Closure to “Comparison of Two Nonparametric Alternatives for Stochastic Generation of Monthly Rainfall” by R. Srikanthan, A. Sharma, and T. A. McMahon

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

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Comparison of methods for filling in gaps in monthly rainfall series in arid regions

International Journal of Climatology ◽

10.1002/joc.7219 ◽

2021 ◽

Author(s):

Zeinab Abu Romman ◽

Jawad Al‐bakri ◽

Mustafa Al Kuisi

Keyword(s):

Arid Regions ◽

Monthly Rainfall ◽

Rainfall Series ◽

Comparison Of Methods

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A Test for Functional Form Against Nonparametric Alternatives

Econometric Theory ◽

10.1017/s0266466600013165 ◽

1992 ◽

Vol 8 (4) ◽

pp. 452-475 ◽

Cited By ~ 72

Author(s):

Jeffrey M. Wooldridge

Keyword(s):

Alternative Model ◽

Regression Models ◽

Functional Form ◽

Parametric Model ◽

Finite Sample ◽

Test Statistic ◽

Sieve Estimation ◽

Finite Sample Properties ◽

Standard Normal ◽

Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

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SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Atmosphere ◽

10.3390/atmos11060602 ◽

2020 ◽

Vol 11 (6) ◽

pp. 602

Author(s):

Luisa Martínez-Acosta ◽

Juan Pablo Medrano-Barboza ◽

Álvaro López-Ramos ◽

John Freddy Remolina López ◽

Álvaro Alberto López-Lambraño

Keyword(s):

Time Series ◽

Water Resources ◽

Autocorrelation Function ◽

Information Criterion ◽

Monthly Rainfall ◽

Statistical Characteristics ◽

Rainfall Time Series ◽

River Watershed ◽

Statistical Measures ◽

Sarima Models

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

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