Autocorrelation

The estimated Autocorrelation series is often an intermediate in spectral analysis. This procedure in the Time menu or the Time toolbar is offered as a means to inspect the estimated ACS. Since this is symmetric for real data, only the positive lags are plotted.

The autocorrelation is computed using an FFT and presented in an AutoSignal Graph.

Normalization

The only adjustment is the maximum lag (MaxLag) to be plotted and the normalization. The 1/N normalizes for data length. The unbiased normalization is 1/(N-abs(lag)). The most common normalization is 1/corr(0) which sets the lag 0 autocorrelation to unity.

White Noise

Inspecting the autocorrelation series is helpful in assessing whether or not a signal is distinguishable from white noise. The first example processes the Fractal!A,Fractal!B data set in sample.xls. This 512 point data set consists of true white noise with a Hurst coefficient of 0.5. The first 50 lags are plotted. Note that the estimated ACS is zero everywhere except at lag 0:

When the data series is persistent (contains a memory effect), the autocorrelation looks quite different. The next plot is for Fractal!A,Fractal!G data set in sample.xls. The data were generated using a Hurst exponent of 0.75:

The last example uses the Fractal!A,Fractal!K data set in sample.xls. The data were generated using a Hurst exponent of 0.95:

List

The List Data option lists the index, lag, and autocorrelation in a three column table. The listing uses the AutoSignal text viewer facility.

Copy

The Copy Data to Clipboard option copies the lag and autocorrelation values to the clipboard. Formats include full precision binary (for spreadsheets such as Excel) and ASCII (for pasting into text editors).

Save

The Save Data to Disk option writes the lag and autocorrelation values to a supported file format. These formats include ASCII, Excel 97, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.

Production Facility

The AutoSignal Automation facility allows unattended processing of large numbers of data sets. The data sets can be consolidated in an Excel file or acquired using a DLL. The graphs can be exported to an MS Word RTF file, while the processed data can be exported to an Excel 95 or Excel 97 file.

If an Automation Session is in progress, the Reset button can be used to terminate the automated processing.