class SARIMAX extends ForecasterVec
The SARIMAX class provides basic time series analysis capabilities for Auto-
Regressive 'AR' Integrated 'I' Moving-Average 'MA' models. In an
'SARIMAX(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. SARIMAX 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) + βχ + 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. Seasonal differencing, autoregressive 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 autoregressive 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. Exogenous/External regressor may also be added to the right-hand size of the model in a similar manner to Regression models. ------------------------------------------------------------------------------
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- SARIMAX
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Instance Constructors
-
new
SARIMAX(y_: VectoD, χ: VectoD, lg: Int, d: Int = 0, dd: Int = 0, period: Int = 1)
- y_
the original input vector (time series data)
- χ
the exogenous vector (time series data)
- lg
the lag for the exogenous variable, note need lg >= horizon h
- d
the order of Integration/simple differencing
- dd
the order of seasonal differencing
- period
the seasonal period
Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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final
def
##(): Int
- Definition Classes
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final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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def
acF: VectoD
Return the autocorrelation.
Return the autocorrelation. Must call 'train' first.
- Definition Classes
- ForecasterVec
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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
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... ) @native() @HotSpotIntrinsicCandidate()
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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
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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)
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var
e: VectoD
- Attributes
- protected
- Definition Classes
- ForecasterVec
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): 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
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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_(y: VectoD, yp: VectoD): SARIMAX
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
vector of observed values
- yp
vector of predicted values
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def
eval_(e: VectoD = residuals, y: VectoD = y, yp: VectoD = fittedValues): SARIMAX
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
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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
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def
f_(z: Double): String
Format a double value.
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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.
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def
fitLabel: Seq[String]
Return the labels for the Quality of Fit (QoF) measures.
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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
-
def
fittedValues(): VectoD
Return the vector of fitted values on the training data.
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final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
-
def
forecast(t: Int = y.dim, h: Int = 1): VectoD
Produce n-steps-ahead forecast for SARIMAX models.
Produce n-steps-ahead forecast for SARIMAX 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
- SARIMAX → ForecasterVec
- See also
ams.sunysb.edu/~zhu/ams586/Forecasting.pdf
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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
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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
- SARIMAX → ForecasterVec
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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
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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
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def
forwardSel(cols: Set[Int], index_q: Int): (Int, ForecasterVec)
Perform forward selection to find the most predictive variable to add the existing model, returning the variable to add and the new 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.
- cols
the lags/columns currently included in the existing model (currently ignored)
- index_q
index of Quality of Fit (QoF) to use for comparing quality
- Definition Classes
- SARIMAX → ForecasterVec → Predictor
- See also
Fitfor index of QoF measures.
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final
def
getClass(): Class[_]
- 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
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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
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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
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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
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val
m: Int
- Attributes
- protected
- Definition Classes
- ForecasterVec
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val
ml: Int
- Attributes
- protected
- Definition Classes
- ForecasterVec
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val
modelConcept: URI
An optional reference to an ontological concept
An optional reference to an ontological concept
- Definition Classes
- Model
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def
modelName: String
Return the model name including its current hyper-parameter.
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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
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
nll(b: VectoD): Double
The negative log-likelihood function to be minimized.
The negative log-likelihood function to be minimized.
- b
the input parameter vector
- See also
spia.uga.edu/faculty_pages/monogan/teaching/ts/Barima.pdf
stats.stackexchange.com/questions/77663/arima-estimation-by-hand
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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
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var
pacf: VectoD
- Attributes
- protected
- Definition Classes
- ForecasterVec
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def
parameter: VectoD
Return the parameter vector.
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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
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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
- SARIMAX → ForecasterVec
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def
predictAllz(): VectoD
Return the vector of predicted values for all zero-centered data.
Return the vector of predicted values for all zero-centered data.
- Definition Classes
- SARIMAX → ForecasterVec
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var
psi: MatriD
- Attributes
- protected
- Definition Classes
- ForecasterVec
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def
report: String
Return a basic report on the trained model.
Return a basic report on the trained model.
- Definition Classes
- ForecasterVec → Model
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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
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def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- ForecasterVec → Predictor
-
def
residuals(): VectoD
Obtain residuals in the original scale
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def
setPQ(p_: Int = 0, q_: Int = 0, pp_: Int = 0, qq_: Int = 0): Unit
Set values for 'p', 'q', 'pp' and 'qq'.
Set values for 'p', 'q', 'pp' and 'qq'.
- p_
the order of the AR part of the model
- q_
the order of the MA part of the model
- pp_
the order of the Seasonal AR part of the model
- qq_
the order of the Seasonal MA part of the model
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def
setTS(ts: VectoD): Unit
Set/change the internal time series.
Set/change the internal time series. May be used to set the time series to a different time window (typically future when new data become available) in order to produce newer forecast (typically with the new data) without re-training the model for parameters (use existing parameters from previous training).
- ts
the new time series
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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(): SARIMAX
Train/fit an
SARIMAXmodel to the times series data.Train/fit an
SARIMAXmodel to the times series data. Must call 'SetPQ' first. -
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 'xp', the vector of fitted values; 'e', the vector of errors; ll, aic, aicc and bic.
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final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
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final
def
wait(arg0: Long): Unit
- Definition Classes
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- @throws( ... ) @native()
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final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
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
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