The models

library(foresightr)
y <- AirPassengers

Every model is a specification: a small list that says what to fit. It can be printed, saved, renamed and combined; it is estimated only by fit_model(), forecast_model() or inside a backtest().

model_log(model_airline())
#> <foresight model> log_arima_011_011
#> ARIMA(0,1,1)(0,1,1) by exact maximum likelihood, on the log scale

Yardsticks

model_naive(), model_drift(), model_mean() and model_seasonal_naive() are what any other model must beat. The seasonal naive forecast with growth = TRUE repeats last year scaled by the growth of the last twelve months, a strong benchmark for revenue.

forecast_model(model_seasonal_naive(growth = TRUE), y, 6)
#>           Jan      Feb      Mar      Apr      May      Jun
#> 1961 463.5677 434.6642 465.7911 512.4813 524.7097 594.7451

Theta and Holt-Winters

model_theta() is the method that won the M3 competition, equivalent to simple exponential smoothing with drift, on the seasonally adjusted series. model_holt_winters() smooths level, trend and a multiplicative seasonal pattern.

fit_model(model_holt_winters(), y)$params
#>        alpha         beta        gamma          phi sse_relative 
#>    0.3000000    0.0200000    0.8000000    1.0000000    0.2195894

Exponential smoothing

model_ets() fits one member of the family by its code (error, trend, season); model_auto_ets() chooses by AICc among those that suit the series.

fit <- fit_model(model_auto_ets(), y)
fit$details$code
#> [1] "MAM"
fit$details[c("alpha", "beta", "gamma")]
#> $alpha
#> [1] 0.7409353
#> 
#> $beta
#> [1] 1e-04
#> 
#> $gamma
#> [1] 1e-04

ARIMA

model_arima() is estimated by exact maximum likelihood. model_auto_arima() chooses the differences by tests and the orders by a stepwise search.

fit <- fit_model(model_auto_arima(), log(y))
c(fit$details$order, fit$details$seasonal_order)
#> [1] 0 1 1 0 1 1
fit$aicc
#> [1] -483.204
exp(predict(fit, 6))
#>           Jan      Feb      Mar      Apr      May      Jun
#> 1961 450.4223 425.7170 479.0062 492.4044 509.0549 583.3447

Prophet-style trend

model_prophet() fits a trend that may bend at many places, shrinking the bends that do not matter to exactly zero, plus Fourier seasonality:

fit <- fit_model(model_prophet(), log(y))
fit$details$changepoints
#>  [1]  10  15  19  28  37  51  60  65  88 101 115

Events and lasting steps are covered in vignette("regressors").

TBATS

model_tbats() handles several seasonal periods, including periods that are not whole numbers (52.18 weeks in a year), with trigonometric terms. Whatever is not fixed is chosen by AIC, which takes seconds.

fit <- fit_model(model_tbats(), y)
fit$details[c("harmonics", "lambda", "trend", "arma")]
#> $harmonics
#> [1] 5
#> 
#> $lambda
#> [1] 2.306312e-05
#> 
#> $trend
#> [1] TRUE
#> 
#> $arma
#> [1] 0 0

Intermittent demand

For series where most periods have no demand, the forecast is a rate: Croston’s method and its SBA and TSB variants.

demand <- c(0, 0, 3, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0)
forecast_model(model_croston("sba"), demand, 3)
#> [1] 0.8762393 0.8762393 0.8762393

Combining models

Any model can run on the log or Box-Cox scale, and on the seasonally adjusted series:

model_name(model_log(model_decomposed(model_auto_ets())))
#> [1] "log_stl_auto_ets"
forecast_model(model_box_cox(model_theta(), "guerrero"), y, 3)
#>           Jan      Feb      Mar
#> 1961 446.6416 437.0833 521.2054

An ensemble learns its weights from its members’ errors on the end of the series; with "stacked" weights, members that add nothing get exactly zero.

fit <- fit_model(model_ensemble(candidates_default(), weighting = "stacked"), y)
round(fit$params[fit$params > 0], 3)
#>                 weight_naive        weight_seasonal_naive 
#>                        0.010                        0.059 
#> weight_seasonal_naive_growth          weight_holt_winters 
#>                        0.046                        0.503 
#>            weight_log_linear 
#>                        0.382

The ready sets

vapply(candidates_default(), model_name, "")
#>  [1] "naive"                 "drift"                 "seasonal_naive"       
#>  [4] "seasonal_naive_growth" "theta"                 "holt_winters"         
#>  [7] "log_linear"            "arima_011_011"         "log_arima_011_011"    
#> [10] "prophet"               "log_prophet"
length(candidates_thorough())
#> [1] 18

candidates_thorough() adds the automatic choices and two ensembles, and takes seconds rather than milliseconds in a backtest.