Performance of multichannel autoregressive spectral estimators

This paper compares and contrasts the performance of multichannel periodogram and autoregressive spectrum analysis techniques periodogram when processing sunspot and world air temperature data, a first order autoregressive process, and an artificial data set of sinusoids in colored noise. It is shown that the high resolution benefit of autoregressive analysis must be tempered by an awareness of a severe feed across effect among the autospectral autoregressive estimates that may prevent multichannel autoregressive spectral estimation from being a viable spectral estimation approach. The feed across effect manifests itself as very sharp spikes in the autospectrum where there should be no spectral energy. The cause is known to be inexact pole-zero cancellation in the autoregressive coeffieient matrix estimates. Performing single channel autoregressive spectral estimates will provide indications of where the feed across effect is occurring. The astronomical literature has applied these multichannel autoregressive techniques to correlate sunspot activity with terrestrial activity such as tides, earth rotation variations, air temperature variations, and drought cycles. High correlation has alledgedly been found. However, the findings of the literature is now in doubt because this author believes that the astrophysical researchers were misled by the feed across anomaly. This paper also serves to correct some errors reported on examples in reference [3].