Packages

class ARIMA extends Error

The ARIMA class provides basic time series analysis capabilities for Auto- Regressive 'AR' Integrated 'I' Moving-Average 'MA' models. In an 'ARIMA(p, d, q)' model, 'p' and 'q' refer to the order of the Auto-Regressive and Moving-Average components of the model; 'd' refers to the order of differencing. ARIMA 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 = c + Σ(φ_i y_t-i) + Σ(θ_i e_t-i) + e_t

where 'c' is a constant, 'φ' is the autoregressive coefficient vector, 'θ' is the moving-average coefficient vector, and 'e' is the noise vector. If 'd' > 0, then the time series must be differenced first before applying the above model. ------------------------------------------------------------------------------

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Instance Constructors

  1. new ARIMA(y: VectoD, t: VectoD, d: Int = 0)

    y

    the input vector (time series data)

    t

    the time vector

    d

    the order of Integration

Value Members

  1. final def !=(arg0: Any): Boolean
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  2. final def ##(): Int
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  3. final def ==(arg0: Any): Boolean
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  4. val acf: VectorD
  5. final def asInstanceOf[T0]: T0
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  6. def clone(): AnyRef
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  7. def difference(): VectorD

    Difference the time series.

  8. def durbinLevinson: MatriD

    Apply the Durbin-Levinson Algorithm to iteratively compute the 'psi' matrix.

    Apply the Durbin-Levinson Algorithm to iteratively compute the 'psi' matrix. The last row of the matrix gives 'AR' coefficients.

    See also

    www.stat.tamu.edu/~suhasini/teaching673/time_series.pdf

  9. final def eq(arg0: AnyRef): Boolean
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  10. def equals(arg0: Any): Boolean
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  11. def est_ar(p_: Int = 1): VectoD

    Estimate the coefficient vector 'φ' for a 'p'th order Auto-Regressive 'AR(p)' model.

    Estimate the coefficient vector 'φ' for a 'p'th order Auto-Regressive 'AR(p)' model.

    x_t = φ_0 * x_t-1 + ... + φ_p-1 * x_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).

    p_

    the order of the AR model

  12. def est_arma(p_: Int = 1, q_: Int = 1): (VectoD, VectoD)

    Estimate the coefficient vectors φ and θ for a ('p'th, 'q'th) order Auto-Regressive Moving-Average 'ARIMA(p, q)' model.

    Estimate the coefficient vectors φ and θ for a ('p'th, 'q'th) order Auto-Regressive Moving-Average 'ARIMA(p, q)' model.

    x_t = φ_0 * x_t-1 + ... + φ_p-1 * x_t-p + θ_0 * e_t-1 + ... + θ_q-1 * e_t-q + e_t

    p_

    the order of the AR part of the model

    q_

    the order of the MA part of the model

    See also

    www.math.kth.se/matstat/gru/sf2943/tsform.pdf

  13. def est_ma(q_: Int = 1): VectoD

    Estimate the coefficient vector 'θ' for a 'q'th order a Moving-Average 'MA(q)' model.

    Estimate the coefficient vector 'θ' for a 'q'th order a Moving-Average 'MA(q)' model.

    x_t = θ_0 * e_t-1 + ... + θ_q-1 * e_t-q + e_t

    q_

    the order of the AR model

  14. def eval(yy: VectoD = y): Unit

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    yy

    the response vector

  15. def finalize(): Unit
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  16. final def flaw(method: String, message: String): Unit
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  17. def forecast_ar(steps: Int = 1): VectoD

    Produce the multi-step forecast for AR models.

  18. def forecast_arma(steps: Int = 1): VectoD

    Produce the one-step forecast for ARMA models

    Produce the one-step forecast for ARMA models

    steps

    the number of steps to forecast, must be at least one.

    See also

    ams.sunysb.edu/~zhu/ams586/Forecasting.pdf

  19. def forecast_ma(steps: Int = 1): VectoD

    Produce the one-step forecast for MA models

    Produce the one-step forecast for MA models

    steps

    the number of steps to forecast, must be at least one.

    See also

    ams.sunysb.edu/~zhu/ams586/Forecasting.pdf

  20. final def getClass(): Class[_]
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  21. def hannanRissanen(): VectoD

    Apply the Hannan-Rissanen Algorithm to estimate the 'ARMA(p, q)' coefficients.

    Apply the Hannan-Rissanen Algorithm to estimate the 'ARMA(p, q)' coefficients.

    See also

    halweb.uc3m.es/esp/Personal/personas/amalonso/esp/TSAtema9.pdf

  22. def hashCode(): Int
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  24. def methodOfInnovations(): VectoD

    Apply the Method of Innovation to estimate coefficients for MA(q) model.

    Apply the Method of Innovation to estimate coefficients for MA(q) model.

    See also

    www.math.kth.se/matstat/gru/sf2943/tsform.pdf

    www.stat.berkeley.edu/~bartlett/courses/153-fall2010/lectures/10.pdf

  25. val mu: Double
  26. final def ne(arg0: AnyRef): Boolean
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  27. final def notify(): Unit
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  28. final def notifyAll(): Unit
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  29. def obj_f(φθ: VectoD): Double

    Compute the objective function for MLE optimization.

    Compute the objective function for MLE optimization. FIX

    φθ

    a single vector of AR and MA coefficients

    See also

    halweb.uc3m.es/esp/Personal/personas/amalonso/esp/TSAtema9.pdf

  30. def optimize_MLE(): VectoD

    Apply the Hannan-Rissanen Algorithm first to estimate the 'ARIMA(p, q)' coefficients, then optimize the parameters using MLE.

    Apply the Hannan-Rissanen Algorithm first to estimate the 'ARIMA(p, q)' coefficients, then optimize the parameters using MLE. FIX

    See also

    halweb.uc3m.es/esp/Personal/personas/amalonso/esp/TSAtema9.pdf

  31. var pacf: VectoD
  32. def plotFunc(fVec: VectoD, name: String): 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

  33. def predict(t: VectoD): Double

    For the last time points in vector 't', predict the value of 'y = f(t)'.

    For the last time points in vector 't', predict the value of 'y = f(t)'.

    t

    the time-vector indicating time points to forecast

  34. def predictAll: VectoD

    For all the time points, predict all the values of 'y = f(t)'.

  35. def predict_ar(transBack: Boolean = true): VectoD

    Return a vector that is the predictions of a 'p'th order Auto-Regressive 'AR(p)' model.

    Return a vector that is the predictions of a 'p'th order Auto-Regressive 'AR(p)' model.

    transBack

    flag that determines whether to return the predicted values in the original scale

  36. def predict_arma(transBack: Boolean = true): VectoD

    Return a vector that is the predictions of a ('p'th, 'q'th) order Auto-Regressive Moving-Average 'ARMA(p, q)' model.

    Return a vector that is the predictions of a ('p'th, 'q'th) order Auto-Regressive Moving-Average 'ARMA(p, q)' model.

    transBack

    flag that determines whether to return the predicted values in the original scale

  37. def predict_ma(transBack: Boolean = true): VectoD

    Return a vector of predictions of an MA model and update the residuals

    Return a vector of predictions of an MA model and update the residuals

    transBack

    flag that determines whether to return the predicted values in the original scale

  38. def setPQ(p_: Int, q_: Int): Unit

    Set values for 'p' and 'q'.

    Set values for 'p' and 'q'.

    p_

    the order of the AR part of the model

    q_

    the order of the MA part of the model

  39. def smooth(l: Int): VectoD

    Smooth the 'y' vector by taking the 'l'th order moving average.

    Smooth the 'y' vector by taking the 'l'th order moving average.

    l

    the number of points to average

  40. final def synchronized[T0](arg0: ⇒ T0): T0
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  41. def toString(): String
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  42. def train(yy: VectoD = y): ARIMA

    Train/fit an ARIMA model to times the series data.

    Train/fit an ARIMA model to times the series data. Must call setPQ first.

    yy

    the response vector to work with

  43. def transformBack(xp: VectoD): VectoD

    Transform the predictions/fitted values of a differenced time series back to the original scale.

    Transform the predictions/fitted values of a differenced time series back to the original scale.

    xp

    the vector of predictions/fitted values of a differenced time series

    See also

    stats.stackexchange.com/questions/32634/difference-time-series-before-arima-or-within-arima

  44. def transformBack_f(xf: VectoD): VectoD

    Transform the forecasted values of a differenced time series back to the original scale.

    Transform the forecasted values of a differenced time series back to the original scale.

    xf

    the vector of forecasted values of a differenced time series

    See also

    stats.stackexchange.com/questions/32634/difference-time-series-before-arima-or-within-arima

  45. final def wait(): Unit
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  46. final def wait(arg0: Long, arg1: Int): Unit
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