Find an invertible representation:

Check if the new process is invertible:

Compare a non-invertible times series with its invertible representation:

Find the invertible representation:

Compare means:

Compare covariance functions:

Compare a non-invertible time series with its invertible representation:

Calculate TransferFunctionModel :

Compare random samples of both processes for a fixed random seed:

Consider a non-invertible process and its invertible representation:

Find the corresponding transfer functions:

Noise for each process simulation would differ, but dependence on past noise is now smaller:

Generate a random sample from a non-invertible process and its invertible representation:

Find the invertible representation:

Generate random samples:

Compare samples:

The sample correlation functions are comparable:

Check if a given time series is invertible:

Plot zeros of transfer function:

Since there are no zeros on the unit circle, the time series has invertible representation:

Check if zeros of the transfer function are inside the unit circle:

ToInvertibleTimeSeries of an invertible process returns the original process:

ToInvertibleTimeSeries scales only the moving average coefficients and the noise variance:

ToInvertibleTimeSeries requires numeric moving-average coefficients:

Use TimeSeriesInvertibility to find conditions for non-numeric coefficients:

ToInvertibleTimeSeries may not exist:

There are zeros of TransferFunctionModel lying on the unit circle:

Compute the zeros: