class AR extends ForecasterVec
The AR class provides basic time series analysis capabilities for Auto-
Regressive 'AR'. 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 = y(t)'
may be predicted based on prior values of 'y' and its noise:
y_t = δ + Σ(φ_k y_t-k)
where 'δ' is a constant, 'φ' is the autoregressive coefficient vector, and 'e' is the noise vector. ----------------------------------------------------------------------------------
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- AR
- ForecasterVec
- Predictor
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- Fit
- Error
- QoF
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Instance Constructors
- new AR(y: VectoD, hparam: HyperParameter = ARMA.hp)
- y
the response vector (time-series data)
- hparam
the hyper-parameters
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def acF: VectoD
Return the autocorrelation.
Return the autocorrelation. Must call 'train' first.
- Definition Classes
- ForecasterVec
- def analyze(x_: MatriD = null, y_: VectoD = y, x_e: MatriD = null, y_e: VectoD = y): ForecasterVec
Analyze a dataset using this model using ordinary training with the 'train' method.
Analyze a dataset using this model using ordinary training with the 'train' method.
- x_
the training/full the data/input matrix (ignore)
- y_
the training/full the response/output vector
- x_e
the test/full data/input matrix (ignore)
- y_e
the test/full response/output vector
- Definition Classes
- ForecasterVec → Predictor
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- def corrMatrix(xx: MatriD): MatriD
Return the correlation matrix for the columns in data matrix 'xx'.
Return the correlation matrix for the columns in data matrix 'xx'.
- xx
the data matrix shose correlation matrix is sought
- Definition Classes
- Predictor
- def diagnose(e: VectoD, yy: VectoD, yp: VectoD, w: VectoD = null, ym_: Double = noDouble): Unit
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses.
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.
- e
the m-dimensional error/residual vector (yy - yp)
- yy
the actual response/output vector to use (test/full)
- yp
the predicted response/output vector (test/full)
- w
the weights on the instances (defaults to null)
- ym_
the mean of the actual response/output vector to use (training/full)
- var e: VectoD
- Attributes
- protected
- Definition Classes
- ForecasterVec
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- def eval(y_e: VectoD = y): ForecasterVec
Compute the error (difference between actual and predicted) and useful diagnostics for the dataset.
Compute the error (difference between actual and predicted) and useful diagnostics for the dataset.
- y_e
the test/full actual response/output vector
- Definition Classes
- ForecasterVec
- def eval(x_e: MatriD, y_e: VectoD): ForecasterVec
Compute the error (difference between actual and predicted) and useful diagnostics for the dataset.
Compute the error (difference between actual and predicted) and useful diagnostics for the dataset.
- x_e
the test/full data/input matrix (ignored, pass null)
- y_e
the test/full actual response/output vector
- Definition Classes
- ForecasterVec → Model
- def evalf(y_e: VectoD, yf: VectoD): ForecasterVec
Compute the error (difference between actual and predicted) and useful diagnostics for the dataset.
Compute the error (difference between actual and predicted) and useful diagnostics for the dataset.
- y_e
the test/full actual response/output vector
- yf
the vector of forecasts
- Definition Classes
- ForecasterVec
- def f_(z: Double): String
Format a double value.
- def fit: VectoD
Return the Quality of Fit (QoF) measures corresponding to the labels given above in the 'fitLabel' method.
Return the Quality of Fit (QoF) measures corresponding to the labels given above in the 'fitLabel' method. 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.
- def fitLabel: Seq[String]
Return the labels for the Quality of Fit (QoF) measures.
- def fitMap: Map[String, String]
Build a map of quality of fit measures (use of
LinkedHashMapmakes it ordered).Build a map of quality of fit measures (use of
LinkedHashMapmakes it ordered).- Definition Classes
- QoF
- final def flaw(method: String, message: String): Unit
- Definition Classes
- Error
- def forecast(t: Int, h: Int = 1): VectoD
Produce a vector of size 'h', of 1 through 'h'-steps ahead forecasts for the model.
Produce a vector of size 'h', of 1 through 'h'-steps ahead forecasts for the model.
forecast the following time points: t, t+1, ..., t-1+h.
Note, invoke 'forecastAll' first to create the 'yf' matrix.
- t
the time point from which to make forecasts
- h
the forecasting horizon, number of steps ahead to produce forecasts
- Definition Classes
- ForecasterVec
- def forecast(yf: MatriD, t: Int, h: Int): VectoD
Produce a vector of size 'h', of 1 through 'h'-steps ahead forecasts for the model.
Produce a vector of size 'h', of 1 through 'h'-steps ahead forecasts for the model.
forecast the following time points: t, t+1, ..., t-1+h.
Note, invoke 'forecastAll' to create the 'yf' matrix.
- yf
the y-forecast matrix for all time and horizons
- t
the time point from which to make forecasts
- h
the forecasting horizon, number of steps ahead to produce forecasts
- Definition Classes
- ForecasterVec
- def forecastAll(h: Int): MatriD
Forecast values for all 'm' time points and all horizons (1 through 'h'-steps ahead).
Forecast values for all 'm' 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, 'yf.col(0)' is set to 'y' (the actual time-series values).
- h
the maximum forecasting horizon, number of steps ahead to produce forecasts
- Definition Classes
- AR → ForecasterVec
- def forecastAll(h: Int, p: Int): MatriD
Forecast values for all time points using 1 through 'h'-steps ahead forecasts.
Forecast values for all time points using 1 through 'h'-steps ahead forecasts. The 'h'-th row of matrix is the horizon 'h' forecast (where 'h = 0' is actual data).
- h
the forecasting horizon, number of steps ahead to produce forecasts, must be > 0
- p
the order of the model (e.g, p in AR, q in MA) or number of values to use in making forecasts, must be > 0
- Definition Classes
- ForecasterVec
- def forecastX(y: VectoD = y, t: Int = y.dim, h: Int = 1): Double
Produce h-steps ahead forecast on the testing data during cross validation.
Produce h-steps ahead forecast on the testing data during cross validation.
- y
the current response vector
- t
the time point to be forecast
- h
the forecasting horizon, number of steps ahead to produce forecast
- Definition Classes
- AR → ForecasterVec
- def forwardSel(cols: Set[Int] = null, index_q: Int = index_rSq): (Int, AR)
Perform forward selection to find the most predictive variables to add the existing model, returning the variables to add and the new model.
Perform forward selection to find the most predictive variables to add the existing model, returning the variables to add and the new model. Note, all lags up and including 'p' define the model. FIX - select subsets of the lags, e.g., Set (1, 2, 5)
- cols
the lags/columns currently included in the existing model (ignored)
- index_q
index of Quality of Fit (QoF) to use for comparing quality
- Definition Classes
- AR → ForecasterVec → Predictor
- See also
Fitfor index of QoF measures.
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def getX: MatriD
Return the 'used' data matrix 'x' (for such models, it's null).
Return the 'used' data matrix 'x' (for such models, it's null).
- Definition Classes
- ForecasterVec → Predictor
- def getY: VectoD
Return the 'used' response vector 'y'.
Return the 'used' response vector 'y'. Mainly for derived classes where 'y' is transformed, e.g.,
TranRegression,Regression4TS.- Definition Classes
- ForecasterVec → Predictor
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def help: String
Return the help string that describes the Quality of Fit (QoF) measures provided by the
Fitclass. - def hparameter: HyperParameter
Return the hyper-parameters.
Return the hyper-parameters.
- Definition Classes
- ForecasterVec → Model
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def ll(ms: Double = mse0, s2: Double = sig2e, m2: Int = m): Double
The log-likelihood function times -2.
The log-likelihood function times -2. Override as needed.
- ms
raw Mean Squared Error
- s2
MLE estimate of the population variance of the residuals
- Definition Classes
- Fit
- See also
www.stat.cmu.edu/~cshalizi/mreg/15/lectures/06/lecture-06.pdf
www.wiley.com/en-us/Introduction+to+Linear+Regression+Analysis%2C+5th+Edition-p-9780470542811 Section 2.11
- val m: Int
- Attributes
- protected
- Definition Classes
- ForecasterVec
- val ml: Int
- Attributes
- protected
- Definition Classes
- ForecasterVec
- val modelConcept: URI
An optional reference to an ontological concept
An optional reference to an ontological concept
- Definition Classes
- Model
- def modelName: String
Return the model name including its current hyper-parameter, e.g., AR(2).
- def mse_: Double
Return the mean of squares for error (sse / df._2).
Return the mean of squares for error (sse / df._2). Must call diagnose first.
- Definition Classes
- Fit
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def pacF: VectoD
Return the partial autocorrelation.
Return the partial autocorrelation. Must call 'train' first.
- Definition Classes
- ForecasterVec
- var pacf: VectoD
- Attributes
- protected
- Definition Classes
- ForecasterVec
- def parameter: VectoD
Return the parameter vector.
- def plotFunc(fVec: VectoD, name: String, show: Boolean = true): Unit
Plot a function, e.g., Auto-Correlation Function 'ACF', Partial Auto-Correlation Function 'PACF'.
Plot a function, e.g., Auto-Correlation Function 'ACF', Partial Auto-Correlation Function 'PACF'.
- fVec
the vector given function values
- name
the name of the function
- show
whether to show the fVec values
- Definition Classes
- ForecasterVec
- def plotFunc2(fVec: VectoD, name: String, show: Boolean = true): Unit
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.
- fVec
the vector given function values
- name
the name of the function
- show
whether to show the fVec values
- Definition Classes
- ForecasterVec
- def predict(z: MatriD): VectoD
Predict the value of 'y = f(z)' for each row of matrix 'z'.
Predict the value of 'y = f(z)' for each row of matrix 'z'.
- z
the new matrix to predict
- Definition Classes
- ForecasterVec → Predictor
- def predict(y_null: VectoD = null): Double
Return the horizon 1 forecast beyond the end of the time-series.
Return the horizon 1 forecast beyond the end of the time-series.
- y_null
the actual response/output vector to use (ignored)
- Definition Classes
- ForecasterVec → Predictor
- def predict(z: VectoI): Double
Given a new discrete data/input vector 'z', predict the 'y'-value of 'f(z)'.
Given a new discrete data/input vector 'z', predict the 'y'-value of 'f(z)'.
- z
the vector to use for prediction
- Definition Classes
- Predictor
- def predictAll(): VectoD
Return the vector of predicted values for all original data.
Return the vector of predicted values for all original data. Undo initial zeroing of the data 'y - mu'.
- Definition Classes
- AR → ForecasterVec
- def predictAllz(): VectoD
Predict values for all time points using 1-step ahead forecasts.
Predict values for all time points using 1-step ahead forecasts. Return a vector that is the predictions (zero-centered) of a 'p'th order Auto-Regressive 'AR(p)' model.
- Definition Classes
- AR → ForecasterVec
- See also
'predictAll' in
ForecasterVecfor uncentered results
- var psi: MatriD
- Attributes
- protected
- Definition Classes
- ForecasterVec
- def report: String
Return a basic report on the trained model.
Return a basic report on the trained model.
- Definition Classes
- ForecasterVec → Model
- def resetDF(df_update: PairD): Unit
Reset the degrees of freedom to the new updated values.
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.
- df_update
the updated degrees of freedom (model, error)
- Definition Classes
- Fit
- def residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- ForecasterVec → Predictor
- def retrain(p_: Int): AR
Retrain/fit an
ARmodel to the times-series data using another order 'p_' Estimate the coefficient vector 'φ' for a 'p'th order Auto-Regressive 'AR(p)' model.Retrain/fit an
ARmodel to the times-series data using another order 'p_' Estimate the coefficient vector 'φ' for a 'p'th order Auto-Regressive 'AR(p)' model. The 'φ' vector is 'p'th row of 'psi' matrix (ignoring the first (0th) column).- p_
another order
- var sig2e: Double
- Attributes
- protected
- Definition Classes
- Fit
- var stats: Stats
- Attributes
- protected
- Definition Classes
- ForecasterVec
- def summary: String
Return a detailed summary of the trained model.
- def summary(b: String, modelEq: String): String
Return a detailed summary of the trained model.
Return a detailed summary of the trained model.
- b
the symbol(s) used for the parameters
- modelEq
the model equation as a string
- Definition Classes
- ForecasterVec
- def summary(b: VectoD, stdErr: VectoD, vf: VectoD, show: Boolean = false): String
Produce a summary report with diagnostics for each predictor 'x_j' and the overall quality of fit.
Produce a summary report with diagnostics for each predictor 'x_j' and the overall quality of fit.
- b
the parameters/coefficients for the model
- vf
the Variance Inflation Factors (VIFs)
- show
flag indicating whether to print the summary
- Definition Classes
- Fit
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def test(modelName: String, doPlot: Boolean = true): Unit
Test the model on the full dataset (i.e., train and evaluate on full dataset).
Test the model on the full dataset (i.e., train and evaluate on full dataset).
- modelName
the name of the model being tested
- doPlot
whether to plot the actual vs. predicted response
- Definition Classes
- Predictor
- def toString(): String
- Definition Classes
- AnyRef → Any
- def train(x_null: MatriD, y_: VectoD): AR
Train/fit an
ARmodel to the times-series data in vector 'y_'.Train/fit an
ARmodel to the times-series data in vector 'y_'. Estimate the coefficient vector 'φ' for a 'p'th order Auto-Regressive 'AR(p)' model.z_t = φ_0 * z_t-1 + ... + φ_p-1 * z_t-p + e_t
Uses the Durbin-Levinson Algorithm to determine the coefficients. The 'φ' vector is 'p'th row of 'psi' matrix (ignoring the first (0th) column).
- x_null
the data/input matrix (ignored)
- y_
the response vector (currently only works for y) - FIX
- Definition Classes
- AR → ForecasterVec → Model
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- var yf: MatriD
- Attributes
- protected
- Definition Classes
- ForecasterVec
- var z: VectoD
- Attributes
- protected
- Definition Classes
- ForecasterVec
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
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- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated