ARSeasonalFit Class

ARSeasonalFit Class

Estimates the optimum seasonality parameters for a time series using an autoregressive model, AR(p), to represent the time series.

Inheritance Hierarchy

System.Object
Imsl.Stat.ARSeasonalFit

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class ARSeasonalFit

<SerializableAttribute>
Public Class ARSeasonalFit

[SerializableAttribute]
public ref class ARSeasonalFit

[<SerializableAttribute>]
type ARSeasonalFit =  class end

The ARSeasonalFit type exposes the following members.

Constructors

	Name	Description
	ARSeasonalFit	Constructor for ARSeasonalFit.

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Methods

	Name	Description
	Compute	Computes the minimum AIC and optimum values for s and d based upon the candidates provided in SInitial and DInitial, and computes the values for the transformed series, .
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetAR	Returns the final autoregressive parameter estimates at the optimum in the transformed series .
	GetDInitial	Returns the candidate values for d to evaluate.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetOptimumD	Returns the optimum values for d selected among the candidates in DInitial.
	GetOptimumS	Returns the optimum values for s selected among the candidates in SInitial.
	GetSInitial	Returns the candidate values for s to evaluate.
	GetTimeSeries	Returns the time series.
	GetTransformedTimeSeries	Returns the transformed series, .
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetDInitial	Sets the candidate values for selecting the optimum seasonal adjustment prior to calling the compute method.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	AIC	The final estimate for Akaike's Information Criterion (AIC) at the optimum.
	AROrder	The optimum number of lags, p, for the optimum autoregressive AR(p) model. This is the value of p for the transformed series, .
	Center	The setting for centering the input time series.
	Exclude	Controls whether to exclude or replace the intial values in the transformed series.
	Maxlag	The maximum lag used to fit the AR(p) model.
	NLost	The number of values in the initial part of the series lost to differencing.

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Remarks

ARMA time series modeling assumes the time series is stationary. Seasonal trends and cycles violate this assumption, which can lead to inaccurate predictions. However, in many cases the nonstationary series can be transformed into a stationary series by first differencing the series. For example, if the correlation is strong from one period to the next, the series might be differenced by a lag of 1. Instead of fitting a model to the original series , the model is fitted to the transformed series: $W_t = Z_t - Z_{t-1}$ . Higher order lags or differences are warranted if the series has cycles every 4 or 13 weeks. Class ARSeasonalFit is designed to help identify the optimum differencing for a series with seasonal trends or cycles.

ARSeasonalFit assumes the original series has no missing values, is equally spaced in time and is not centered before computing the optimum differencing. However, by default the transformed series is centered using the mean of that series. Users can change this default setting with the Center property. If Center is set to None the series is not centered, if set to Mean the series is centered using the mean of the series, and if it is set to Median, the series is centered using the median of the series. If Center is set to Mean or Median then the differenced series, is centered before determination of minimum AIC and optimum lag.

For every combination of rows in SInitial and DInitial, the series is converted to the seasonally adjusted series using the following computation

$W_t(s,d) = \Delta^{d_1}_{s_1}\Delta^{d_2}_{s_2} \cdots\Delta^{d_m}_{s_m}Z_t=\prod\limits_{i=1}^{m}\sum\limits_{j=0}^{d_i} {{d_i}\choose{j}}{(-1)}^jB^{j\cdot s_i}Z_t$

where $s := (s_1,\ldots,s_m)$ , $d := (d_1,\ldots,d_m)$ represent specific rows of arrays SInitial and DInitial respectively, and m is the number of differences, or m=SInitial.GetLength(1).

This transformation of the series to is computed using the Difference class. After this transformation the transformed series

is centered, unless None is specified, and the ARAutoUnivariate class is used to automatically determine the optimum lag for an AR(p) representation for

This procedure is repeated for every possible combination of rows in SInitial and DInitial. The series with the minimum AIC is identified as the optimum representation and returned in the methods and properties AROrder, GetOptimumS, GetOptimumD, AIC, and GetAR. The transformed series with the minium AIC can be retrieved from the GetTransformedTimeSeries method.

Reference

Imsl.Stat Namespace

Other Resources

Example