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Since the previous post on “The Creation of ADAM“, I had difficulties finding time to code anything, but I still managed to fix some bugs, implement a couple of features and make changes, important enough to call the next version of package smooth “3.1.0”. Here is what’s new:

1. A new algorithm for ARIMA order selection in ADAM via auto.adam() function. The algorithm is explained in the draft of my online textbook. This is a more efficient algorithm than the previous one (which was originally implemented for auto.ssarima()) in terms of computational time and forecast accuracy. We will see how it performs on a dataset in the R experiment below.
2. We no longer depend on forecast package, and we now use forecast() method from greybox package. Hopefully, this will not lead to conflicts between the packages, but if it does, please, let me know, and I will fix them. The main motivation for this move was the amount of packages forecast relies on, making R download half of CRAN, whenever you need to install forecast for the first time. This is a bit irritating and complicates testing process. Furthermore, Rob Hyndman’s band of programmers now focuses on tideverts packages, and forecast is not included in that infrastructure, so inevitably it will become obsolete, and we would all need to move away from forecast anyway.
3. ves() and viss() functions have been moved from smooth package to a new one called legion. The package is in development stage and will be released closer to the end of March 2021. It will focus on multivariate models for time series analysis and for forecasting, such as Vector Exponential Smoothing, Vector ARIMA etc.
4. ADAM now also supports Gamma distribution via the respective parameter in adam() function. There is some information about that in the draft of the online textbook on ADAM.
5. Finally, msdecompose() function (for multiplies seasonal decomposition) now has a built-in mechanism of missing data interpolation based on polynomials and Fourier series. The same mechanism is now used in adam().

### A small competition in R

I will not repeat the code from the previous post, you can copy and paste it in your R script and run to replicate the experiment described there. But I will provide the results of the experiment applied with functions from smooth v3.1.0. Here are the two final tables with error measures:

Means:
MASE RMSSE Coverage Range  sMIS  Time
ADAM-ETS(ZZZ)  2.415 2.098    0.888 1.398 2.437 0.654
ADAM-ETS(ZXZ)  2.250 1.961    0.895 1.225 2.092 0.497
ADAM-ARIMA     2.326 2.007    0.841 0.848 3.101 3.029
ADAM-ARIMA-old 2.551 2.203    0.862 0.968 3.098 5.990
ETS(ZXZ)       2.279 1.977    0.862 1.372 2.490 1.128
ETSHyndman     2.263 1.970    0.882 1.200 2.258 0.404
AutoSSARIMA    2.482 2.134    0.801 0.780 3.335 1.700
AutoARIMA      2.303 1.989    0.834 0.805 3.013 1.385

Medians:
MASE RMSSE Range  sMIS  Time
ADAM-ETS(ZZZ)  1.362 1.215 0.671 0.917 0.396
ADAM-ETS(ZXZ)  1.327 1.184 0.675 0.909 0.310
ADAM-ARIMA     1.324 1.187 0.630 0.917 2.818
ADAM-ARIMA-old 1.476 1.300 0.769 1.006 3.525
ETS(ZXZ)       1.335 1.198 0.616 0.931 0.551
ETSHyndman     1.323 1.181 0.653 0.925 0.164
AutoSSARIMA    1.419 1.271 0.577 0.988 0.909
AutoARIMA      1.310 1.182 0.609 0.881 0.322

In the tables above, the models that perform the best in terms of selected error measures are marked in boldface, the new ADAM ARIMA is in dark red, while the old one is in grey colour. We can see that while the new ADAM ARIMA does not beat the benchmark models, such as ETS(Z,X,Z) or even auto.arima(), it is doing much better than the previous version of ADAM ARIMA in terms of accuracy and computational time and does not fail as badly. The new algorithm is definitely better than the one implemented in auto.ssarima() function from smooth. When it comes to prediction intervals, the ADAM ARIMA outperforms both auto.arima() from forecast package and auto.ssarima() from smooth in terms of coverage, getting closer to the nominal 95% confidence level.

I am still not totally satisfied with ADAM ARIMA in case of optimised initials (it seems to work well in case of initial="backcasting") and will continue working in this direction, but at least now it works better than in smooth v3.0.1. I also plan to improve the computational speed of ADAM with factor variables, plan to work on development of classes for predicted explanatory variables and then make all smooth functions agnostic of the classes of data. If you have any suggestions, please file an issue on github.

Till next time!

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