Denoising Techniques in Time-series Forecasting
Often, before being able to use a time-series, it is necessary to make it more smooth,
or remove the noise that is always present in time-series.
Classical approaches to this problem have always been to apply a moving average
or an exponential moving average to the time-series to obtain the denoised or smoothed
one. As you can read in this article it is
however very dangerous to use moving averages on time-series because they normally
change the statistical properties of the time-series.
Another approach has recently emerged that is based on Wavelet Transforms. This
method has a very interesting property that is, together with denoising and smoothing
the time-series it maintains the time synchronization with the original time-series.
Let's consider the following dataset:
this could be representing a classical business time-series (demand for a particular
good, price of a stock).
On this time-series we will apply an adaptive response rate exponential smoothing
that is classically used to smooth the time-series and a Daubechies denoising algorithm.
In the following picture you can see the graphical effect of both:
As you can see from the picture the Adaptive response rate algorithm (as any moving
average) is partially lagged and "late" with respect to the original time-series
while the Daubechies denoising is perfectly on time.
Of course both algorithms are changing the statistical properties of the time-series
as already described in another article.