Corrigendum: Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model and Some of Its Properties, Communications in Statistics—Theory and Methods, Volume 37 Issue No. 8, January 2008, Pages 1266–1273

This article refers to:

Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model and Some of Its Properties

In Mahendran Shitan, Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model and Some of its Properties, Commun. Statist.—Theory Meth., Volume 37, Issue No. 8, January 2008, Pages 1266–1273, the author had inadvertently missed out an important reference relevant to his article, namely,

Boissy, Y., Bhattacharya, B. B., Li, X., Richardson, G. D. (2005). Parameter estimates for fractional autoregressive spatial processes. The Annals of Statistics 33(6):2553–2567.

This reference should be included in the reference list.

Other corrections are as follows.

1. In the Abstract the fourth sentence in the published version reads:

“Spatial data may also exhibit a long memory structure and in order to model such structure we introduce a new class of models to be called as the Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model and discuss some of its properties.”

In the corrected version it should read as:

“Spatial data may also exhibit a long memory structure and in order to model such structure we consider the Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model and discuss some of its properties.”

2. In the Introduction section, the first and second sentence of Paragraph 5 (page 1267) of the published version reads as follows:

“It is conceivable that in some cases spatial data may also exhibit a long memory structure. In order to model such data, we introduce a new class of models to be called as Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model.”

The corrected version should read as:

“It is conceivable that in some cases spatial data may also exhibit a long memory structure. Boissy et al. (2005) had extended the long memory concept from time series to the spatial context and introduced the fractional autoregressive model given as,

where ∇ ^d  = (1 − B ₁) ^{d ₁} (1 − B ₂) ^{d ₂} and amongst others established the strong consistency of the Whittle's estimator for the parameters of the model. Independently, we considered the model termed as Fractionally Integrated Separable Spatial Autoregressive (FISSAR) Model.” The reason for this is that it is possible to construct a non-separable counterpart which will be discussed in a future paper.

3. On page 1269 (published version) at the end of the proof of Proposition 2 to include the following sentence.

“This result agrees with the last equation on page 2554 of Boissy et al. (2005) paper.

4. On page 1270 of the published version reads:

The corrected version should read as follows:

5. The first sentence of the Conclusion section (page 1272) of the published version reads as:

“The objective of this research is to introduce a new class of models called FISSAR models and to establish some of its properties.”

The corrected version should read as: “The objective of this research is to consider a class of models called FISSAR models and to establish some of its properties.”

The author regrets the inadvertent errors as he was unaware of the partial overlap with Boissy et al. work at the time of publication.