$$\newcommand{\mathbbm}[1]{\boldsymbol{\mathbf{#1}}}$$

## 19.3 Cheat sheet for adam() function

This section summarises the main ways of using adam() in R, with references to the chapters and sections where specific elements were discussed.

Estimate the best ETS model for the provided data (Section 15.1):

ourModel <- adam(y)

The best ETS, taking the last 10 observations of time series as a holdout to test the performance of model:

ourModel <- adam(y, h=10, holdout=TRUE)

Build a pure multiplicative seasonal ETS with an arbitrary seasonal lag of 7 (can be applied to an object y of any class, including ts, vector, matrix, zoo, tibble, etc):

ourModel <- adam(y, model="YYM", lags=7)

Estimate the best ARIMA model for the provided data (assuming seasonal lag of 7, Section 15.2):

ourModel <- adam(y, model="NNN", lags=7,
orders=list(ar=c(3,2),
i=c(2,1),
ma=c(3,2),
select=TRUE))

Build ARIMA(0,1,1) with drift (Chapter 8 for the general ARIMA and Section 8.1.4 for the one with constant):

ourModel <- adam(y, model="NNN",
orders=c(0,1,1), constant=TRUE)

Estimate ETS(A,N,N)+ARIMA(1,0,0) model (Sections 8.4 and 9.4):

ourModel <- adam(y, model="ANN", orders=c(1,0,0))

Use Generalised Normal distribution for the residuals of ADAM ETS(A,A,N) (Sections 5.5, 6.5, and 11.1):

ourModel <- adam(y, model="AAN", distribution="dgnorm")

Select the best distribution for the specific ADAM ETS(A,A,N) (Chapter 15):

ourModel <- auto.adam(y, model="AAN")

Select the most appropriate ETSX model for the provided data (which can be any two-dimensional object, such as matrix, data.frame, or tibble, see Chapter 10):

ourModel <- adam(data)

Specify, which explanatory variables to include and in what form (Section 10.1):

ourModel <- adam(data, formula=y~x1+x2+I(x2^2))

Select the set of explanatory variables for ETSX(M,N,N) based on AIC (Section 15.3):

ourModel <- adam(data, model="MNN",
regressors="select", ic="AIC")

Estimate ETS(A,Ad,N) model using a multistep loss function, GTMSE (Section 11.3):

ourModel <- adam(y, model="AAdN",
h=10, loss="GTMSE")

Estimate ARIMA(1,1,2) using a multistep loss function (Section 11.3) with backcasting of initials (Section 11.4):

ourModel <- adam(y, model="NNN", orders=c(1,1,2),
h=10, loss="GTMSE", initial="backcasting")

Select and estimate the most appropriate ETS model on the data with multiple frequencies (Chapter 12):

ourModel <- adam(y, model="ZXZ", lags=c(24,24*7,24*365))

Select and estimate the triple seasonal ARIMA on the data with multiple frequencies (Chapter 12):

ourModel <- adam(y, model="NNN", lags=c(1,24,24*7,24*365),
orders=list(ar=c(3,2,2,2),
i=c(2,1,1,1),
ma=c(3,2,2,2),
select=TRUE),
initial="backcasting")

Apply an automatically selected occurrence part of the model to intermittent data (Section 13.1):

oesModel <- oes(y, model="YYY", occurrence="auto")

Use the estimated occurrence model in adam() to model intermittent data (Section 13.2):

ourModel <- adam(y, model="YYY", occurrence=oesModel)

Or alternatively just use the same model for occurrence and demand sizes part (Chapter 13):

ourModel <- adam(y, model="YYY", occurrence="auto")

Estimate the scale model for previously estimated ADAM (Chapter 17):

scaleModel <- sm(ourModel, model="YYY")

Implant the scale model into the ADAM for future use (e.g. for forecasting):

mergedModel <- implant(ourModel, scaleModel)

Produce diagnostic plots to see if the ADAM can be improved any further (Chapter 14):

par(mfcol=c(2,2))
plot(ourModel, which=c(1,2,4,6))

Extract conventional, standardised, and studentised residuals (Chapter 14):

residuals(ourModel)
rstandard(ourModel)
rstudent(ourModel)

Plot time series decomposition according to ADAM ETS (Section 4.1):

plot(ourModel, which=12)

Produce point forecast and prediction interval from ADAM for 10 steps ahead (Chapter 18):

forecast(ourModel, h=10, interval="prediction")

Produce point forecast and prediction interval for ADAM, cumulative over the lead time of 10 (Subsection 18.4.3):

forecast(ourModel, h=10, interval="prediction",
cumulative=TRUE)

Produce point forecast and empirical prediction interval for upper bound (upper quantile of distribution, Sections 18.3.5 and 18.4.2):

forecast(ourModel, h=10, interval="empirical",
side="upper")

Produce summary of ADAM (Chapter 16):

summary(ourModel)

Reapply ADAM with randomly selected initials and parameters (to capture the uncertainty of parameters) and produce forecasts from each of these models (Section 16.5):

reapply(ourModel)
reforecast(ourModel, h=10, interval="prediction")

Extract multistep forecast errors from ADAM (Subsection 14.7.3):

rmultistep(ourModel, h=10)

Extract covariance matrix of multistep forecast errors from ADAM (Section 11.3):

multicov(ourModel, h=10)

Extract actual and fitted values from ADAM:

actuals(ourModel)
fitted(ourModel)