
│
├── Main.m: The main function. A 3 dimensional TV-MVAR realization, driven by homoskedastic and heteroskedastic noise,
│ is simulated. The TV model coefficients are saved on the folder data/TVcoef.mat. The coefficients were
│ selected in such a way that the MVAR model was stable at each time point. The simulated process is then
│ identified using recursive methods (conventional Kalman Filter and proposed Kalman Filter). The model and
│ the recursive estimators hyperparameters are optimized using a mixed integer Genetic Algorithm (GA). TV-
│ MVAR measures of Coherence (COH), Partial Coherence (PCOH), Directed Coherence (DC) and Generalized
│ Partial Directed Coherence (gPDC) are also computed and compared with the true simulated ones. For
| multiple realizations as shown in paper [1] the Main function code can be adapted easily
│
├── createsimulationset.m: This function creates a simulation realization of a 3 dimensional TV-MVAR process of order 2. The driving
│ noise can be either homoskedastic or heteroskedastic (i.e. its variance is time-varying). The TV
│ coefficients of the model (same as the ones depicted in Fig.1a of []) are save on the folder
│ /data/TVcoef.mat
│
├── MVAR_KF.m: Function optimized by the GA for the case were the TV-MVAR coefficients are estimated using the
│ conventional KF
│
├── MVAR_MKFA.m: Function optimized by the GA for the case were the TV-MVAR coefficients are estimated using the
│ proposed KF (MKFA)
│
├── MVAR_MKFA2.m: Function optimized by the GA for the case were the TV-MVAR coefficients are estimated using the
│ proposed KF (MKFA - improved version)
│
├── GA_MVAR_KF.m: Function that initializes the GA optimization procedure for MVAR_KF
│
├── GA_MVAR_MKFA.m: Function that initializes the GA optimization procedure for MVAR_MKFA
│
├── GA_MVAR_MKFA2.m: Function that initializes the GA optimization procedure for MVAR_MKFA2
│
├── simulate_MVAR_KF.m: Function that simulates and save the results of MVAR_KF using the GA optimized model and estimator
│ hyperparameters
│
├── simulate_MVAR_MKFA.m: Function that simulates and save the results of MVAR_MKFA using the GA optimized model and estimator
│ hyperparameters
│
├── simulate_MVAR_MKFA2.m: Function that simulates and save the results of MVAR_MKFA2 using the GA optimized model and estimator
│ hyperparameters
│
├── smooth_MVAR_KF.m: Function that smooths the estimated TV-MVAR coefficients from MVAR_KF using the Rauch-Tung-Striebel fixed-
│ interval equations (smoothing is applied after MVAR_KF GA optimization)
│
├── smooth_MVAR_MKFA.m: Function that smooths the estimated TV-MVAR coefficients from MVAR_MKFA using the Rauch-Tung-Striebel
│ fixed-interval equations (smoothing is applied after MVAR_MKFA GA optimization)
│
├── smooth_MVAR_MKFA2.m: Function that smooths the estimated TV-MVAR coefficients from MVAR_MKFA2 using the Rauch-Tung-Striebel
│ fixed-interval equations (smoothing is applied after MVAR_MKFA2 GA optimization)
│
├── estimate_GARCH.m: Function that fits GARCH models to the squared residuals in case heteroskedasticity is present in the data
│
├── estimate_MVARmeasures.m: Function that estimates the TV-MVAR measures of COH, PCOH, DC and gPDC
│
├── MVAR_measures.m: Function called at each time point from estimate_MVARmeasures.m that computes the TV-MVAR measures of COH,
│ PCOH, DC and gPDC in the frequency domain. This function was inspired by the eMVAR - Extended Multivariate
│ Autoregressive Modelling Toolbox of Lucas Faes http://www.lucafaes.net/emvar.html and specifically the
│ fdmvar.m script
│
├── plot_MVARmeasures.m: Function that plots the real and estimated TV-MVAR measures
│
├── colorcet.m: Function by Peter Kovesi for perceptually uniform color maps
│
├── mexhowto: Folder with images related to building mex files
│
├── TVcoef.mat: Mat file necessary for running the simulations. It contains the true TV-MVAR coefficients
Once Main.m is finished running the following figures are saved in the current folder:
KFCOH.png: TV Coherence from one TV-MVAR realization estimated using the conventional KF
KFPCOH.png: TV Partial Coherence from one TV-MVAR realization estimated using the conventional KF
KFDC.png: TV Directed Coherence from one TV-MVAR realization estimated using the conventional KF
KFgPDC.png: TV Generalized Partial Directed Coherence from one TV-MVAR realization estimated using the conventional KF
MKFACOH.png: TV Coherence from one TV-MVAR realization estimated using the proposed KF (MKFA)
MKFAPCOH.png: TV Partial Coherence from one TV-MVAR realization estimated using the proposed KF (MKFA)
MKFADC.png: TV Directed Coherence from one TV-MVAR realization estimated using the proposed KF (MKFA)
MKFAgPDC.png: TV Generalized Partial Directed Coherence from one TV-MVAR realization estimated using the proposed KF (MKFA)
MKFA2COH.png: TV Coherence from one TV-MVAR realization estimated using the improved version of the proposed KF (MKFA2)
MKFA2PCOH.png: TV Partial Coherence from one TV-MVAR realization estimated using the improved version of the proposed KF (MKFA2)
MKFA2DC.png: TV Directed Coherence from one TV-MVAR realization estimated using the improved version of the proposed KF (MKFA2)
MKFA2gPDC.png: TV Generalized Partial Directed Coherence from one TV-MVAR realization estimated using the improved version of the
proposed KF (MKFA2)
The output file contains the text printed in the command window; each step as well as the total computation time. At the end, 2 tables are also included. The first contains the Normalized Mean Squared Error (NMSE) between true and predicted TV-MVAR measures and the second one the Mean Squared Error (MSE) between true and predicted TV-MVAR coefficients using all 3 methods (i.e. the conventional KF, the proposed KF and the improved version of the proposed KF)
In the reproducible run the TV-MVAR process is driven by heteroskedastic noise
All the results are saved to the file: RES.mat
Mex files in combination with parallel computing decrease significantly the runtime of the GA optimization framework. The scripts that can be compiled to mex files through matlab coder are: MVAR_KF.m, MVAR_MKFA.m and MVAR_MKFA2.m. To create mex files follow the steps depicted in the images:
For MVAR_KF the inputs are of type: X: double 1xInf Y: double 3x:1000 (note that you can change this based on the size of your data) metric: double 1x1 ignore: double 1x1
For MVAR_MKFA the inputs are of type: X: double 1xInf Y: double 3x:1000 (note that you can change this based on the size of your data) metric: double 1x1 ignore: double 1x1
For MVAR_MKFA2 the inputs are of type: X: double 1xInf Y: double 3x:1000 (note that you can change this based on the size of your data) metric: double 1x1 ignore: double 1x1 pmax: double 1x1
The mex file is stored in the current folder. To call for example MVAR_KF as mex, instead of MVAR_KF(....) type MVAR_KF_mex(.....). More details inside the code.
[1] K. Kostoglou, A.D. Robertson, B. J. MacIntosh, G. D. Mitsis, "A novel framework for estimating time-varying multivariate autoregressive models and application to cardiovascular responses to acute exercise", Accepted, Transactions on Biomedical Engineering (TBME)
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