How do I compare two multivariate timeseries? NARMAX?

I have two datasets in form of time-series: (Y_1(t), X_1(t)) and (Y_2(t), X_2(t)), which comes from measurements of the same object during two repetitions of the same experiment in two different structures(a dynamic driving cycle for the same IC engine).

Y is my response signal, measured CO2 level X contains information about environmental variables, such as humidity, pressure and temperature, and measurements of factors which affects Y, such as speed, momentum, humidity, flows, exhaust pressure&temperature, etc., for a total of 15 variables.

What is the most informative way to compare Y_1 and Y_2? I would like to be either be able to say that the Y_1 differs from Y_2 in a predictable way, due to a given change in a given variable contained in X or that the differences between Y_1 and Y_2 are not explainable by a change in X. Can creating a NARX/NARMAX model for either of them help me in any way?

Thanks in advance!

[Greg Heath]

QUES: WHAT OR WHERE IS NARMAX???

ANS: I GUESS I FORGOT:

https://www.mathworks.com/matlabcentral/answers/346926-how-do-i-update-narx-network-to-a-narmax-network-using-the-matlab-neural-network-toolbox

[Matt Tlom]

Hi Greg! Yes, I meant NARX when referring to the Neural Network Time Series Tool. I do not think I need NARMAX in my case. Do you have any recommendation about how to use NARX in the Matlab NNTS tool for comparing my two datasets?

Thanks in advance

Answer 1

[Carl]

Hi Matteo. How to compare Y_1 and Y_2 in an informative way is a very broad question, and I think it would mostly depend on what specific information you're looking for. See the following page for a list of MATLAB functions for analyzing time series data in the System Identification Toolbox:

https://www.mathworks.com/help/ident/time-series-model-identification.html

As well as using NARX and time-delay neural networks:

https://www.mathworks.com/help/nnet/modeling-and-prediction-with-narx-and-time-delay-networks.html

Alternatively, you can perform some type of regression on your X and Y data. The Statistics and Machine Learning Toolbox has a variety of regression models for this:

https://www.mathworks.com/help/stats/functionlist.html#predictive-modeling

[Greg Heath]

The Neural Network Toolbox does not have NARMAX and NARXMAX.

However, they probably are in one of the other toolboxes.

Greg

[Greg Heath]

NARMAX and NARXMAX are not available in MATLAB.

The "MA" stands for "MovingAverage" and the above functions appear to differ from NAR and NARX by including linear combinations of past errors as feedback signals.

However, since

 error = target-output

it looks like they can only be used as long as target data is available.

Greg

Answer 2

[Greg Heath]

I assume both Y and X are multi-dimensional yielding multidimensional DX = X2-X1 and DY = Y1-Y2.

Then the best way that I can think of explaining differences is to curvefit both DX and DY. Then plot

 DYi vs DXj   where i and j represent dimension indices, not data points.

Hope this helps

Thank you for formally accepting my answer

Greg