Likelihoodbased strategies for estimating unknown parameters and predicting missing data in the simultaneous autoregressive model We attempt a threestage 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 loglikelihood 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 loglikelihood 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 loglikelihood 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.

Generalizing the Theta method for automatic forecasting Abstract   The Theta method became popular due to its superior performance in the M3 forecasting competition. Since then, although it has been shown that Theta provides accurate forecasts for various types of data, being a solid benchmark to beat, limited research has been conducted to exploit its full potential and generalize its reach. This paper examines three extensions on Thetaxe2x80x99s framework to boost its performance. This includes (i) considering both linear and nonlinear trends, (ii) allowing to adjust the slope of such trends, and (iii) introducing a multiplicative expression of the underlying forecasting model along with the existing, additive one. The proposed modifications transform Theta into a generalized forecasting algorithm, suitable for automatic time series predictions. The proposed algorithm is evaluated using the series of the M, M3, and M4 competitions. Such an evaluation shows that the proposed approach produces more accurate forecasts than the original, classic Theta, both in terms of point forecasts and prediction intervals, and is also more accurate than other wellknown methods for yearly series.