Class SarimaModel in package sarima

Class SarimaModel in package sarima.

Objects from the Class

Class "SarimaModel" represents standard SARIMA models. Objects can be created by calls of the form new("SarimaModel", ..., ar, ma, sar, sma), using named arguments in the form slotname = value, where slotname is one of the slots, see below. The arguments have natural defaults. It may be somewhat surprising though that the default for the variance of the innovations (slot "sigma2") is NA. The rationale for this choice is that for some calculations the innovations' variance is not needed and, more importantly, it is far too easy to forget to include it in the model (at least for the author) when the variance matters. The latter may may lead silently to wrong results if the "natural" default value of one is used when sigma2 matters.

The models may be specified in intercept (center = 0) or mean-corrected (intercept = 0) form. Setting both to non-zero values is accepted but rarely needed.

If you waih to modify an existing object from class "SarimaModel", give it as an unnamed argument to "new" and specify only the slots to be changed, see the examples.

Use as.SarimaModel to convert a model fitted with stats::arima() to "SarimaModel".

Slots

center:

Object of class "numeric", a number, the ARIMA equation is for X(t) - center.

intercept:

Object of class "numeric", a number, the intercept in the ARIMA equation.

sigma2:

Object of class "numeric", a positive number, the innovations variance.

nseasons:

Object of class "numeric", a positive integer, the number of seasons. For non-seasonal models this is NA.

iorder:

Object of class "numeric", non-negative integer, the integration order.

siorder:

Object of class "numeric", non-negative integer, the seasonal integration order.

ar:

Object of class "BJFilter", the non-seasonal AR part of the model.

ma:

Object of class "SPFilter", the non-seasonal MA part of the model.

sar:

Object of class "BJFilter", the seasonal AR part of the model.

sma:

Object of class "SPFilter", the seasonal MA part of the model.

Extends

Class "VirtualFilterModel", directly. Class "SarimaSpec", directly. Class "SarimaFilter", by class "SarimaSpec", distance 2. Class "VirtualSarimaFilter", by class "SarimaSpec", distance 3. Class "VirtualCascadeFilter", by class "SarimaSpec", distance 4. Class "VirtualMonicFilter", by class "SarimaSpec", distance 5.

Methods

SARIMA models contain as special cases a number of models. The one-argument method of modelCoef is essentially a definition of model coefficients for SARIMA models. The two-argument methods request the model coefficients according to the convention of the class of the second argument. The second argument may also be a character string naming the target class.

Essentially, the methods for modelCoef are a generalisation of as() methods and can be interpreted as such (to an extent, the result is not necessarilly from the target class, not least because the target class may be virtual).

modelCoef

signature(object = "SarimaModel", convention = "missing"): Converts object to "SarimaFilter".

modelCoef

signature(object = "SarimaModel", convention = "SarimaFilter"): Converts object to "SarimaFilter", equivalent to the one-argument call modelCoef(object).

modelCoef

signature(object = "SarimaModel", convention = "ArFilter"): Convert object to "ArFilter". An error is raised if object has non-trivial moving average part.

modelCoef

signature(object = "SarimaModel", convention = "MaFilter"): Convert object to "MaFilter". An error is raised if object has non-trivial autoregressive part.

modelCoef

signature(object = "SarimaModel", convention = "ArmaFilter"): Convert object to "ArmaFilter". This operation always successeds.

modelCoef

signature(object = "SarimaModel", convention = "character"): The second argument gives the name of the target class. This is conceptually equivalent to modelCoef(object, new(convention)).

modelOrder gives the order of the model according to the conventions of the target class. An error is raised if object is not compatible with the target class.

modelOrder: signature(object = "SarimaModel", convention = "ArFilter"): ...
modelOrder: signature(object = "SarimaModel", convention = "ArmaFilter"): ...
modelOrder: signature(object = "SarimaModel", convention = "ArmaModel"): ...
modelOrder: signature(object = "SarimaModel", convention = "ArModel"): ...
modelOrder: signature(object = "SarimaModel", convention = "MaFilter"): ...
modelOrder: signature(object = "SarimaModel", convention = "MaModel"): ...
modelOrder: signature(object = "SarimaModel", convention = "missing"): ...

The polynomials associated with object can be obtained with the following methods. Note that target "ArmaFilter" gives the fully expanded products of the AR and MA polynomials, as needed, e.g., for filtering.

modelPoly

signature(object = "SarimaModel", convention = "ArmaFilter"): ` Gives the fully expanded polynomials as a list

modelPoly

signature(object = "SarimaModel", convention = "missing"): Gives the polynomials associated with the model as a list.

modelPolyCoef

signature(object = "SarimaModel", convention = "ArmaFilter"): Give the coefficients of the fully expanded polynomials as a list.

modelPolyCoef

signature(object = "SarimaModel", convention = "missing"): Gives the coefficients of the polynomials associated with the model as a list.

Author

Georgi N. Boshnakov

Examples

ar1 <- new("SarimaModel", ar = 0.9)
ar1c <- new("SarimaModel", ar = 0.9, intercept = 3)
ar1c
#> An object of class "SarimaModel"
#> Model: Phi(B)X(t) = intercept + e(t)
#> 
#> intercept:  3 
#> sigmaSq:  NA 
#> Non-seasonal model 
#> Order of differencing:  0 
#> 
#> ar coefficients:   0.9
#> ma coefficients:    <None>
ar1m <- new("SarimaModel", ar = 0.9, center = 1)
ar1m
#> An object of class "SarimaModel"
#> Model: Phi(B)(X(t) - center) = e(t)
#> 
#> mean:  1 
#> sigmaSq:  NA 
#> Non-seasonal model 
#> Order of differencing:  0 
#> 
#> ar coefficients:   0.9
#> ma coefficients:    <None>

sm0 <- new("SarimaModel", nseasons = 12)
sm1 <- new("SarimaModel", nseasons = 12, intercept = 3)
sm1
#> An object of class "SarimaModel"
#> Model: X(t) = intercept + e(t)
#> 
#> intercept:  3 
#> sigmaSq:  NA 
#> Period:  12 
#> Order of differencing:  0 
#> Order of seasonal differencing:  0 
#> 
#> ar coefficients:    <None>
#> ma coefficients:    <None>
#> seasonal ar coefficients:   <None>
#> seasonal ma coefficients:   <None>
## alternatively, pass a model and modify with named arguments
sm1b <- new("SarimaModel", sm0, intercept = 3)
identical(sm1, sm1b) # TRUE
#> [1] TRUE

## in the above models sigma2 is NA

## sm2 - from scratch, the rest modefy an existing model
sm2  <- new("SarimaModel", ar = 0.9, nseasons = 12, intercept = 3, sigma2 = 1)
sm2a <- new("SarimaModel", sm0, ar = 0.9, intercept = 3, sigma2 = 1)
sm2b <- new("SarimaModel", sm1, ar = 0.9, sigma2 = 1)
sm2c <- new("SarimaModel", ar1c, nseasons =12, sigma2 = 1)
identical(sm2, sm2a) # TRUE
#> [1] TRUE
identical(sm2, sm2b) # TRUE
#> [1] TRUE
identical(sm2, sm2c) # TRUE
#> [1] TRUE

sm3 <- new("SarimaModel", ar = 0.9, sar = 0.8, nseasons = 12, intercept = 3,
           sigma2 = 1)
sm3b <- new("SarimaModel", sm2, sar = 0.8)
identical(sm3, sm3b) # TRUE
#> [1] TRUE

## The classic 'airline model' (from examples for AirPassengers)
(fit <- arima(log10(AirPassengers), c(0, 1, 1),
              seasonal = list(order = c(0, 1, 1), period = 12)))
#> 
#> Call:
#> arima(x = log10(AirPassengers), order = c(0, 1, 1), seasonal = list(order = c(0, 
#>     1, 1), period = 12))
#> 
#> Coefficients:
#>           ma1     sma1
#>       -0.4018  -0.5569
#> s.e.   0.0896   0.0731
#> 
#> sigma^2 estimated as 0.0002543:  log likelihood = 353.96,  aic = -701.92

as.SarimaModel(fit)
#> An object of class "SarimaModel"
#> Model: (1-B)(1-B^s)X(t) = Theta(B)Theta_s(B^s)e(t)
#> 
#> Intercept:  0 
#> SigmaSq:  0.0002542551 
#> Period:  12 
#> Order of differencing:  1 
#> Order of seasonal differencing:  1 
#> 
#> ar coefficients:    <None>
#> ma coefficients:   -0.401828384120966
#> seasonal ar coefficients:   <None>
#> seasonal ma coefficients:  -0.556945059922282

Objects from the Class

Slots

Extends

Methods

Author

See also

Examples