The AR class provides basic time series analysis capabilities for Auto-Regressive (AR) models. In an AR(p) model, p refers to the order of the Auto-Regressive components of the model. AR models are often used for forecasting. Given time series data stored in vector y, its next value y_t+1 = y(t+1) may be predicted based on prior values of y and its noise: y_t+1 = δ + Σ(φ_j y_t-j) + e_t+1 where δ is a constant, φ is the auto-regressive coefficient vector, and e_t+1 is the noise term.
Value parameters
- hparam
-
the hyper-parameters
- tt
-
the time vector, if relevant (time index may suffice)
- y
-
the response vector (time series data)
Attributes
- Companion
- object
- Graph
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- Supertypes
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trait Correlogramtrait Forecastertrait Modelclass FitItrait Fittrait FitMclass Objecttrait Matchableclass AnyShow all
Members list
Value members
Concrete methods
Produce a vector of size h, of 1 through h-steps ahead forecasts for the model. forecast the following time points: t+1, ..., t-1+h. Note, must create the yf matrix before calling the forecast method. Intended to work with rolling validation (analog of predict method)
Produce a vector of size h, of 1 through h-steps ahead forecasts for the model. forecast the following time points: t+1, ..., t-1+h. Note, must create the yf matrix before calling the forecast method. Intended to work with rolling validation (analog of predict method)
Value parameters
- h
-
the forecasting horizon, number of steps ahead to produce forecasts
- t
-
the time point from which to make forecasts
- y_
-
the actual values to use in making predictions
- yf
-
the forecasting matrix (time x horizons)
Attributes
Forecast values for all y_.dim time points at horizon h (h-steps ahead). Assign to forecasting matrix and return h-step ahead forecast. For 1-step ahead (h = 1), y_t = δ + φ_0 y_t-1 + φ_1 y_t-2 + ... + φ_p-1 y_t-p When k < 0 let y_k = y_0 (i.e., assume first value repeats back in time).
Forecast values for all y_.dim time points at horizon h (h-steps ahead). Assign to forecasting matrix and return h-step ahead forecast. For 1-step ahead (h = 1), y_t = δ + φ_0 y_t-1 + φ_1 y_t-2 + ... + φ_p-1 y_t-p When k < 0 let y_k = y_0 (i.e., assume first value repeats back in time).
Value parameters
- h
-
the forecasting horizon, number of steps ahead to produce forecasts
- y_
-
the actual values to use in making forecasts
- yf
-
the forecasting matrix (time x horizons)
Attributes
Return the parameter vector for the AR(p) model.
Predict a value for y_t+1 using the 1-step ahead forecast. y_t+1 = δ + φ_0 y_t + φ_1 y_t-1 + ... + φ_p-1 y_t-(p-1) When t-j is negative, use y_0
Predict a value for y_t+1 using the 1-step ahead forecast. y_t+1 = δ + φ_0 y_t + φ_1 y_t-1 + ... + φ_p-1 y_t-(p-1) When t-j is negative, use y_0
Value parameters
- t
-
the time point from which to make prediction
- y_
-
the actual values to use in making predictions
Attributes
Allow users to set the parameter/coefficient vector the values they want, e.g., custom values or from another optimizer.
Allow users to set the parameter/coefficient vector the values they want, e.g., custom values or from another optimizer.
Value parameters
- phi
-
the custom values for the parameter vector
Attributes
Test PREDICTIONS of an AR 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.
Test PREDICTIONS of an AR 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.
Value parameters
- x_null
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the data/input matrix (ignored, pass null)
- y_
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the testing/full response/output vector
Attributes
Test FORECASTS of an AR forecasting model y_ = f(lags (y_)) + e and return its forecasts 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 and forecastAll before testF.
Test FORECASTS of an AR forecasting model y_ = f(lags (y_)) + e and return its forecasts 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 and forecastAll before testF.
Value parameters
- h
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the forecasting horizon, number of steps ahead to produce forecasts
- y_
-
the testing/full response/output vector
Attributes
Train/fit an AR model to the times-series data in vector y_. Estimate the coefficient vector φ for a p-th order Auto-Regressive AR(p) model. Uses Durbin-Levinson Algorithm (in Correlogram) to determine the coefficients. The φ vector is p-th row of psi matrix (ignoring the first (0th) column).
Train/fit an AR model to the times-series data in vector y_. Estimate the coefficient vector φ for a p-th order Auto-Regressive AR(p) model. Uses Durbin-Levinson Algorithm (in Correlogram) to determine the coefficients. The φ vector is p-th row of psi matrix (ignoring the first (0th) column).
Value parameters
- x_null
-
the data/input matrix (ignored, pass null)
- y_
-
the training/full response vector (e.g., full y)
Attributes
Inherited methods
Return the autocorrelation vector (ACF).
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
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.
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.
Value parameters
- w
-
the weights on the instances (defaults to null)
- y
-
the actual response/output vector to use (test/full)
- yp
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the predicted response/output vector (test/full)
Attributes
- See also
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Regression_WLS - Definition Classes
- Inherited from:
- Fit
Diagnose the health of the model by computing the Quality of Fit (QoFI) metrics/measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted. Note: wis should be computed separately.
Diagnose the health of the model by computing the Quality of Fit (QoFI) metrics/measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted. 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:
- FitI
Diagnose the health of the model by computing the Quality of FitI (QoFI) measures,
Diagnose the health of the model by computing the Quality of FitI (QoFI) measures,
Value parameters
- alphas
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the array of prediction levels
- low
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the lower bounds for various alpha levels
- up
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the upper bounds for various alpha levels
- y
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the given time-series (must be aligned with the interval forecast)
- yp
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the point prediction mean/median
Attributes
- Inherited from:
- FitI
Apply the Durbin-Levinson Algorithm to iteratively compute the psi matrix. The last/p-th row of the matrix gives AR coefficients. Note, also known as Levinson-Durbin.
Apply the Durbin-Levinson Algorithm to iteratively compute the psi matrix. The last/p-th row of the matrix gives AR coefficients. Note, also known as Levinson-Durbin.
Value parameters
- g
-
the auto-covariance vector (gamma)
- ml
-
the maximum number of lags
Attributes
- See also
- Inherited from:
- Correlogram
Return the Quality of FitI (QoFI) measures corresponding to the labels given. Override to add more quality of fit measures.
Forecast values for all y_.dim time points and all horizons (1 through h-steps ahead). Record these in the yf matrix, where yf(t, k) = k-steps ahead forecast for y_t Note, column 0, yf(?, 0), is set to y (the actual time-series values). Forecast recursively down diagonals in the yf forecasting matrix. The top right and bottom left triangles in yf matrix are not forecastable.
Forecast values for all y_.dim time points and all horizons (1 through h-steps ahead). Record these in the yf matrix, where yf(t, k) = k-steps ahead forecast for y_t Note, column 0, yf(?, 0), is set to y (the actual time-series values). Forecast recursively down diagonals in the yf forecasting matrix. The top right and bottom left triangles in yf matrix are not forecastable.
Value parameters
- h
-
the maximum 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_
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the aligned actual values to use in making forecasts
- yfh
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the forecast vector at horizon h
Attributes
- Inherited from:
- Forecaster
Perform forward selection to find the most predictive variable to add the existing model, returning the variable to add and the new model. May be called repeatedly. Note, all lags up and including 'p|q' define the model.
Perform forward selection to find the most predictive variable to add the existing model, returning the variable to add and the new model. May be called repeatedly. Note, all lags up and including 'p|q' define the model.
Value parameters
- cols
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the lags/columns currently included in the existing model (currently ignored)
- idx_q
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index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Forecaster
Perform forward selection to find the most predictive lags/variables to have in the model, returning the variables added and the new Quality of Fit (QoF) measures for all steps.
Perform forward selection to find the most predictive lags/variables to have in the model, returning the variables added and the new Quality of Fit (QoF) measures for all steps.
Value parameters
- cross
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whether to include the cross-validation QoF measure (currently ignored)
- idx_q
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index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - 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 response vector y. Mainly for derived classes where y is transformed, e.g., ARX.
Return the used response vector y. Mainly for derived classes where y is transformed, e.g., ARX.
Attributes
- Inherited from:
- Forecaster
Return the help string that describes the Quality of FitI (QoFI) measures provided by the FitI class. Override to correspond to fitLabel.
Return the hyper-parameters.
The log-likelihood function times -2. Override as needed.
The log-likelihood function times -2. Override as needed.
Value parameters
- ms
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raw Mean Squared Error
- s2
-
MLE estimate of the population variance of the residuals
Attributes
- See also
- Inherited from:
- Fit
Make a Correlogram, i.e., compute stats, psi and pacf.
Make a Correlogram, i.e., compute stats, psi and pacf.
Value parameters
- y_
-
the current (e.g., training) times-series to use (defaults to full y)
Attributes
- Inherited from:
- Correlogram
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 partial autocorrelation vector (PACF).
Plot a function, e.g., Auto-Correlation Function (ACF), Partial Auto-Correlation Function (PACF) with confidence bound.
Plot a function, e.g., Auto-Correlation Function (ACF), Partial Auto-Correlation Function (PACF) with confidence bound.
Value parameters
- fVec
-
the vector given function values
- name
-
the name of the function
- show
-
whether to show the fVec values
Attributes
- Inherited from:
- Correlogram
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 corresponding to the given vector y_.
Predict all values corresponding to the given vector y_.
Value parameters
- y_
-
the actual values to use in making predictions
Attributes
- Inherited from:
- Forecaster
Return the psi matrix.
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.
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:
- FitI
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
Return basic statistics on time-series y or y_.
Produce a QoF summary for a model with diagnostics for each predictor x_j and the overall Quality of Fit (QoF). Note: `Fac_Cholesky is used to compute the inverse of xtx.
Produce a QoF summary for a model with diagnostics for each predictor x_j and the overall Quality of Fit (QoF). Note: `Fac_Cholesky is used to compute the inverse of xtx.
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
- Inherited from:
- Fit
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
Inherited fields
The optional reference to an ontological concept