Estimating an Autoregressive Current Effects Model of Sales Response When Observations Are Aggregated over Time: Least Squares versus Maximum Likelihood

1988 ◽  
Vol 25 (3) ◽  
pp. 301 ◽  
Author(s):  
Wilfried R. Vanhonacker
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Sales Response ◽  
Over Time

Estimating an Autoregressive Current Effects Model of Sales Response when Observations are Aggregated over Time: Least Squares versus Maximum Likelihood

1988 ◽  
Vol 25 (3) ◽  
pp. 301-307
Author(s):  
Wilfried R. Vanhonacker
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Serial Correlation ◽  
Mean Squared Error ◽  
Generalized Least Squares ◽  
Parameter Estimates ◽  
Squared Error ◽  
Positive Serial Correlation ◽  
Serial Correlation Coefficient ◽  
Over Time

Estimating autoregressive current effects models is not straightforward when observations are aggregated over time. The author evaluates a familiar iterative generalized least squares (IGLS) approach and contrasts it to a maximum likelihood (ML) approach. Analytic and numerical results suggest that (1) IGLS and ML provide good estimates for the response parameters in instances of positive serial correlation, (2) ML provides superior (in mean squared error) estimates for the serial correlation coefficient, and (3) IGLS might have difficulty in deriving parameter estimates in instances of negative serial correlation.

scholarly journals Validation and Comparison of Different Statistical Models for the Prediction of Water Main Pipe Breaks in a Municipal Network in Québec, Canada

2016 ◽  
Vol 29 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Sophie Duchesne ◽  
Babacar Toumbou ◽  
Jean-Pierre Villeneuve
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Method ◽  
Water Main ◽  
Pipe Replacement ◽  
The Impact ◽  
Over Time ◽  
Observation Period

In this study, three models for the simulation of the number of breaks in a water main network are presented and compared: linear regression, the Weibull-Exponential-Exponential (WEE), and the Weibull-Exponential-Exponential-Exponential (WEEE) models. These models were calibrated using a database of recorded breaks in a real water main network of a municipality in the province of Québec, for the observation period 1976 to 1996, with the least squares and the maximum likelihood methods. The ability of these models to predict breaks over time was then evaluated by comparing the predicted number of breaks for the years 1997 to 2007 with the observed breaks in the network over the same time period. Results show that if the period of observation is short (around 20 years), calibration of the WEE and WEEE models with the maximum likelihood method leads to estimates that are closer to the observations than when these models are calibrated with the least squares method. When the observation period is longer (around 30 years), the predictions obtained with the models calibrated using the maximum likelihood or the least squares methods are similar. However, the use of the maximum likelihood method for calibration is only possible when data for the occurrence of each break for each pipe of the network are available (a pipe being a homogeneous network segment between two adjacent street junctions). If this is not the case, a trend line will be sufficient to predict the number of breaks over time, though this type of curve does not allow to account for pipe replacement scenarios. If the only information available is the total number of breaks on the network each year, then the impact of replacement scenarios could be simulated with the WEE and WEEE models calibrated using the least squares method.

Identification of Structural Parameters in Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 428-438 ◽  
Author(s):  
Marc P. Mignolet ◽  
Chung-Chih Lin
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Structural Model ◽  
Structural Parameters ◽  
Model Parameters ◽  
Disk Model ◽  
Response Data ◽  
State Response ◽  
Bladed Disk ◽  
True Model

The present investigation focused on the estimation of the parameters of a structural model to represent “at best” a set of measurements of the steady state response of a mistuned bladed disk. The applicability of the least squares and maximum likelihood approaches to the identification of the bladed disk model from this data is first investigated. The advantages and drawbacks of these techniques motivate the introduction of a new mixed least squares-maximum likelihood formulation which is shown to recover well the true model parameters from noisy simulated response data.

Classification Based on Multivariate Repeated Measures with Time Effect on Mean Vector and an AR (1) Correlation Structure on the Repeated Measures

2005 ◽  
Vol 57 (1-2) ◽  
pp. 49-66 ◽  
Author(s):  
Anuradba Roy ◽  
Ravindra Khattree
Keyword(s):  
Maximum Likelihood ◽  
Repeated Measures ◽  
Likelihood Estimation ◽  
Covariance Matrices ◽  
Time Effect ◽  
Population Parameters ◽  
Time Effects ◽  
Mean Vectors ◽  
Mean Vector ◽  
Over Time

In repeated measures studies how observations change over time is often of prime interest. Modelling this time effect in the context of discrimination, is the objective of this article. We study the problem of classification with multiple q-variate observations with time effect on each individual. The covariance matrices as well as mean vectors are mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population parameters are provided.

WAVELET ESTIMATORS FOR LONG MEMORY IN STOCK MARKETS

2009 ◽  
Vol 12 (03) ◽  
pp. 297-317 ◽  
Author(s):  
ANOUAR BEN MABROUK ◽  
HEDI KORTAS ◽  
SAMIR BEN AMMOU
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Stock Returns ◽  
Long Memory ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Estimation Accuracy ◽  
Approximate Maximum Likelihood ◽  
Approximate Maximum Likelihood Estimator ◽  
Wavelet Estimators

In this paper, fractional integrating dynamics in the return and the volatility series of stock market indices are investigated. The investigation is conducted using wavelet ordinary least squares, wavelet weighted least squares and the approximate Maximum Likelihood estimator. It is shown that the long memory property in stock returns is approximately associated with emerging markets rather than developed ones while strong evidence of long range dependence is found for all volatility series. The relevance of the wavelet-based estimators, especially, the approximate Maximum Likelihood and the weighted least squares techniques is proved in terms of stability and estimation accuracy.

scholarly journals On the equivalence between total least squares and maximum likelihood PCA

2005 ◽  
Vol 544 (1-2) ◽  
pp. 254-267 ◽  
Author(s):  
M. Schuermans ◽  
I. Markovsky ◽  
Peter D. Wentzell ◽  
S. Van Huffel
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Total Least Squares
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