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Time Series (SMAPE (One value to predict SMAPE is 0 when the predicted…
Time Series
SMAPE
One value to predict
SMAPE is 0 when the predicted value is equal to the true value.
Under estimate is penalized more than an
over estimate
.
Function is
non-convex
for values
above the true
value. This may lead to
many local minima
Two values to predict
In this case there are
two global minima
with SMAPE = 80 for the two cases where our constant prediction is equal to one of the value in the true series.
The function reaches a
local maxima
with SMAPE = 100 for y_pred = 3.
And the value of the
median
(y_pred = 5) is about 95.24, i.e. it is
significantly higher
than the global minima.
More points, uniformly sampled distribution
Minimum
of the smape function is met
near the median
which is good. It could explain why the public kernels do well.
skewed distribution
again the
median does well
.
one zero
The function is
discontinue at 0
.
It is equal to 200 everywhere except at 0 where it equals 0.
Two zeros
Two
local minima at 100
when y_pred equals one of the values in the y_true series.
There is a
discontinuity at 0
.
The
mathematical limit
of the series SMAPE(0, x) when x tends to 0 is
200
. It means that there is no local maxima near 0 as the value 200 cannot be reached. But we can get values as close as we want to 200
More zeros
median is really not a good choice
here and that
0 would be way better.
Moreover, a gradient descent from anywhere except 0 will miss the global minima, by large.
Discontinuity at 0
makes it
tricky
to optimize SMAPE with constant predictions
Fast Fourier Transform
peaks in FFT show strongest frequencies in the periodic signal
Autocorrelation & Partial Autocorrelation
Statsmodels
Moving Average
Process / model
Median filter
can be used to remove extremely short spikes
Memory Management
ARIMA / ARMA
