lpredict

  LPREDICT estimates the values of a data set before/after the observed set.

  LPREDICT uses linear prediction to extrapolate data, typically a
  timeseries. Note that this is not the same as linear extrapolation. 
  A window of autocorrelation coefficients is moved beyond the data
  limits to extrapolate the data. For a discussion, see Press et. al. [1].

  The required coefficients are derived from a call to LPC in MATLAB's
  Signal Processing Toolbox

  Example:
  y=LPREDICT(x, np, npred, pos)
  [y, a]=LPREDICT(x, np, npred, pos)
       x:       the input data series as a column vector or a matrix 
                    with series organized in columns
       np:      the number of predictor coefficients to use (>=2)
       npred:   the number of data values to return in the output
       pos:     a string 'pre' or 'post' (default: post)
                    This determines whether extrapolation occurs before or
                    after the observed series x.

       y:       the output, appropriately sequenced for concatenation with
                    input x
       a:       the coefficients returned by LPC (organized in rows).
                    These can be used to check the quality/stability of the
                    fit to the observed data as described in the
                    documenation to the LPC function.

  The output y is given by:
        y(k) = -a(2)*y(k-1) - a(3)*y(k-2) - ... - a(np)*y(k-np)
                 where y(n) => x(end-n) for n<=0

  Note that sum(-a(2:end))is always less than unity. The output will
  therefore approach zero as npred increases. This may be a problem if x
  has a large DC offset. Subtract the the column mean(s) of x from x on
  input and add them to the output column(s) to restore DC. For a more
  accurate DC correction, see [1].

  To pre-pend data, the input sequence is reversed and the output is
  similarly reversed before being returned. The output may always be
  vertically concatenated with the input to extend the timeseries e.g:
        k=(1:100)';
        x=exp(-k/100).*sin(k/5);
        x=[lpredict(x, 5, 100, 'pre'); x; lpredict(x, 5, 100, 'post')];


  See also LPC

  References:
  [1] Press et al. (1992) Numerical Recipes in C. (Ed. 2, Section 13.6).

  Toolboxes Required: Signal Processing

  Revisions:    10.07 renamed to avoid filename clash with System ID
                      Toolbox
                      DC correction help text corrected.

  -------------------------------------------------------------------------
  Author: Malcolm Lidierth 10/07
  Copyright © The Author & King's College London 2007
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