IMSL C# Numerical Library

ARSeasonalFit.GetTransformedTimeSeries Method 

Returns the transformed series, W_t(s,d).

public double[] GetTransformedTimeSeries();

Return Value

A double array of length z.Length or z.Length-NLost, depending upon the setting for the Exclude property.

Remarks

W_t(s,d) is an array of length z.Length or z.Length-NLost containing the optimum seasonally adjusted, autoregressive series, where NLost is the first lost observations in this series that are dropped due to differencing. If the missing values are not dropped the first NLost values of W_t will be set to Double.NaN. The NLost property can be used to obtain the number of lost observations.

The seasonal adjustment is done by selecting optimum values for d_1,\ldots,d_m, s_1,\ldots,s_m and p in the AR model, where m is number of differences, m=sIinitial.GetLength(1) :

\phi_p(B)(\Delta_{s_1}^{d_1}\Delta_{s_2}^{d_2}
            \ldots\Delta_{s_m}^{d_m}Z_t-\mu) = a_t\rm{,}
where \{Z_t\} is the original time series, B is the backward shift operator defined by B^kZ_t=Z_{t-k} \rm{, \,\,with }\,\, k\ge0, a_t is Gaussian white noise with E[a_t]=0 and \mbox{Var}[a_t]= 
            \sigma^2, \phi_p(B)= 1-\phi_1B - \phi_2B^2 - \cdots - \phi_pB^p,\,\,\,\,
            0\le{p}\le\rm{maxlag}, \Delta_s^d=(1-B^s)^d, with s \gt 0, 
            d \ge 0, and \mu is a centering parameter for the differenced series.

Exceptions

Exception TypeCondition
MatrixSingularException is thrown if the input matrix is singular.
TooManyCallsException is thrown if the number of calls to the function has exceeded the maximum number of iterations times the number of moving average (MA) parameters + 1.
IncreaseErrRelException is thrown if the bound for the relative error is too small.
NewInitialGuessException is thrown if the iteration has not made good progress.
IllConditionedException is thrown if the problem is ill-conditioned.
TooManyIterationsException is thrown if the maximum number of iterations is exceeded.
TooManyFunctionEvaluationsException is thrown if the maximum number of function evaluations is exceeded.
TooManyJacobianEvalException is thrown if the maximum number of Jacobian evaluations is exceeded.
NonStationaryException is thrown if the final maximum likelihood estimates for the time series are nonstationary.
SingularTriangularMatrixException is thrown if the input triangular matrix is singular.

See Also

ARSeasonalFit Class | Imsl.Stat Namespace