Packages

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. ----------------------------------------------------------------------------------

Linear Supertypes
ForecasterVec, Predictor, Model, Fit, Error, QoF, AnyRef, Any
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  1. AR
  2. ForecasterVec
  3. Predictor
  4. Model
  5. Fit
  6. Error
  7. QoF
  8. AnyRef
  9. Any
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Instance Constructors

  1. new AR(y: VectoD, hparam: HyperParameter = ARMA.hp)

    y

    the response vector (time-series data)

    hparam

    the hyper-parameters

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. def acF: VectoD

    Return the autocorrelation.

    Return the autocorrelation. Must call 'train' first.

    Definition Classes
    ForecasterVec
  5. 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
    ForecasterVecPredictor
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  8. 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
  9. 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)

    Definition Classes
    FitQoF
    See also

    Regression_WLS

  10. var e: VectoD
    Attributes
    protected
    Definition Classes
    ForecasterVec
  11. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  13. 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
  14. 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
    ForecasterVecModel
  15. 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
  16. def f_(z: Double): String

    Format a double value.

    Format a double value.

    z

    the double value to format

    Definition Classes
    QoF
  17. 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.

    Definition Classes
    FitQoF
  18. def fitLabel: Seq[String]

    Return the labels for the Quality of Fit (QoF) measures.

    Return the labels for the Quality of Fit (QoF) measures. Override to add additional QoF measures.

    Definition Classes
    FitQoF
  19. def fitMap: Map[String, String]

    Build a map of quality of fit measures (use of LinkedHashMap makes it ordered).

    Build a map of quality of fit measures (use of LinkedHashMap makes it ordered).

    Definition Classes
    QoF
  20. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  21. 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
  22. 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
  23. 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
    ARForecasterVec
  24. 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
  25. 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
    ARForecasterVec
  26. 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
    ARForecasterVecPredictor
    See also

    Fit for index of QoF measures.

  27. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  28. 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
    ForecasterVecPredictor
  29. 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
    ForecasterVecPredictor
  30. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  31. def help: String

    Return the help string that describes the Quality of Fit (QoF) measures provided by the Fit class.

    Return the help string that describes the Quality of Fit (QoF) measures provided by the Fit class. Override to correspond to 'fitLabel'.

    Definition Classes
    FitQoF
  32. def hparameter: HyperParameter

    Return the hyper-parameters.

    Return the hyper-parameters.

    Definition Classes
    ForecasterVecModel
  33. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  34. 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

  35. val m: Int
    Attributes
    protected
    Definition Classes
    ForecasterVec
  36. val ml: Int
    Attributes
    protected
    Definition Classes
    ForecasterVec
  37. val modelConcept: URI

    An optional reference to an ontological concept

    An optional reference to an ontological concept

    Definition Classes
    Model
  38. def modelName: String

    Return the model name including its current hyper-parameter, e.g., AR(2).

    Return the model name including its current hyper-parameter, e.g., AR(2).

    Definition Classes
    ARModel
  39. 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
  40. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  41. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  42. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  43. def pacF: VectoD

    Return the partial autocorrelation.

    Return the partial autocorrelation. Must call 'train' first.

    Definition Classes
    ForecasterVec
  44. var pacf: VectoD
    Attributes
    protected
    Definition Classes
    ForecasterVec
  45. def parameter: VectoD

    Return the parameter vector.

    Return the parameter vector.

    Definition Classes
    ARModel
  46. 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
  47. 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
  48. 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
    ForecasterVecPredictor
  49. 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
    ForecasterVecPredictor
  50. 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
  51. 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
    ARForecasterVec
  52. 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
    ARForecasterVec
    See also

    'predictAll' in ForecasterVec for uncentered results

  53. var psi: MatriD
    Attributes
    protected
    Definition Classes
    ForecasterVec
  54. def report: String

    Return a basic report on the trained model.

    Return a basic report on the trained model.

    Definition Classes
    ForecasterVecModel
  55. 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
  56. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    ForecasterVecPredictor
  57. def retrain(p_: Int): AR

    Retrain/fit an AR model 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 AR model 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

  58. var sig2e: Double
    Attributes
    protected
    Definition Classes
    Fit
  59. var stats: Stats
    Attributes
    protected
    Definition Classes
    ForecasterVec
  60. def summary: String

    Return a detailed summary of the trained model.

  61. 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
  62. 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
  63. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  64. 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
  65. def toString(): String
    Definition Classes
    AnyRef → Any
  66. def train(x_null: MatriD, y_: VectoD): AR

    Train/fit an AR model to the times-series data in vector 'y_'.

    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.

    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
    ARForecasterVecModel
  67. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  68. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  69. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  70. var yf: MatriD
    Attributes
    protected
    Definition Classes
    ForecasterVec
  71. var z: VectoD
    Attributes
    protected
    Definition Classes
    ForecasterVec

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated

Inherited from ForecasterVec

Inherited from Predictor

Inherited from Model

Inherited from Fit

Inherited from Error

Inherited from QoF

Inherited from AnyRef

Inherited from Any

Ungrouped