# CompactDirectForecaster

## Description

`CompactDirectForecaster`

is a compact version of a `DirectForecaster`

model object for direct forecasting. The compact model does not include the time series data
(`X`

and `Y`

) used for training the full model.
Therefore, you cannot perform some tasks, such as a cross-validation, using the compact
model.

## Creation

Create a `CompactDirectForecaster`

object from a full `DirectForecaster`

model object by using `compact`

.

## Properties

### Data Properties

`CategoricalPredictors`

— Indices of categorical exogenous predictors

positive integer vector | `[]`

This property is read-only.

Indices of categorical exogenous predictors, specified as a positive integer vector.
Each index value in `CategoricalPredictors`

indicates that the
corresponding exogenous predictor listed in `PredictorNames`

is
categorical. If none of the exogenous predictors are categorical, then this property is
empty (`[]`

).

**Data Types: **`double`

`PredictorNames`

— Names of exogenous predictors

cell array of character vectors

This property is read-only.

Names of the exogenous predictors, specified as a cell array of character vectors. The
order of the elements in `PredictorNames`

corresponds to the order of
the exogenous predictors in the data argument used to train the model.

**Data Types: **`cell`

`ResponseName`

— Name of response variable

character vector

This property is read-only.

Name of the response variable, specified as a character vector.

**Data Types: **`char`

### Forecasting Properties

`Horizon`

— Future time steps at which to forecast

positive integer vector

This property is read-only.

Future time steps at which to forecast, specified as a positive integer vector.
`Learners`

contains a trained regression model for each horizon
step. For example, if the `Horizon`

value of a direct forecasting
model `Mdl`

is `[1 3]`

, then
`Mdl.Learners`

contains two regression models: one that forecasts
at horizon step `1`

, and one that forecasts at horizon step
`3`

.

**Data Types: **`double`

`LeadingPredictorLags`

— Predictor lags used for preparing leading exogenous predictors

nonnegative integer vector | cell array of nonnegative integer vectors | `[]`

This property is read-only.

Leading predictor lags used for preparing leading exogenous predictors, specified as a nonnegative integer vector or cell array of nonnegative integer vectors.

If

`LeadingPredictorLags`

is a vector, then for each element`i`

in the vector, the software shifts the leading exogenous predictors backward in time by`i`

steps, relative to the horizon time step. The software uses the resulting features as predictors. When the`LeadingPredictorLags`

value is`0`

, the software uses the unshifted leading predictors.For example, if the

`Horizon`

value of a direct forecasting model is`3`

and the`LeadingPredictorLags`

value is`0`

, then the software uses the unshifted leading predictor values at horizon step`3`

as predictor values.If

`LeadingPredictorLags`

is a cell array, then the numeric values in element`i`

of the cell array indicate the lags for leading exogenous predictor`i`

.

If no leading predictor lags are used, then this property is empty (`[]`

).

**Data Types: **`double`

| `cell`

`LeadingPredictors`

— Indices of leading exogenous predictors

positive integer vector | `[]`

This property is read-only.

Indices of the leading exogenous predictors, specified as a positive integer vector. Leading predictors are predictors for which future values are known. Each index value in `LeadingPredictors`

indicates that the corresponding exogenous predictor listed in `PredictorNames`

is leading. If no exogenous predictors are leading predictors, then this property is empty (`[]`

).

**Data Types: **`double`

`Learners`

— Compact regression models trained at different horizon steps

cell array of regression model objects

This property is read-only.

Compact regression models trained at different horizon steps, specified as a cell array of regression model objects. That is, for a direct forecasting model `Mdl`

, the software trains the regression model `Mdl.Learners{1}`

at horizon step `Mdl.Horizon(1)`

.

This table lists the possible compact regression models.

Regression Model Type | Model Object |
---|---|

Bagged or boosted ensemble of trees | `CompactRegressionEnsemble` |

General additive model (GAM) | `CompactRegressionGAM` |

Gaussian process regression (GPR) | `CompactRegressionGP` |

Kernel model | `RegressionKernel` |

Linear model | `RegressionLinear` |

Support vector machine (SVM) | `CompactRegressionSVM` |

Decision tree | `CompactRegressionTree` |

**Data Types: **`cell`

`MaxLag`

— Maximum lag value

nonnegative integer scalar

This property is read-only.

Maximum lag value, specified as a nonnegative integer scalar. The `MaxLag`

value depends on the values in `ResponseLags`

,
`PredictorLags`

, and `LeadingPredictorLags`

.
Specifically, the software computes the maximum lag as
follows:

```
MaxLag = max([0,ResponseLags,PredictorLags, ...
LeadingPredictorLags - min(Horizon) + 1])
```

**Data Types: **`double`

`PredictorLags`

— Predictor lags used for preparing nonleading exogenous predictors

positive integer vector | cell array of positive integer vectors | `[]`

This property is read-only.

Predictor lags used for preparing nonleading exogenous predictors, specified as a positive integer vector or cell array of positive integer vectors.

If

`PredictorLags`

is a vector, then for each element`i`

in the vector, the software shifts the nonleading exogenous predictors backward in time by`i`

steps and uses the resulting features as predictors.If

`PredictorLags`

is a cell array, then the numeric values in element`i`

of the cell array indicate the lags for nonleading exogenous predictor`i`

.

If no predictor lags are used, then this property is empty (`[]`

).

**Data Types: **`double`

| `cell`

`ResponseLags`

— Response lags used for preparing predictors

positive integer vector | `[]`

This property is read-only.

Response lags used for preparing predictors, specified as a positive integer vector.
Each element in `ResponseLags`

indicates the number of time steps by
which to shift the response backward in time. The resulting feature is used as a
predictor. If no response lags are used, then this property is empty
(`[]`

).

**Data Types: **`double`

### Prepared Data Properties

`PreparedCategoricalPredictors`

— Indices of prepared categorical predictors

positive integer vector | `[]`

This property is read-only.

Indices of the prepared categorical predictors, specified as a positive integer vector. Each index value in `PreparedCategoricalPredictors`

indicates that the corresponding predictor listed in `PreparedPredictorNames`

is categorical. If no prepared predictors are categorical predictors, then this property is empty (`[]`

).

**Data Types: **`double`

`PreparedPredictorNames`

— Names of prepared predictors

cell array of character vectors

This property is read-only.

Names of the prepared predictors, specified as a cell array of character vectors. These
prepared predictors include variables created from both the exogenous predictor
variables and the response variable used to train the direct forecasting model. Not
every predictor is used at every horizon step. To see which predictors are used at a
specific horizon step, consult the `PreparedPredictorsPerHorizon`

table.

**Data Types: **`cell`

`PreparedPredictorsPerHorizon`

— Prepared predictors at each horizon step

table of logical values

This property is read-only.

Prepared predictors at each horizon step, specified as a table of logical values. Each row of the table corresponds to a horizon step, and each column of the table corresponds to a prepared predictor as listed in `PreparedPredictorNames`

.

For a direct forecasting model `Mdl`

, the logical value in row `i`

and column `j`

indicates whether the software uses prepared predictor `Mdl.PreparedPredictorNames(j)`

at horizon step `Mdl.Horizon(i)`

. If the value is `1`

(`true`

), then the software uses the predictor. If the value is `0`

(`false`

), then the software does not use the predictor.

**Data Types: **`table`

`PreparedResponseNames`

— Names of prepared responses at each horizon step

cell array of character vectors

This property is read-only.

Names of the prepared responses at each horizon step, specified as a cell array of character
vectors. That is, element `i`

of
`PreparedResponseNames`

is the name of the response variable at
the horizon step specified by element `i`

of
`Horizon`

.

For example, given a direct forecasting model `Mdl`

, the name of the response
variable at horizon step `Mdl.Horizon(1)`

,
`Mdl.PreparedResponseNames{1}`

, matches the response variable name
used in the first regression model in `Learners`

(`Mdl.Learners{1}.ResponseName`

).

**Data Types: **`cell`

## Object Functions

`loss` | Loss at each horizon step |

`predict` | Predict response at time steps in observed test data |

`forecast` | Forecast response at time steps beyond available data |

`preparedPredictors` | Obtain prepared data used for training or testing in direct forecasting |

## Examples

### Reduce Size of Direct Forecasting Model

Reduce the size of a full direct forecasting model by removing the training data from the model. You can use a compact model to improve memory efficiency.

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")

Create a full direct forecasting model by using the data in `Tbl`

. 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(Tbl,"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: [465]

`Mdl`

is a `DirectForecaster`

object. By default, the horizon is one step ahead. That is, `Mdl`

predicts a value that is one step into the future.

Reduce the size of the model by using the `compact`

object function.

compactMdl = compact(Mdl)

compactMdl = CompactDirectForecaster 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]

`compactMdl`

is a `CompactDirectForecaster`

model object. `compactMdl`

contains fewer properties than the full model `Mdl`

.

Display the amount of memory used by each direct forecasting model.

whos("Mdl","compactMdl")

Name Size Bytes Class Attributes Mdl 1x1 110401 timeseries.forecaster.DirectForecaster compactMdl 1x1 42541 timeseries.forecaster.CompactDirectForecaster

The full model is larger than the compact model.

## More About

### Direct Forecasting

Direct forecasting is a forecasting technique that uses separate models to predict the response values at different future time steps (horizon steps). This technique differs from recursive forecasting, where one model is used to predict values at multiple horizon steps.

The software prepares the predictor data for each model and then uses the model to forecast at a particular horizon step.

For more information, see `PreparedPredictorsPerHorizon`

and `Horizon`

.

### Forecasting Data

The `directforecaster`

function accepts data sets with regularly sampled values
that include a response variable and exogenous predictors (optional). That is, the time
steps between consecutive observations are the same. In this context, exogenous predictors
are predictors that are not derived from the response variable.

Consider the following data set.

In this example, the row times in `MeasurementTime`

show that the time difference between consecutive observations is one hour. The times `18-Dec-2015 14:00:00`

and `18-Dec-2015 15:00:00`

are future time steps that exist beyond the available data. They represent the first and second horizon steps. (See `Horizon`

.)

Suppose the `Temp`

variable is the response variable. The
`Pressure`

, `WindSpeed`

, and
`WorkHours`

variables are exogenous predictors. The
`WorkHours`

variable is a leading exogenous predictor because its
future values are known. (See `LeadingPredictors`

.)

Before fitting a forecasting model, the software creates time-shifted features from the response and exogenous predictors based on user-specified lag values. In this example, the red rectangles indicate a `ResponseLags`

value of `1`

, `PredictorLags`

value of `[1 2 3]`

, and `LeadingPredictorLags`

value of `[0 1]`

at horizon step `1`

(`18-Dec-2015 14:00:00`

).

## Version History

**Introduced in R2023b**

## See Also

`DirectForecaster`

| `compact`

| `loss`

| `predict`

| `forecast`

| `preparedPredictors`

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