Likelihood-based strategies for estimating unknown parameters and predicting missing data in the simultaneous autoregressive model

Takafumi Kato ()
Additional contact information
Takafumi Kato: Nagoya University

Journal of Geographical Systems, 2020, vol. 22, issue 1, No 7, 143-176

Abstract: Abstract We attempt a three-stage comparison of several strategies for estimating parameters and predicting data in the simultaneous autoregressive model, which is a regression model with spatial autocorrelation in the disturbance between locations as the unit of observation. These strategies differ according to the formulation of the log-likelihood function containing a parametric weight matrix. In the first stage, a chain of logical reasoning is used to obtain theoretical findings by assuming that the data generating model and the data fitting model coincide. We consider the possibility that a subset of locations may be included in neither the parameter estimation nor the data prediction. In the second stage, a series of Monte Carlo experiments are conducted to supplement the theoretical comparison by considering also a mismatch between the two models. The prevalent strategy is defined as an approach that is not based on the exact log-likelihood function, regardless of the setting. The use of this strategy indicates that the parameter estimators do not reflect the mutual connection between all the locations included in the prediction. In the third stage, an empirical comparison is made to confirm the findings from the experimental comparison by using data observed in the real world. We conclude that the reasonable choice is not the prevalent strategy, but a strategy that can be defined as an approach based on the exact log-likelihood function, depending on the setting. The reasonable strategy tailors the parameter estimators to suit the mutual connection between all the locations included in the prediction.

Keywords: Conditional autoregressive model; Correlation function; Maximum likelihood; Simultaneous autoregressive model; Weight matrix (search for similar items in EconPapers)
JEL-codes: C13 C21 C53 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10109-019-00316-z Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:jgeosy:v:22:y:2020:i:1:d:10.1007_s10109-019-00316-z

Ordering information: This journal article can be ordered from
http://www.springer. ... ce/journal/10109/PS2

DOI: 10.1007/s10109-019-00316-z

Access Statistics for this article

Journal of Geographical Systems is currently edited by Manfred M. Fischer and Antonio Páez

More articles in Journal of Geographical Systems from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().