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In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussionthis discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForeCA.

In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForeCA.

In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForeCA.

added missing 'e' in ForCA; added examples for Omega() and reference to ForeCA
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edit approved Aug 12, 2015 at 3:38
Georg M. Goerg
edit approved Aug 12, 2015 at 3:38
Georg M. Goerg
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 library(pracma)
series1 <- approx_entropyset.seed(AirPassengers10)
series1
[1] 0all.5157758
series2series <- approx_entropylist(sunspot.year)series1 = AirPassengers,
                    series2
[1] 0= sunspot.762243year,
                    series3 <-= approx_entropy(rnorm(1:500)) # <== size increased
 sapply(all.series, approx_entropy)
  series1   series2   series3 
[1]  0.5157758 0.7622430 1.4714724741971

In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForCA: http://cran.r-project.org/web/packages/ForeCAForeCA.

library(ForeCA)
sapply(all.series,
       Omega, spectrum.control = list(method = "wosa"))
 series1   series2   series3 
 41.239218 25.333105  1.171738

Here $\Omega \in [0, 1]$ is a measure of forecastability where $\Omega(white noise) = 0\%$ and $\Omega(sinusoid) = 100 \%$.

References

Balasis, G., Daglis, I. A., Anastasiadis, A., & Eftaxias, K. (2011). Detection of dynamical complexity changes in Dst time sSeries using entropy concepts and rescaled range analysis. In W. Liu and M. Fujimoto (Eds.), The Dynamic Magnetosphere, IAGA Special Sopron Book, Series 3, 211. doi:10.1007/978-94-007-0501-2_12. Springer. Retrieved from http://members.noa.gr/anastasi/papers/B29.pdf

Georg M. Goerg (2013): Forecastable Component Analysis. JMLR, W&CP (2) 2013: 64-72. http://machinelearning.wustl.edu/mlpapers/papers/goerg13

library(pracma)
series1 <- approx_entropy(AirPassengers)
series1
[1] 0.5157758
series2 <- approx_entropy(sunspot.year)
series2
[1] 0.762243
series3 <- approx_entropy(rnorm(1:500)) # <== size increased
series3
[1] 1.471472

In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForCA: http://cran.r-project.org/web/packages/ForeCA.

References

Balasis, G., Daglis, I. A., Anastasiadis, A., & Eftaxias, K. (2011). Detection of dynamical complexity changes in Dst time sSeries using entropy concepts and rescaled range analysis. In W. Liu and M. Fujimoto (Eds.), The Dynamic Magnetosphere, IAGA Special Sopron Book, Series 3, 211. doi:10.1007/978-94-007-0501-2_12. Springer. Retrieved from http://members.noa.gr/anastasi/papers/B29.pdf

 library(pracma)
 set.seed(10)
 all.series <- list(series1 = AirPassengers,
                    series2 = sunspot.year,
                    series3 = rnorm(500)) # <== size increased
 sapply(all.series, approx_entropy)
  series1   series2   series3 
  0.5157758 0.7622430 1.4741971

In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForeCA.

library(ForeCA)
sapply(all.series,
       Omega, spectrum.control = list(method = "wosa"))
 series1   series2   series3 
 41.239218 25.333105  1.171738

Here $\Omega \in [0, 1]$ is a measure of forecastability where $\Omega(white noise) = 0\%$ and $\Omega(sinusoid) = 100 \%$.

References

Balasis, G., Daglis, I. A., Anastasiadis, A., & Eftaxias, K. (2011). Detection of dynamical complexity changes in Dst time sSeries using entropy concepts and rescaled range analysis. In W. Liu and M. Fujimoto (Eds.), The Dynamic Magnetosphere, IAGA Special Sopron Book, Series 3, 211. doi:10.1007/978-94-007-0501-2_12. Springer. Retrieved from http://members.noa.gr/anastasi/papers/B29.pdf

Georg M. Goerg (2013): Forecastable Component Analysis. JMLR, W&CP (2) 2013: 64-72. http://machinelearning.wustl.edu/mlpapers/papers/goerg13

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Aleksandr Blekh
Aleksandr Blekh
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Parameters m and r, involved in calculation of approximate entropy (ApEn) of time series, are window (sequence) length and tolerance (filter value), correspondingly. In fact, in terms of m, r as well as N (number of data points), ApEn is defined as "natural logarithm of the relative prevalence of repetitive patterns of length m as compared with those of length m + 1" (Balasis, Daglis, Anastasiadis & Eftaxias, 2011, p. 215):

$$ ApEn(m, r, N) = \Phi^m(r) - \Phi^{m+1}(r), $$

$\text{where }$

$$ \Phi^m(r) = {\LARGE{\Sigma}_i} lnC^m_i(r)/(N - m + 1) $$

Therefore, it appears that changing the tolerance r allows to control the (temporal) granularity of determining time series' entropy. Nevertheless, using the default values for both m and r parameters in pracma package's entropy function calls works fine. The only fix that needs to be done to see the correct entropy values relation for all three time series (lower entropy for more well-defined series, higher entropy for more random data) is to increase the length of random data vector:

library(pracma)
series1 <- approx_entropy(AirPassengers)
series1
[1] 0.5157758
series2 <- approx_entropy(sunspot.year)
series2
[1] 0.762243
series3 <- approx_entropy(rnorm(1:500)) # <== size increased
series3
[1] 1.471472

The results are as expected - as the predictability of fluctuations decreases from most determined series1 to most random series 3, their entropy consequently increases: ApEn(series1) < ApEn(series2) < ApEn(series3).

In regard to other measures of forecastability, you may want to check mean absolute scaled errors (MASE) - see this discussion for more details. Forecastable component analysis also seems to be an interesting and new approach to determining forecastability of time series. And, expectedly, there is an R package for that, as well - ForCA: http://cran.r-project.org/web/packages/ForeCA.

References

Balasis, G., Daglis, I. A., Anastasiadis, A., & Eftaxias, K. (2011). Detection of dynamical complexity changes in Dst time sSeries using entropy concepts and rescaled range analysis. In W. Liu and M. Fujimoto (Eds.), The Dynamic Magnetosphere, IAGA Special Sopron Book, Series 3, 211. doi:10.1007/978-94-007-0501-2_12. Springer. Retrieved from http://members.noa.gr/anastasi/papers/B29.pdf