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Trend
calculation - full technical definition
Equal
weight is given to each value in the series, and no adjustments
are made to favour recent performance. No distinction is made
between a negative statistic with a reducing trend, and a positive
statistic with an increasing trend.
The calculation
method is described in three stages below. The description assumes
the reader is familiar with the following statistical expressions:
mean
iteration
correlation
weighted average
compound rate of growth
discounted rate of growth
coefficient of correlation
least squares linear regression
Stage
1: Taking the series of values, the ‘least- squares linear
regression’ is calculated, and expressed as a percentage of
the mean. The result is translated into a compound equivalent,
Rate 1.
Stage
2: A process of iteration is used to establish a notional
compound rate, Rate 2, which meets two conditions. First, Rate
2 produces a notional data set which has the same linear regression
as the original series of values. Second, if Rate 2 is used
to discount the mean of the original series of values to the
base date, the result is equal to the base value of the notional
data set.
When the
actual rate, Rate 1, is in fact a consistent year on year rate
of change, the notional data set produced by Rate 2 matches
the original series of values, and Rate 2 is identical to Rate
1.
Stage
3: The correlation coefficient of (a) the original series
of values, to (b) the notional dataset produced by Rate 2, is
used to weight the average of Rates 1 and 2, which in turn gives
the Trend result.
If the original
series of values correlates perfectly with the notional data
set produced by Rate 2, then Rate 2 is the Trend result. If,
on the other hand, the original series of values does not correlate
at all with the notional data set, then Rate 1 is the Trend
result.
If Rate 1
reveals an adverse trend, i.e. a declining positive trend, or
an increase in negative trend, the Trend result is taken to
be Rate 1. If attempts to establish Rate 2 point to a base value
of zero or below, i.e. recovery from a negative position, the
Trend result is also taken to be Rate 1.
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