I have been trying to figure out how to to generate a time series dataset for feedforward neural network.

Let's say I want to simulate a time series dataset with lenght n and order m using feedforward neural network by following steps:

1- firstly I randomly initial m values for weights, biases and data using uniform distribution with the specific parametes as mean and variance

2- secondly I calculate the n elements of time series data using feedforward neural network function

3- thirdly I randomly generate white noise using normal distribution with the specific parametes as mean and variance

4- then I adding generated white noise to my n elements of time series data which calculated form second step

I have found resource related to adding white noise to series and I see at the first we should generate n time series data completly and then we should adding white noise to each elements of generated time series. So when we want generate first element (m+1 element) we should not adding white noise to it. Therfor the next data elements as m+2, m+3, m+4,... generate using feedforward neural network function whithout the effects of white noise of m+1, m+2, m+3 ,...

As I see the data generation using feedforward neural network by above steps led to same constant value when m is smal (equel to 1 or 2,3) and led to zero when m is large (m=6,7,..14) and my data series whithout white noise is same to a const line for smal value of m, and is a zero for large value of m! And finally by adding white noise to it my simulated series is same to generated white noise.

What I am trying to find out for simulate a time series dataset for feedforward neural network?

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