naginterfaces.library.rand.times_​smooth_​exp

naginterfaces.library.rand.times_smooth_exp(mode, n, itype, p, param, init, var, comm, statecomm, e)[source]

times_smooth_exp simulates from an exponential smoothing model, where the model uses either single exponential, double exponential or a Holt–Winters method.

For full information please refer to the NAG Library document for g05pm

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g05/g05pmf.html

Parameters
modeint

Indicates if times_smooth_exp is continuing from a previous call or, if not, how the initial values are computed.

Values for , and , for , are supplied in .

times_smooth_exp continues from a previous call using values that are supplied in [‘r’]. [‘r’] is not updated.

times_smooth_exp continues from a previous call using values that are supplied in [‘r’]. [‘r’] is updated.

nint

The number of terms of the time series being generated.

itypeint

The smoothing function.

Single exponential.

Brown’s double exponential.

Linear Holt.

Additive Holt–Winters.

Multiplicative Holt–Winters.

pint

If or , the seasonal order, , otherwise is not referenced.

paramfloat, array-like, shape

Note: the required length for this argument is determined as follows: if : ; if : ; if : ; otherwise: .

The smoothing parameters.

If or , and any remaining elements of are not referenced.

If , , , and any remaining elements of are not referenced.

If or , , , and and any remaining elements of are not referenced.

initfloat, array-like, shape

Note: the required length for this argument is determined as follows: if : ; if : ; if : ; otherwise: .

If , the initial values for , and , for , used to initialize the smoothing.

If , and any remaining elements of are not referenced.

If or , and and any remaining elements of are not referenced.

If or , , and to hold the values for , for .

Any remaining elements of are not referenced.

varfloat

The variance, of the Normal distribution used to generate the errors . If then Normally distributed errors are not used.

commdict, communication object, modified in place

Communication structure for the reference vector.

If or , this argument must have been initialized by a prior call to times_smooth_exp.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

efloat, array-like, shape

If and , a vector from which the errors, are randomly drawn, with replacement.

If , is not referenced.

Returns
xfloat, ndarray, shape

The generated time series, , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: , or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: , , , or .

(errno )

On entry, .

Constraint: if or , .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: if , .

(errno )

On entry, .

Constraint: .

(errno )

On entry, some of the elements of the array [‘r’] have been corrupted or have not been initialized.

(errno )

On entry, [‘state’] vector has been corrupted or not initialized.

(errno )

Model unsuitable for multiplicative Holt–Winter, try a different set of parameters.

Notes

times_smooth_exp returns , a realization of a time series from an exponential smoothing model defined by one of five smoothing functions:

Single Exponential Smoothing

Brown Double Exponential Smoothing

Linear Holt Exponential Smoothing

Additive Holt–Winters Smoothing

Multiplicative Holt–Winters Smoothing

where is the mean, is the trend and is the seasonal component at time with being the seasonal order. The errors, are either drawn from a normal distribution with mean zero and variance or randomly sampled, with replacement, from a user-supplied vector.

References

Chatfield, C, 1980, The Analysis of Time Series, Chapman and Hall