class SARIMA extends ARIMA
The SARIMA class provides basic time series analysis capabilities for Auto-
Regressive 'AR' Integrated 'I' Moving-Average 'MA' models. In a
'SARIMA(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. 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_i y_t-i) + Σ(θ_i e_t-i) + e_t
where 'δ' is a constant, 'φ' is the auto-regressive 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. Seasonal differencing, auto-regressive and moving average factors can be incorporated into the model by applying seasonal differencing (possibly in addition to simple differencing) first, then add the seasonal auto-regressive and moving average terms, that rely on lagged values and errors, respectively, from one or more seasonal periods in the past, on the right hand side of the equation. ------------------------------------------------------------------------------
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- SARIMA
- ARIMA
- ARMA
- ForecasterVec
- Predictor
- Model
- Fit
- Error
- QoF
- AnyRef
- Any
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Instance Constructors
- new SARIMA(y: VectoD, d: Int = 0, dd: Int = 0, period: Int = 2)
- y
the original input vector (time series data)
- d
the order of Integration/simple differencing
- dd
the order of seasonal differencing
- period
the seasonal period (at least 2)
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
- var cap: Int
- Attributes
- protected
- Definition Classes
- ARMA
- 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 differenced: Boolean
- Attributes
- protected
- Definition Classes
- ARMA
- 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 eval_(e: VectoD = residuals, y: VectoD = y, yp: VectoD = predictAll ()): ARMA
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.
- e
vector of residuals
- y
vector of observed values
- yp
vector of predicted values
- Definition Classes
- ARMA
- 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 = y.dim, h: Int = 1): VectoD
Produce h-steps-ahead forecast for SARIMA models.
Produce h-steps-ahead forecast for SARIMA models.
- t
the time point from which to make forecasts (in the original scale)
- h
the number of steps to forecast, must be at least one
- Definition Classes
- SARIMA → ARIMA → ARMA → ForecasterVec
- See also
ams.sunysb.edu/~zhu/ams586/Forecasting.pdf
- 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 = 1): 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
- Definition Classes
- ARIMA → ARMA → 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 forecastAll2(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). Do not forecast errors, rather use observed errors from training and make sure not to use errors that would correspond to knowing future errors (all future errors should be assumed to be 0).
- h
the maximum forecasting horizon, number of steps ahead to produce forecasts
- def forecastX(y: VectoD, t: Int, 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. Likely to need overriding.
- y
the current response vector
- t
the time point/index to be forecast
- h
the forecasting horizon, number of steps ahead to produce forecast
- Definition Classes
- ForecasterVec
- def forwardSel(cols: Set[Int] = null, index_q: Int = index_rSq): (Int, ARMA)
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
- ARMA → ForecasterVec → Predictor
- See also
Fitfor index of QoF measures.
- def forwardSel2(step: VectoI = VectorI (1, 1), cols: Set[Int] = null, index_q: Int = index_rSq): (Int, ARMA)
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)
- step
the amount to increment p and q for each iteration
- 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
- ARMA
- 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
- def init(v: VectoD): Unit
Initialize variables based on the working time-series 'v'.
- 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.
- 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
- var mu: Double
- Attributes
- protected
- Definition Classes
- ARMA
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def nll(b: VectoD): Double
The negative log-likelihood function to be minimized.
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- var p: Int
- Attributes
- protected
- Definition Classes
- ARMA
- 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 (concatenation of φ, θ, φφ and θθ).
- var params: Int
- Attributes
- protected
- Definition Classes
- ARMA
- 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/fitted values on the training/full data.
Return the vector of predicted/fitted values on the training/full data. Based on 'zp' calculated in the 'updateFittedValues' method.
- Definition Classes
- SARIMA → ARIMA → ARMA → ForecasterVec
- def predictAllz(): VectoD
Return the vector of zero-centered predicted/fitted values on the training/full dataset.
Return the vector of zero-centered predicted/fitted values on the training/full dataset. Based on 'zp' calculated in the 'updateFittedValues' method.
- Definition Classes
- ARMA → ForecasterVec
- var psi: MatriD
- Attributes
- protected
- Definition Classes
- ForecasterVec
- var q: Int
- Attributes
- protected
- Definition Classes
- ARMA
- 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 residuals: VectoD
Obtain residuals/errors in the original scale.
- def setPQ(pq: VectoI): SARIMA
Set values for the models orders 'p', 'q', 'pp' and 'qq'.
- def showParameterEstimates(): Unit
Show estimates for parameters.
Show estimates for parameters.
- Definition Classes
- ARMA
- var sig2: Double
- Attributes
- protected
- Definition Classes
- ARMA
- var sig2e: Double
- Attributes
- protected
- Definition Classes
- Fit
- var stats: Stats
- Attributes
- protected
- Definition Classes
- ForecasterVec
- 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(): SARIMA
Train/fit an
SARIMAmodel to the times series data. - def train(x_null: MatriD, y_: VectoD): ForecasterVec
Given a time-series 'y_', train the forecasting function 'y = f(y_)', where 'f(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(y_)', where 'f(y_)' is a function of the lagged values of 'y_', by fitting its parameters.
- x_null
the training/full data/input matrix (ignored, pass 'null')
- y_
the training/full response/output vector
- Definition Classes
- ForecasterVec → Model
- def updateFittedValues(): Double
Update the vector of fitted values 'zp', the vector of errors 'e', and return the negative log-likelihood '-ll'.
- 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
- var zp: VectoD
- Attributes
- protected
- Definition Classes
- ARMA
- var δ: Double
- Attributes
- protected
- Definition Classes
- ARMA
- var θ: VectoD
- Attributes
- protected
- Definition Classes
- ARMA
- var μ: Double
- Attributes
- protected
- Definition Classes
- ARMA
- var σ2: Double
- Attributes
- protected
- Definition Classes
- ARMA
- var φ: VectoD
- Attributes
- protected
- Definition Classes
- ARMA
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated