Let fy1 yng be a sample from a stationary process. Suggest a procedure to determine if the stochastic process is the sum of a constant and a white noise? Let f"1ng be Gaussian white noise with...

Let fy1 yng be a sample from a stationary process. Suggest a

procedure to determine if the stochastic process is the sum of a constant and

a white noise?

Let f"1ng be Gaussian white noise with zero-mean and unit variance

and suppose that we are interested in simulating a Gaussian stationary

process fy1; y2 yng with autocovariance function and mean _. Show

that this process can be simulated by generating a sample of the white noise

" = f"1 ng and then obtaining y = _ + A", where A is a square matrix

satisfying AA0 = 􀀀 with 􀀀i;j = (i 􀀀 j).