forecast

Forecast response at time steps beyond available data

Since R2023b

Syntax

forecastY = forecast(Mdl,PastTbl)

forecastY = forecast(Mdl,PastX,PastY)

forecastY = forecast(Mdl,PastX)

forecastY = forecast(Mdl,PastY)

forecastY = forecast(___,LeadingData=leadingData)

Description

forecastY = forecast(Mdl,PastTbl) forecasts the response at each horizon step in Mdl.Horizon beyond the time step of the latest observation in the past data PastTbl. Before forecasting, the function uses the data PastTbl to prepare lagged predictors. Then, for each horizon step in the direct forecasting model Mdl, the function uses the corresponding model in Mdl.Learners to forecast the response.

This syntax is appropriate when Mdl does not use leading exogenous predictors. That is, Mdl.LeadingPredictors is empty.

forecastY = forecast(Mdl,PastX,PastY) returns forecast responses using the past exogenous predictor data PastX and the past response data PastY. This syntax is appropriate when Mdl uses nonleading exogenous predictors and lagged response variables as predictors, but does not use leading exogenous predictors. That is, Mdl.PredictorNames and Mdl.ResponseLags are nonempty, and Mdl.LeadingPredictors is empty.

forecastY = forecast(Mdl,PastX) returns forecast responses using the past exogenous predictor data PastX. This syntax is appropriate when Mdl does not use lagged response variables or leading exogenous predictors as predictors. That is, Mdl.ResponseLags and Mdl.LeadingPredictors are empty.

forecastY = forecast(Mdl,PastY) returns forecast responses using the past response data PastY. This syntax is appropriate when Mdl does not use exogenous predictors. That is, Mdl.PredictorNames and Mdl.LeadingPredictors are empty.

forecastY = forecast(___,LeadingData=leadingData) specifies leading predictor data at time steps beyond the past data, in addition to any of the input argument combinations in previous syntaxes. This syntax assumes that Mdl uses leading exogenous predictors, and that max(Mdl.Horizon) is greater than or equal to min(Mdl.LeadingPredictorLags) + 1. To identify the variables that leadingData must include, use Mdl.PredictorNames(Mdl.LeadingPredictors).

Examples

Predict Response for Observed Test Data and Forecast Response Beyond Available Data

After creating a DirectForecaster object, see how the model performs on observed test data by using the predict object function. Then use the model to forecast at time steps beyond the available data by using the forecast object function.

Load the sample file TemperatureData.csv, which contains average daily temperatures from January 2015 through July 2016. Read the file into a table. Observe the first eight observations in the table.

temperatures = readtable("TemperatureData.csv");
head(temperatures)

    Year       Month       Day    TemperatureF
    ____    ___________    ___    ____________

    2015    {'January'}     1          23     
    2015    {'January'}     2          31     
    2015    {'January'}     3          25     
    2015    {'January'}     4          39     
    2015    {'January'}     5          29     
    2015    {'January'}     6          12     
    2015    {'January'}     7          10     
    2015    {'January'}     8           4     

For this example, use a subset of the temperature data that omits the first 100 observations.

Tbl = temperatures(101:end,:);

Create a datetime variable t that contains the year, month, and day information for each observation in Tbl. Then, use t to convert Tbl into a timetable.

numericMonth = month(datetime(Tbl.Month, ...
    InputFormat="MMMM",Locale="en_US"));
t = datetime(Tbl.Year,numericMonth,Tbl.Day);
Tbl.Time = t;
Tbl = table2timetable(Tbl);

Plot the temperature values in Tbl over time.

plot(Tbl.Time,Tbl.TemperatureF)
xlabel("Date")
ylabel("Temperature in Fahrenheit")

Partition the temperature data into training and test sets by using tspartition. Reserve 20% of the observations for testing.

partition = tspartition(size(Tbl,1),"Holdout",0.20);
trainingTbl = Tbl(training(partition),:);
testTbl = Tbl(test(partition),:);

Create a full direct forecasting model by using the data in trainingTbl. Train the model using a decision tree learner. All three of the predictors (Year, Month, and Day) are leading predictors because their future values are known. To create new predictors by shifting the leading predictor and response variables backward in time, specify the leading predictor lags and the response variable lags.

Mdl = directforecaster(trainingTbl,"TemperatureF", ...
    Learner="tree", ...
    LeadingPredictors="all",LeadingPredictorLags={0:1,0:1,0:7}, ...
    ResponseLags=1:7)

Mdl = 
  DirectForecaster

                  Horizon: 1
             ResponseLags: [1 2 3 4 5 6 7]
        LeadingPredictors: [1 2 3]
     LeadingPredictorLags: {[0 1]  [0 1]  [0 1 2 3 4 5 6 7]}
             ResponseName: 'TemperatureF'
           PredictorNames: {'Year'  'Month'  'Day'}
    CategoricalPredictors: [2]
                 Learners: {[1x1 classreg.learning.regr.CompactRegressionTree]}
                   MaxLag: [7]
          NumObservations: [372]

Mdl is a DirectForecaster model object. By default, the horizon is one step ahead. That is, Mdl predicts a value that is one step into the future.

For each test set observation, predict the temperature value using Mdl.

predictedY = predict(Mdl,testTbl)

predictedY=93×1 timetable
       Time        TemperatureF_Step1
    ___________    __________________

    16-Apr-2016          49.398      
    17-Apr-2016          39.419      
    18-Apr-2016          39.419      
    19-Apr-2016          45.333      
    20-Apr-2016          35.867      
    21-Apr-2016          34.222      
    22-Apr-2016          45.333      
    23-Apr-2016          66.392      
    24-Apr-2016          44.111      
    25-Apr-2016              49      
    26-Apr-2016              49      
    27-Apr-2016          34.222      
    28-Apr-2016          43.333      
    29-Apr-2016          34.222      
    30-Apr-2016          34.222      
    01-May-2016          34.222      
      ⋮

Plot the true response values and the predicted response values for the test set observations.

plot(testTbl.Time,testTbl.TemperatureF)
hold on
plot(predictedY.Time,predictedY.TemperatureF_Step1,"--")
hold off
legend("True","Predicted",Location="southeast")
xlabel("Date")
ylabel("Temperature in Fahrenheit")

Overall, the direct forecasting model is able to predict the trend in temperatures.

Retrain the direct forecasting model using the training and test data. To forecast temperatures one week beyond the available data, specify the horizon steps as one to seven steps ahead.

finalMdl = directforecaster(Tbl,"TemperatureF", ...
    Learner="tree", ...
    LeadingPredictors="all",LeadingPredictorLags={0:1,0:1,0:7}, ...
    ResponseLags=1:7,Horizon=1:7)

finalMdl = 
  DirectForecaster

                  Horizon: [1 2 3 4 5 6 7]
             ResponseLags: [1 2 3 4 5 6 7]
        LeadingPredictors: [1 2 3]
     LeadingPredictorLags: {[0 1]  [0 1]  [0 1 2 3 4 5 6 7]}
             ResponseName: 'TemperatureF'
           PredictorNames: {'Year'  'Month'  'Day'}
    CategoricalPredictors: [2]
                 Learners: {7x1 cell}
                   MaxLag: [7]
          NumObservations: [465]

finalMdl is a DirectForecaster model object that consists of seven regression models: finalMdl.Learners{1}, which predicts one step into the future; finalMdl.Learners{2}, which predicts two steps into the future; and so on.

Because finalMdl uses the unshifted values of the leading predictors Year, Month, and Day as predictor values, you must specify these values for the specified horizon steps in the call to forecast. For the week after the last available observation in Tbl, create a timetable forecastData with the year, month, and day values.

forecastTime = Tbl.Time(end,:)+1:Tbl.Time(end,:)+7;
forecastYear = year(forecastTime);
forecastMonth = month(forecastTime,"name");
forecastDay = day(forecastTime);
forecastData = timetable(forecastTime',forecastYear', ...
    forecastMonth',forecastDay',VariableNames=["Year","Month","Day"])

forecastData=7×3 timetable
       Time        Year     Month      Day
    ___________    ____    ________    ___

    18-Jul-2016    2016    {'July'}    18 
    19-Jul-2016    2016    {'July'}    19 
    20-Jul-2016    2016    {'July'}    20 
    21-Jul-2016    2016    {'July'}    21 
    22-Jul-2016    2016    {'July'}    22 
    23-Jul-2016    2016    {'July'}    23 
    24-Jul-2016    2016    {'July'}    24 

Forecast the temperature at each horizon step using finalMdl.

forecastY = forecast(finalMdl,Tbl,LeadingData=forecastData)

forecastY=7×1 timetable
       Time        TemperatureF
    ___________    ____________

    18-Jul-2016       62.375   
    19-Jul-2016         64.5   
    20-Jul-2016       66.889   
    21-Jul-2016       66.889   
    22-Jul-2016         70.5   
    23-Jul-2016        74.25   
    24-Jul-2016        74.25   

Plot the observed temperatures for the test set data and the forecast temperatures.

plot(testTbl.Time,testTbl.TemperatureF)
hold on
plot([testTbl.Time(end);forecastY.Time], ...
    [testTbl.TemperatureF(end);forecastY.TemperatureF],"--")
hold off
legend("Observed Data","Forecast Data", ...
    Location="southeast")
xlabel("Date")
ylabel("Temperature in Fahrenheit")

Input Arguments

Mdl — Direct forecasting model

DirectForecaster model object | CompactDirectForecaster model object

Direct forecasting model, specified as a DirectForecaster or CompactDirectForecaster model object.

PastTbl — Past data

table | timetable

Past data, specified as a table or timetable. Each row of PastTbl corresponds to one observation, and each column corresponds to one variable. PastTbl must have the same data type as the predictor data argument used to train Mdl, and must include all variables used to create lagged predictors (including the response variable when Mdl.ResponseLags is nonempty).

PastX — Past exogenous predictor data

numeric matrix | table | timetable

Past exogenous predictor data, specified as a numeric matrix, table, or timetable. Each row of PastX corresponds to one observation, and each column corresponds to one predictor. PastX must have the same data type as the predictor data argument used to train Mdl, and must include all variables used to create lagged predictors.

PastY — Past response data

numeric vector | one-column table | one-column timetable

Past response data, specified as a numeric vector, one-column table, or one-column timetable. Each row of PastY corresponds to one observation.

• If PastX is a numeric matrix, then PastY must be a numeric vector.

• If PastX is a table, then PastY must be a numeric vector or one-column table.

• If PastX is a timetable or it is not specified, then PastY must be a numeric vector, one-column table, or one-column timetable. If PastX is not specified and Mdl.X or Mdl.Y is a timetable, then PastY must be a timetable.

If you specify both PastX and PastY, then they must have the same number of observations.

leadingData — Leading predictor data at time steps beyond past data

numeric matrix | table | timetable

Leading predictor data at time steps beyond the past data, specified as a numeric matrix, table, or timetable. Each row of leadingData corresponds to one observation, and each column corresponds to one predictor. leadingData must have the same data type as the predictor data argument used to train Mdl, and must contain all variables used for preparing leading predictors. leadingData must contain at least max(Mdl.Horizon)-min(Mdl.LeadingPredictorLags) observations.

Output Arguments

forecastY — Forecast responses

numeric vector | table | timetable

Forecast responses, returned as a numeric vector, table, or timetable.

• forecastY has the same data type as the past predictor data PastTbl or PastX when the predictor data is specified. Otherwise, forecastY has the same data type as PastY.

• forecastY is of size h-by-1, where h is the number of horizon steps (that is, the number of elements in Mdl.Horizon).

Limitations

• When you use the forecast object function, the past data must contain at least Mdl.MaxLag observations. The software requires these observations for creating lagged and leading predictors.

Tips

• When Mdl.LeadingPredictors is nonempty and max(Mdl.Horizon) is less than min(Mdl.LeadingPredictorLags) + 1, you do not have to specify leadingData. In this case, consider whether to specify the leading exogenous predictors as nonleading exogenous predictors when training the direct forecasting model.

Version History

Introduced in R2023b