The ARX_Quad_D class provides basic time series analysis capabilities for ARX_Quad_D models. ARX_Quad_D models are often used for forecasting. ARX_Quad_D uses DIRECT (as opposed to RECURSIVE) multi-horizon forecasting. Given time series data stored in vector y, its next value y_t = combination of last p values.
y_t = b dot x_t + e_t
where y_t is the value of y at time t and e_t is the residual/error term.
Value parameters
- bakcast
-
whether a backcasted value is prepended to the time series (defaults to false)
- fname
-
the feature/variable names
- hh
-
the maximum forecasting horizon (h = 1 to hh)
- hparam
-
the hyper-parameters (defaults to
MakeMatrix4TS.hp) - n_exo
-
the number of exogenous variables
- tForms
-
the map of transformations applied
- tRng
-
the time range, if relevant (time index may suffice)
- x
-
the data/input matrix (lagged columns of y) @see
ARX_Quad_D.apply - y
-
the response/output matrix (column per horizon) (time series data)
Attributes
- Companion
- object
- Graph
-
- Supertypes
-
class ARX_Dclass Forecaster_Dclass Forecastertrait Modeltrait ForecastMatrixclass Diagnosertrait Fittrait FitMclass Objecttrait Matchableclass AnyShow all
Members list
Value members
Inherited methods
Align the actual response vector for comparison with the predicted/forecasted response vector, returning a time vector and sliced response vector.
Align the actual response vector for comparison with the predicted/forecasted response vector, returning a time vector and sliced response vector.
Value parameters
- tr_size
-
the size of the intial training set
- y
-
the actual response for the full dataset (to be sliced)
Attributes
- Inherited from:
- Forecaster
Return the maximum lag used by the model (its capacity to look into the past). Models that use more than one past value to make predictions/forecasts must override this method, e.g., ARMA (2, 3) should set the cap to max(p, q) = 3.
Return the maximum lag used by the model (its capacity to look into the past). Models that use more than one past value to make predictions/forecasts must override this method, e.g., ARMA (2, 3) should set the cap to max(p, q) = 3.
Attributes
- Inherited from:
- Forecaster
Attributes
- Inherited from:
- Forecaster
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted. For time series, the first few predictions use only part of the model, so may be skipped.
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted. For time series, the first few predictions use only part of the model, so may be skipped.
Value parameters
- w
-
the weights on the instances (defaults to null)
- y
-
the actual response/output vector to use (test/full)
- yp
-
the predicted response/output vector (test/full)
Attributes
- Definition Classes
- Inherited from:
- Diagnoser
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, for all horizons and print the results in a table. For time series, the first few predictions use only part of the model, so may be skipped. The version is for models that perform DIRECT multi-horizon forecasting.
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, for all horizons and print the results in a table. For time series, the first few predictions use only part of the model, so may be skipped. The version is for models that perform DIRECT multi-horizon forecasting.
Value parameters
- yf
-
the entire FORECAST MATRIX
- yy
-
the actual response/output matrix over all horizons
Attributes
- Inherited from:
- ForecastMatrix
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, for all horizons and print the results in a table. For time series, the first few predictions use only part of the model, so may be skipped. The version is for models that perform RECURSIVE multi-horizon forecasting.
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, for all horizons and print the results in a table. For time series, the first few predictions use only part of the model, so may be skipped. The version is for models that perform RECURSIVE multi-horizon forecasting.
Value parameters
- rRng
-
the time range, defaults to null (=> full time range)
- sft
-
the amount of shift for yfh (FIX - ideally unify the code and remove sft)
- showYf
-
the amount of shift for yfh (FIX - ideally unify the code and remove sft)
- y_
-
the actual response/output vector
- yf
-
the entire FORECAST MATRIX
Attributes
- Inherited from:
- ForecastMatrix
Diagnose the health of the model by computing the Quality of Fit (QoF) metrics/measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted. Include interval measures. Note: wis should be computed separately.
Diagnose the health of the model by computing the Quality of Fit (QoF) metrics/measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted. Include interval measures. Note: wis should be computed separately.
Value parameters
- alpha
-
the nominal level of uncertainty (alpha) (defaults to 0.9, 90%)
- low
-
the predicted lower bound
- up
-
the predicted upper bound
- w
-
the weights on the instances (defaults to null)
- y
-
the actual response/output vector to use (test/full)
- yp
-
the point prediction mean/median
Attributes
- See also
-
Regression_WLS - Inherited from:
- Fit
Diagnose the health of the model by computing the Quality of Fit (QoF) measures,
Diagnose the health of the model by computing the Quality of Fit (QoF) measures,
Value parameters
- alphas
-
the array of prediction levels
- low
-
the lower bounds for various alpha levels
- up
-
the upper bounds for various alpha levels
- y
-
the given time-series (must be aligned with the interval forecast)
- yp
-
the point prediction mean/median
Attributes
- Inherited from:
- Fit
Return the Quality of Fit (QoF) measures corresponding to the labels given. Note, if sse > sst, the model introduces errors and the rSq may be negative, otherwise, R^2 (rSq) ranges from 0 (weak) to 1 (strong). Override to add more quality of fit measures.
Return the Quality of Fit (QoF) measures corresponding to the labels given. Note, if sse > sst, the model introduces errors and the rSq may be negative, otherwise, R^2 (rSq) ranges from 0 (weak) to 1 (strong). Override to add more quality of fit measures.
Attributes
- Definition Classes
- Inherited from:
- Fit
Produce a vector of size hh, h = 1 to hh-steps ahead forecasts for the model, i.e., forecast the following time points: t+1, ..., t+h. Intended to work with rolling validation (analog of predict method).
Produce a vector of size hh, h = 1 to hh-steps ahead forecasts for the model, i.e., forecast the following time points: t+1, ..., t+h. Intended to work with rolling validation (analog of predict method).
Value parameters
- t
-
the time point from which to make forecasts
- y_
-
the actual values to use in making predictions
Attributes
- Definition Classes
-
ARX_D -> Forecaster
- Inherited from:
- ARX_D
Forecast values for all y_.dim time points all horizons h (h-steps ahead). Assign into FORECAST MATRIX and return the forecast matrix.
Forecast values for all y_.dim time points all horizons h (h-steps ahead). Assign into FORECAST MATRIX and return the forecast matrix.
Value parameters
- y_
-
the matrix of actual response values
Attributes
- Definition Classes
- Inherited from:
- ARX_D
Forecast values for all y_.dim time points and all horizons (1 through hh-steps ahead). Record these in the FORECAST MATRIX yf, where
Forecast values for all y_.dim time points and all horizons (1 through hh-steps ahead). Record these in the FORECAST MATRIX yf, where
yf(t, h) = h-steps ahead forecast for y_t
Value parameters
- y_
-
the actual values to use in making forecasts
Attributes
- Inherited from:
- Forecaster
Forecast values for all y_.dim time points at horizon h (h-steps ahead). Assign into FORECAST MATRIX and return the h-steps ahead forecast. Note, predictAll provides predictions for h = 1 and for random walk the forecast across all horizons is the same.
Forecast values for all y_.dim time points at horizon h (h-steps ahead). Assign into FORECAST MATRIX and return the h-steps ahead forecast. Note, predictAll provides predictions for h = 1 and for random walk the forecast across all horizons is the same.
Value parameters
- h
-
the forecasting horizon, number of steps ahead to produce forecasts
- y_
-
the actual values to use in making forecasts
Attributes
- Inherited from:
- Forecaster
Forecast intervals for all y_.dim time points at horizon h (h-steps ahead). Create prediction intervals (two vectors) for the given time points at level p. Caveat: assumes errors follow a Normal distribution. Override this method to handle other cases.
Forecast intervals for all y_.dim time points at horizon h (h-steps ahead). Create prediction intervals (two vectors) for the given time points at level p. Caveat: assumes errors follow a Normal distribution. Override this method to handle other cases.
Value parameters
- h
-
the forecasting horizon, number of steps ahead to produce forecasts
- p
-
the level (1 - alpha) for the prediction interval
- y_
-
the aligned actual values to use in making forecasts
- yfh
-
the forecast vector at horizon h
Attributes
- Inherited from:
- Forecaster
Return the feature/variable names. Override for models like SARIMAX.
Return the feature/variable names. Override for models like SARIMAX.
Attributes
- Inherited from:
- Forecaster
Return the used data/input matrix. Model that use x should override.
Return the used data/input matrix. Model that use x should override.
Attributes
- Inherited from:
- Forecaster
Return the used response/output vector y.
Return the the y-transformation.
Return the used response matrix y, if needed.
Return the used response matrix y, if needed.
Attributes
- See also
-
neuralnet.PredictorMV - Inherited from:
- Model
Return the used response/output vector yb (y prepended by one backcast value).
Return the used response/output vector yb (y prepended by one backcast value).
Attributes
- Inherited from:
- Forecaster
Return the used FORECAST MATRIX yf.
Return the used response/output matrix y.
Return the help string that describes the Quality of Fit (QoF) measures provided by the Fit trait. Override to correspond to fitLabel.
Return the hyper-parameters.
Perform In-Sample Testing (In-ST), i.e. train and test on the full data set.
Perform In-Sample Testing (In-ST), i.e. train and test on the full data set.
Value parameters
- showYf
-
whether to show the forecast matrix
- skip
-
the number of initial time points to skip (due to insufficient past)
Attributes
- Inherited from:
- Forecaster
The log-likelihood function times -2. Override as needed.
The log-likelihood function times -2. Override as needed.
Value parameters
- ms
-
raw Mean Squared Error
- s2
-
MLE estimate of the population variance of the residuals
Attributes
- See also
- Inherited from:
- Fit
Make the full FORECAST MATRIX where the zeroth column holds the actual time series and the last column is its time/time index. Columns 1, 2, ... hh are for h steps ahead forecasts.
Make the full FORECAST MATRIX where the zeroth column holds the actual time series and the last column is its time/time index. Columns 1, 2, ... hh are for h steps ahead forecasts.
Value parameters
- hh
-
the maximum forecasting horizon, number of steps ahead to produce forecasts
- y_
-
the actual time series vector to use in making forecasts
Attributes
- Inherited from:
- ForecastMatrix
Models need to provide a means for updating the Degrees of Freedom (DF).
Models need to provide a means for updating the Degrees of Freedom (DF).
Value parameters
- size
-
the size of dataset (full, train, or test)
Attributes
- Definition Classes
- Inherited from:
- Forecaster_D
Return the mean of the squares for error (sse / df). Must call diagnose first.
Return the mean of the squares for error (sse / df). Must call diagnose first.
Attributes
- Inherited from:
- Fit
Attributes
- Inherited from:
- Forecaster
Return the vector of parameter/coefficient values (they are model specific). Override for models with other parameters besides bb(?, 0).
Return the vector of parameter/coefficient values (they are model specific). Override for models with other parameters besides bb(?, 0).
Attributes
- Definition Classes
- Inherited from:
- Forecaster_D
Predict a value for y_t using the 1-step ahead forecast.
Predict a value for y_t using the 1-step ahead forecast.
y_t = b_0 + b_1 y_t-1 + b_2 y_t-2 + ... + b_p y_t-p = b dot x_t
Value parameters
- t
-
the time point being predicted
- y_
-
the actual values to use in making predictions (ignored)
Attributes
- Inherited from:
- ARX_D
Predict a value for y_t using the 1-step ahead forecast.
Predict a value for y_t using the 1-step ahead forecast.
y_t = f (y_t-1, ...) = y_t-1 (random walk -- use previous value)
Override for other models.
Value parameters
- t
-
the time point being predicted
- y_
-
the actual values to use in making predictions
Attributes
- Inherited from:
- Forecaster
The standard signature for prediction does not apply to time series.
The standard signature for prediction does not apply to time series.
Attributes
- Inherited from:
- Forecaster
Predict all values (for all horizons) corresponding to the given time series vector y_. Create FORECAST MATRIX yf and return it. Note forecastAll simply returns the values produced by predictAll.
Predict all values (for all horizons) corresponding to the given time series vector y_. Create FORECAST MATRIX yf and return it. Note forecastAll simply returns the values produced by predictAll.
Value parameters
- y_
-
the actual time series values to use in making predictions
Attributes
- Inherited from:
- Forecaster_D
Predict all values corresponding to the given time series vector y_. Update FORECAST MATRIX yf and return PREDICTION VECTOR yp as second (1) column of yf with last value removed.
Predict all values corresponding to the given time series vector y_. Update FORECAST MATRIX yf and return PREDICTION VECTOR yp as second (1) column of yf with last value removed.
Value parameters
- y_
-
the actual time series values to use in making predictions
Attributes
- See also
-
forecastAllto forecast beyond horizon h = 1. - Inherited from:
- Forecaster
Return the coefficient of determination (R^2). Must call diagnose first.
Return the coefficient of determination (R^2). Must call diagnose first.
Attributes
- Inherited from:
- FitM
Return a basic report on a trained and tested multi-variate model.
Return a basic report on a trained and tested multi-variate model.
Value parameters
- ftMat
-
the matrix of qof values produced by the
Fittrait
Attributes
- Inherited from:
- Model
Return a basic report on a trained and tested model.
Return a basic report on a trained and tested model.
Value parameters
- ftVec
-
the vector of qof values produced by the
Fittrait
Attributes
- Inherited from:
- Model
Reset the degrees of freedom to the new updated values. For some models, the degrees of freedom is not known until after the model is built.
Reset the degrees of freedom to the new updated values. For some models, the degrees of freedom is not known until after the model is built.
Value parameters
- df_update
-
the updated degrees of freedom (model, error)
Attributes
- Inherited from:
- Fit
Return the vector of residuals/errors.
Use rolling-validation to compute test Quality of Fit (QoF) measures by dividing the dataset into a TRAINING SET (tr) and a TESTING SET (te). as follows: [ <-- tr_size --> | <-- te_size --> ] Calls forecast for h-steps ahead out-of-sample forecasts. Return the forecasted values in the FORECAST MATRIX,.
Use rolling-validation to compute test Quality of Fit (QoF) measures by dividing the dataset into a TRAINING SET (tr) and a TESTING SET (te). as follows: [ <-- tr_size --> | <-- te_size --> ] Calls forecast for h-steps ahead out-of-sample forecasts. Return the forecasted values in the FORECAST MATRIX,.
Value parameters
- growing
-
whether the training grows as it roll or kepps a fixed size
- rc_
-
the retraining cycle (number of forecasts until retraining occurs)
Attributes
- Definition Classes
- Inherited from:
- Forecaster_D
Set the number of data points/elements to skip at the beginning of a time series for purposes of diagnosis or computing a loss function. For In-Sample, the first value (time t = 0) is not forecastable without backcasting.
Set the number of data points/elements to skip at the beginning of a time series for purposes of diagnosis or computing a loss function. For In-Sample, the first value (time t = 0) is not forecastable without backcasting.
Value parameters
- skip
-
skip this many elements at the beginning of the time series
Attributes
- Inherited from:
- Diagnoser
Show the prediction interval forecasts and relevant QoF metrics/measures.
Show the prediction interval forecasts and relevant QoF metrics/measures.
Value parameters
- h
-
the forecasting horizon
- low
-
the predicted lower bound
- qof_all
-
all the QoF metrics (for point and interval forecasts)
- up
-
the predicted upper bound
- yfh
-
the forecasts for horizon h
- yy
-
the aligned actual response/output vector to use (test/full)
Attributes
- Inherited from:
- Fit
Return the slanted/diagonalized-down version of the forecast matrix where each row is at a fixed time point and, for example, the random walk model simply pushes the values down diagonals. Note unshiftDiag reverses the process. Also reset the last column that holds the time index to 0, 1, 2, 3, ...
Return the slanted/diagonalized-down version of the forecast matrix where each row is at a fixed time point and, for example, the random walk model simply pushes the values down diagonals. Note unshiftDiag reverses the process. Also reset the last column that holds the time index to 0, 1, 2, 3, ...
Value parameters
- yf
-
the current forecast matrix
Attributes
- Inherited from:
- ForecastMatrix
Return the symmetric Mean Absolute Percentage Error (sMAPE) score. Caveat: y_i = yp_i = 0 => no error => no percentage error
Return the symmetric Mean Absolute Percentage Error (sMAPE) score. Caveat: y_i = yp_i = 0 => no error => no percentage error
Value parameters
- e_
-
the error/residual vector (if null, recompute)
- y
-
the given time-series (must be aligned with the forecast)
- yp
-
the forecasted time-series
Attributes
- Inherited from:
- FitM
Return the sum of the squares for error (sse). Must call diagnose first.
Return the sum of the squares for error (sse). Must call diagnose first.
Attributes
- Inherited from:
- FitM
Compute the sum of squares errors (loss function), assuming the first 'skip' errors are zero.
Compute the sum of squares errors (loss function), assuming the first 'skip' errors are zero.
Value parameters
- y
-
the actual response vector
- yp
-
the predicted response vector (one-step ahead)
Attributes
- Inherited from:
- Diagnoser
Produce a QoF summary for a model with diagnostics for each predictor 'x_j' and the overall Quality of Fit (QoF).
Produce a QoF summary for a model with diagnostics for each predictor 'x_j' and the overall Quality of Fit (QoF).
Value parameters
- b_
-
the parameters/coefficients for the model
- fname_
-
the array of feature/variable names
- vifs
-
the Variance Inflation Factors (VIFs)
- x_
-
the testing/full data/input matrix
Attributes
- Definition Classes
- Inherited from:
- ARX_D
Test PREDICTIONS of a forecasting model y_ = f(lags (y_)) + e and return its predictions and QoF vector. Testing may be in-sample (on the training set) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train before test. Must override to get Quality of Fit (QoF).
Test PREDICTIONS of a forecasting model y_ = f(lags (y_)) + e and return its predictions and QoF vector. Testing may be in-sample (on the training set) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train before test. Must override to get Quality of Fit (QoF).
Value parameters
- x_null
-
the data/input matrix
- y_
-
the actual testing/full response/output matrix
Attributes
- Inherited from:
- Forecaster_D
Test PREDICTIONS of a forecasting model y_ = f(lags (y_)) + e and return its predictions and QoF vector. Testing may be in-sample (on the training set) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train before test. Must override to get Quality of Fit (QoF).
Test PREDICTIONS of a forecasting model y_ = f(lags (y_)) + e and return its predictions and QoF vector. Testing may be in-sample (on the training set) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train before test. Must override to get Quality of Fit (QoF).
Value parameters
- x_null
-
the data/input matrix (ignored, pass null)
- y_
-
the actual testing/full response/output vector
Attributes
- Inherited from:
- Forecaster
Test FORECASTS of a forecasting model y_ = f(lags (y_)) + e and RETURN (1) aligned actual values, (2) its forecasts and (3) QoF vector. Testing may be in-sample (on the training set) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train and forecastAll before testF.
Test FORECASTS of a forecasting model y_ = f(lags (y_)) + e and RETURN (1) aligned actual values, (2) its forecasts and (3) QoF vector. Testing may be in-sample (on the training set) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train and forecastAll before testF.
Value parameters
- h
-
the forecasting horizon, number of steps ahead to produce forecasts
- y_
-
the testing/full response/output vector
Attributes
- Inherited from:
- Forecaster
Given a time series y_, train the forecasting function y_ = f(lags (y_)) + e, where f(lags (y_)) is a function of the lagged values of y_, by fitting its parameters.
Given a time series y_, train the forecasting function y_ = f(lags (y_)) + e, where f(lags (y_)) is a function of the lagged values of y_, by fitting its parameters.
Value parameters
- x_null
-
the data/input matrix (ignored, pass null)
- y_
-
the testing/full response/output vector (e.g., full y)
Attributes
- Inherited from:
- Forecaster
Train and test the forecasting model y_ = f(y-past) + e and report its QoF and plot its predictions. Return the predictions and QoF.
Train and test the forecasting model y_ = f(y-past) + e and report its QoF and plot its predictions. Return the predictions and QoF.
Value parameters
- y_
-
the training/full response/output vector (defaults to full y)
- yy
-
the testing/full response/output vector (defaults to full y)
Attributes
- Inherited from:
- Forecaster
Train and test the forecasting model y_ = f(y-past) + e and report its QoF and plot its predictions. Return the predictions and QoF. NOTE: must use trainNtest_x when an x matrix is used, such as in ARY_D.
Train and test the forecasting model y_ = f(y-past) + e and report its QoF and plot its predictions. Return the predictions and QoF. NOTE: must use trainNtest_x when an x matrix is used, such as in ARY_D.
Value parameters
- x_
-
the training/full data/input matrix (defaults to full x)
- xx
-
the testing/full data/input matrix (defaults to full x)
- y_
-
the training/full response/output vector (defaults to full y)
- yy
-
the testing/full response/output vector (defaults to full y)
Attributes
- Inherited from:
- Forecaster_D
Train/fit an ARX_D model to the times-series data in vector y_. Estimate the coefficient mattrix bb for a p-th order Auto-Regressive ARX_D(p) model. Uses OLS Matrix Fatorization to determine the coefficients, i.e., the bb matrix.
Train/fit an ARX_D model to the times-series data in vector y_. Estimate the coefficient mattrix bb for a p-th order Auto-Regressive ARX_D(p) model. Uses OLS Matrix Fatorization to determine the coefficients, i.e., the bb matrix.
Value parameters
- x_
-
the data/input matrix (e.g., full x)
- y_
-
the training/full response vector (e.g., full y)
Attributes
- Inherited from:
- ARX_D
Inherited fields
The optional reference to an ontological concept
The name for the model (or modeling technique).