ATA  R Documentation 
ATA
is a generic function for Ata Method forecasting.
The Ata method based on the modified simple exponential smoothing as described in Yapar, G. (2016) <doi:10.15672/HJMS.201614320580> ,
Yapar G., Capar, S., Selamlar, H. T., Yavuz, I. (2017) <doi:10.15672/HJMS.2017.493> and Yapar G., Selamlar, H. T., Capar, S., Yavuz, I. (2019)
<doi:10.15672/hujms.461032> is a new univariate time series forecasting method which provides innovative solutions to issues faced during
the initialization and optimization stages of existing methods.
Forecasting performance of the Ata method is superior to existing methods both in terms of easy implementation and accurate forecasting.
It can be applied to nonseasonal or seasonal time series which can be decomposed into four components (remainder, level, trend and seasonal).
This methodology performed well on the M3 and M4competition data.
ATA( X, Y = NULL, parP = NULL, parQ = NULL, parPHI = NULL, model.type = NULL, seasonal.test = NULL, seasonal.model = "decomp", seasonal.period = NULL, seasonal.type = NULL, seasonal.test.attr = NULL, find.period = NULL, accuracy.type = NULL, nmse = 3, level.fixed = FALSE, trend.opt = "none", h = NULL, train_test_split = NULL, holdout = FALSE, holdout.adjustedP = TRUE, holdout.set_size = NULL, holdin = FALSE, transform.order = "before", transform.method = NULL, transform.attr = NULL, lambda = NULL, shift = 0, initial.level = NULL, initial.trend = NULL, ci.level = 95, start.phi = NULL, end.phi = NULL, size.phi = NULL, negative.forecast = TRUE, print.out = TRUE, plot.out = TRUE )
X 
A numeric vector or time series of class 
Y 
A numeric vector or time series of class 
parP 
Value of Level parameter 
parQ 
Value of Trend parameter 
parPHI 
Value of Damping Trend parameter 
model.type 
An onecharacter string identifying method using the framework terminology. The letter "A" for additive model, the letter "M" for multiplicative model.
If NULL, both letters will be tried and the best model (according to the accuracy measure 
seasonal.test 
Testing for stationary and seasonality. If TRUE, the method firstly uses 
seasonal.model 
A string identifying method for seasonal decomposition. If NULL, "decomp" method is default. c("none", "decomp", "stl", "stlplus", "tbats", "stR") phrases of methods denote

seasonal.period 
Value(s) of seasonal periodicity. If NULL, 
seasonal.type 
An onecharacter string identifying method for the seasonal component framework. The letter "A" for additive model, the letter "M" for multiplicative model.
If NULL, both letters will be tried and the best model (according to the accuracy measure 
seasonal.test.attr 
Attributes set for unit root, seasonality tests, X13ARIMA/SEATS and X11. If NULL, corrgram.tcrit=1.28, uroot.test="adf", suroot.test="correlogram", suroot.uroot=TRUE, uroot.type="trend", uroot.alpha=0.05, suroot.alpha=0.05, uroot.maxd=2, suroot.maxD=1, suroot.m=frequency(X), uroot.pkg="urca", multi.period="min", x13.estimate.maxiter=1500, x13.estimate.tol=1.0e5, x11.estimate.maxiter=1500, x11.estimate.tol=1.0e5. If you want to change, please use 
find.period 
Find seasonal period(s) automatically. If NULL, 0 is default. When

accuracy.type 
Accuracy measure for optimization of the best ATA Method forecasting. IF NULL,

nmse 
If accuracy.type == "AMSE" or "GAMSE", nmse provides the number of steps for average multistep MSE ('2<=nmse<=30'). 
level.fixed 
If TRUE, "pStarQ" –> First, fits ATA(p,0) where p = p* is optimized for q=0. Then, fits ATA(p*,q) where q is optimized for p = p*. 
trend.opt 
When

h 
The number of steps to forecast ahead.
When the parameter is NULL; if the frequency of 
train_test_split 
If 
holdout 
Default is FALSE. If TRUE, ATA Method uses the holdout forecasting for accuracy measure to select the best model. In holdout forecasting, the last few data points are removed from the data series. The remaining historical data series is called insample data (training set), and the holdout data is called validation set (holdout set). If TRUE, holdout.set_size will used for holdout data. 
holdout.adjustedP 
Default is TRUE. If TRUE, parP will be adjusted by length of training  validation sets and insample set when the holdout forecasting is active. 
holdout.set_size 
If 
holdin 
Default is FALSE. If TRUE, ATA Method uses the holdin forecasting for accuracy measure to select the best model. In holdin forecasting, the last hlength data points are used for accuracy measure. 
transform.order 
If "before", BoxCox transformation family will be applied and then seasonal decomposition techniques will be applied. If "after", seasonal decomposition techniques will be applied and then BoxCox transformation family will be applied. 
transform.method 
Transformation method –> "Box_Cox", "Sqrt", "Reciprocal", "Log", "NegLog", "Modulus", "BickelDoksum", "Manly", "Dual", "YeoJohnson", "GPower", "GLog". If the transformation process needs shift parameter,

transform.attr 
Attributes set for BoxCox transformation. If NULL, bcMethod = "loglik", bcLower = 0, bcUpper = 1, bcBiasAdj = FALSE. If you want to change, please use 
lambda 
BoxCox power transformation family parameter. If NULL, data transformed before model is estimated. 
shift 
BoxCox power transformation family shifting parameter. If NULL, data transformed before model is estimated. 
initial.level 
If NULL, FALSE is default. If FALSE, ATA Method calculates the pth observation in 
initial.trend 
If NULL, FALSE is default. If FALSE, ATA Method calculates the qth observation in 
ci.level 
Confidence Interval levels for forecasting. 
start.phi 
Lower boundary for searching 
end.phi 
Upper boundary for searching 
size.phi 
Increment step for searching 
negative.forecast 
Negative values are allowed for forecasting. Default value is TRUE. If FALSE, all negative values for forecasting are set to 0. 
print.out 
Default is TRUE. If FALSE, summary of ATA Method is not shown. 
plot.out 
Default is TRUE. If FALSE, graphics of ATA Method are not shown. 
Returns ATA(p,q,phi)(E,T,S) applied to X
.
Returns an object of class ata
. The generic accessor functions ATA.Forecast
and ATA.Accuracy
extract useful features of the value returned by ATA
and associated functions.
ata
object is a list containing at least the following elements
actual : The original time series.
fitted : Fitted values (onestep forecasts). The mean is of the fitted values is calculated over the ensemble.
level : Estimated level values.
trend : Estimated trend values.
residuals : Original values minus fitted values.
coefp : The weights attached to level observations.
coefq : The weights attached to trend observations.
p : Optimum level parameter.
q : Optimum trend parameter.
phi : Optimum damped trend parameter.
model.type: Form of trend.
h : The number of steps to forecast ahead.
forecast : Point forecasts as a time series.
out.sample: Test set as a time series.
method : The name of the optimum forecasting method as a character string for ATA(P,Q,PHI)(Error,Trend,Season).
initial.level : Selected initial level values for the time series forecasting method.
initial.trend : Selected initial trend values for the time series forecasting method.
level.fixed : A choice of optional levelfixed trended methods.
trend.opt : A choice of optional trend and level optimized trended methods (none, trend.fixed or trend.search).
transform.method : BoxCox power transformation family method –> Box_Cox, Sqrt, Reciprocal, Log, NegLog, Modulus, BickelDoksum, Manly, Dual, YeoJohnson, GPower, GLog.
transform.order : Define how to apply BoxCox power transformation techniques, before or after seasonal decomposition.
lambda : BoxCox power transformation family parameter.
shift : BoxCox power transformation family shifting parameter.
accuracy.type : Accuracy measure that is chosen for model selection.
nmse : The number of steps for average multistep MSE.
accuracy : In and out sample accuracy measures and its descriptives that are calculated for optimum model are given.
par.specs : Parameter sets for Information Criteria.
holdout : Holdout forecasting is TRUE or FALSE.
holdout.training : Training set in holdout forecasting.
holdout.validation: Validation set in holdout forecasting.
holdout.forecast : Holdout forecast.
holdout.accuracy : Accuracy measure chosen for model selection in holdout forecasting.
holdin : Holdin forecasting is TRUE or FALSE.
is.season : Indicates whether it contains seasonal pattern.
seasonal.model : The name of the selected decomposition method.
seasonal.type : Form of seasonality.
seasonal.period : The number of seasonality periods.
seasonal.index : Weights of seasonality.
seasonal : Estimated seasonal values.
seasonal.adjusted : Deseasonalized time series values.
execution.time : The real and CPU time 'in seconds' spent by the system executing that task, including the time spent executing runtime or system services on its behalf.
calculation.time : How much real time 'in seconds' the currently running R process has already taken.
Ali Sabri Taylan and Hanife Taylan Selamlar
#'\insertRefyapar2017msesATAforecasting
#'\insertRefyapar2018mhesATAforecasting
#'\insertRefyapar2018msesATAforecasting
#'\insertRefyapar2019ataATAforecasting
forecast
, stlplus
, stR
, stl
, decompose
,
tbats
, seasadj
, seasonal
.
trainATA < head(touristTR, 84) testATA < window(touristTR, start = 2015, end = 2016.917) ata_fit < ATA(trainATA, h=24, parQ = 1, seasonal.test = TRUE, seasonal.model = "stl") ata_fc < ATA.Forecast(ata_fit, out.sample = testATA) ata_accry < ATA.Accuracy(ata_fc)
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