The theta method of Assimakopoulos and Nikolopoulos (2000) is equivalent to simple exponential smoothing with drift. This is demonstrated in Hyndman and Billah (2003).

THETA(formula, ...)

## Arguments

formula Model specification. Not used.

## Value

A model specification.

## Details

The series is tested for seasonality using the test outlined in A&N. If deemed seasonal, the series is seasonally adjusted using a classical multiplicative decomposition before applying the theta method. The resulting forecasts are then reseasonalized.

More general theta methods are available in the forecTheta package.

## Specials

### season

The season special is used to specify the parameters of the seasonal adjustment via classical decomposition.

season(period = NULL, method = c("multiplicative", "additive"))

 period The periodic nature of the seasonality. This can be either a number indicating the number of observations in each seasonal period, or text to indicate the duration of the seasonal window (for example, annual seasonality would be "1 year"). method The type of classical decomposition to apply. The original Theta method always used multiplicative seasonal decomposition, and so this is the default.

## References

Assimakopoulos, V. and Nikolopoulos, K. (2000). The theta model: a decomposition approach to forecasting. International Journal of Forecasting 16, 521-530.

Hyndman, R.J., and Billah, B. (2003) Unmasking the Theta method. International J. Forecasting, 19, 287-290.

## Author

Rob J Hyndman, Mitchell O'Hara-Wild

## Examples

# Theta method with transform
deaths <- as_tsibble(USAccDeaths)
deaths %>%
model(theta = THETA(log(value))) %>%
forecast(h = "4 years") %>%
autoplot(deaths)

# Compare seasonal specifications
library(tsibbledata)
library(dplyr)
aus_retail %>%
filter(Industry == "Clothing retailing") %>%
model(theta_multiplicative = THETA(Turnover ~ season(method = "multiplicative")),
accuracy()
#> # A tibble: 16 x 12
#>    State   Industry  .model .type     ME   RMSE    MAE     MPE  MAPE  MASE RMSSE
#>    <chr>   <chr>     <chr>  <chr>  <dbl>  <dbl>  <dbl>   <dbl> <dbl> <dbl> <dbl>
#>  1 Austra… Clothing… theta… Trai… 0.0732  0.889  0.646  0.288   5.80 0.511 0.508
#>  2 Austra… Clothing… theta… Trai… 0.168   1.52   1.03   1.76   10.4  0.812 0.871
#>  3 New So… Clothing… theta… Trai… 2.49   14.1   10.3    0.688   4.16 0.551 0.576
#>  4 New So… Clothing… theta… Trai… 4.74   28.0   17.5    2.13    7.38 0.932 1.15
#>  5 Northe… Clothing… theta… Trai… 0.0266  0.422  0.320  0.225   5.67 0.417 0.418
#>  6 Northe… Clothing… theta… Trai… 0.0324  0.506  0.393  0.415   7.60 0.512 0.501
#>  7 Queens… Clothing… theta… Trai… 1.12    9.01   6.13   0.612   4.75 0.497 0.539
#>  8 Queens… Clothing… theta… Trai… 1.70   16.3   10.8    2.09   10.9  0.874 0.978
#>  9 South … Clothing… theta… Trai… 0.167   2.95   2.01   0.0804  5.27 0.400 0.406
#> 10 South … Clothing… theta… Trai… 0.245   4.51   2.96   0.590   7.89 0.591 0.621
#> 11 Tasman… Clothing… theta… Trai… 0.0485  1.28   0.861 -0.0436  6.18 0.505 0.470
#> 12 Tasman… Clothing… theta… Trai… 0.0780  1.77   1.06   0.561   7.36 0.620 0.649
#> 13 Victor… Clothing… theta… Trai… 1.48   10.5    7.75   0.465   4.22 0.476 0.473
#> 14 Victor… Clothing… theta… Trai… 2.89   20.9   13.8    1.54    7.37 0.845 0.939
#> 15 Wester… Clothing… theta… Trai… 0.323   3.82   2.78   0.362   4.49 0.455 0.481
#> 16 Wester… Clothing… theta… Trai… 0.559   6.44   4.56   1.28    8.13 0.746 0.812
#> # … with 1 more variable: ACF1 <dbl>