Integrate Package: `smooth`

[mdancho84]

Investigate and implement smooth package. What makes immediate sense are:

• [ ] ADAM: Augmented Dynamic Adaptive Model https://forecasting.svetunkov.ru/en/2021/01/13/the-creation-of-adam-next-step-in-statistical-forecasting/
• [ ] exp_smoothing(): The smooth::es() function can handle xregs, which currently the forecast::ets() method cannot. This can be an additional engine in exp_smoothing().
• [ ] arima_reg(): A Seasonal ARIMA auto.ssarima() / ssarima() implemented in state space. These can be additional engines in arima_reg().

There are a number of other algorithms that will be reviewed.

1. adam - Advanced Dynamic Adaptive Model, implementing ETS, ARIMA and regression and their combinations;
2. es - the ETS function. It can handle exogenous variables and has a handy "holdout" parameter. There are several cost function implemented, including trace forecast based ones. Model selection is done via branch and bound algorithm and there's a possibility to use AIC weights in order to produce combined forecasts. Finally, all the possible ETS functions are implemented here.
3. ces - Complex Exponential Smoothing. Function estimates CES and makes forecast. See documentation for details.
4. gum - Generalised Exponential Smoothing. Next step from CES. The paper on this is in the process.
5. sma - Simple Moving Average in state space form.
6. ssarima - SARIMA estimated in state space framework.
7. msarima - Multiple seasonal ARIMA, allows multiple seasonalities and works in a finite time.
8. auto.ces - selection between seasonal and non-seasonal CES models.
9. auto.ssarima - selection between different State-Space ARIMA models.
10. auto.msarima - selection between different multiple SARIMA models.
11. auto.gum - automatic selection of the most appropriate GUM model.
12. sim.es - simulation of data using ETS framework with a predefined (or random) smoothing parameters and initial values.
13. sim.ssarima - simulation of data using State-Space ARIMA framework with a predefined (or randomly generated) parameters and initial values.
14. sim.ces - simulation of data using CES with a predefined (or random) complex smoothing parameters and initial values.
15. sim.gum - simulation functions for GUM.
16. sim.sma - simulates data from SMA.
17. oes - occurrence state space exponential smoothing model. This function models the part with data occurrences using one of the following methods: fixed, odds ratio, inverse odds ratio, direct or general. It can also select the most appropriate between the five.
18. sowhat - returns the ultimate answer to any question.
19. smoothCombine - the function that combines forecasts from es(), ces(), gum(), ssarima() and sma() functions.
20. cma - Centred Moving Average. This is the function used for smoothing of time series, not for forecasting.
21. msdecompose - multiple seasonal decomposition based on centred moving averages.

Resources:

• GitHub: https://github.com/config-i1/smooth

[AlbertoAlmuinha]

Hi Matt,

I have implemented the Adam and Auto.Adam algorithms and I think tomorrow will upload a PR. Just a doubt, I have called “adam_reg()” with adam and auto_adam engines…Is it ok? Or do you prefer other names?

[mdancho84]

That is perfect. adam_reg() is great.

[mdancho84]

I've just merged #130 and I'll begin some more detailed reviews today.