Trend calculation

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> Only if you're working in exact arithmetic. Most

> statistics requiring forming sums, which can be an

> easy way of getting loss of precision.

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You are right, but it is rare case when 64 bit double is not enough. To loose precission with doubles you will have to have a sum about 2^40 times bigger than elements you add.

sztejkata at 2007-7-15 15:34:25 >

There is a general approach which is often used in real

world time series forecasting.

1. Plot the series and examine the features of the graph.

Look for trends, seasonal components, apparent sharp

changes in behavior, and outlying points.

2. Remove the seasonal components and the trend to get

the residuals.

3. Choose a model to fit the residuals in order to

determine how likely the assumtions are.

The trend can be functions like a

f(t) = a0 + a1*t +...+ an*t^n or harmonic functions

like f(t) = a0 + sum (ai*cos(ki*t) + bi*sin(ki*t) where

ai and bi are unknown parameters and ki are fixed

frequencies. If the variables {X1, ..., Xn} are

independent and identically distributed, you can compute

the parameters above by minimizing sum(xt-f(t))^2.

parza at 2007-7-15 15:34:25 >