Modelling non-stationary annual maximum flood heights in the lower Limpopo River basin of Mozambique

Maposa, Daniel; Cochran, James J.; Lesaoana, Maseka

doi:10.4102/jamba.v8i1.185

Cited by 13 publications

(15 citation statements)

References 13 publications

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“…Furthermore, since the fundamental approach of this study is on the use of extreme value statistics using the block maxima, only the annual maximum value for each year was recorded and plotted in Figure 1. It is assumed that these AM1 data series are independent and identically distributed (iid) since they are blocked by years [9][10][11][12]. Similarly, it is also assumed that the annual maxima moving sums are also iid.…”

Section: Results and Conclusionmentioning

confidence: 99%

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Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood Heights Time Series Models in the Lower Limpopo River Basin of Mozambique

Maposa¹

2019

Recent Advances in Flood Risk Management

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In this paper we fit a generalised extreme value (GEV) distribution to annual maxima flood heights time series models: annual daily maxima (AM1), annual maxima of 2 days (AM2), annual maxima of 5 days (AM5) and annual maxima of 10 days (AM10). The study is aimed at identifying suitable annual maxima moving sums that can be used to best model extreme flood heights in the lower Limpopo River basin of Mozambique, and hence construct flood frequency tables. The study established that models AM5 and AM10 were suitable annual maxima time series models for Chokwe and Sicacate, respectively. This study also revealed that the year 2000 flood height was a very rare extreme event. Flood frequency tables were constructed for the two sites Chokwe and Sicacate in the lower Limpopo River basin of Mozambique and these tables can be used to predict the return periods and their corresponding return levels at the sites and their neighbourhood. It is our hope that these long term forecasts will complement the short term flood forecasting and early warning systems in the basin in reducing the associated risk and mitigating the deleterious impacts of these floods on humans and property. Recent Advances in Flood Risk Management 2The combination of these two approaches is hoped to go a long way towards disaster reduction and mitigation efforts in the basin.

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Section: Results and Conclusionmentioning

confidence: 99%

“…The approach used in this study is block maxima. In hydrological studies, when sample sizes are large it is natural to block observations by years [9,10].…”

Section: Study Sites Data and Block Maxima Moving Sumsmentioning

confidence: 99%

Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood Heights Time Series Models in the Lower Limpopo River Basin of Mozambique

Maposa¹

2019

Recent Advances in Flood Risk Management

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“…. , X n constitute five day maximum losses that are distributed with the GEVD in model ( 5), Maposa et al (2016) showed that in period t, r t follows GEVD(µ(t), ξ, σ) and Bee (2012) emphasised that µ(t) = µ 0 + µ t 1 for a linear variation in location with an intercept parameter µ 0 and a slope parameter µ 1 , that expresses the rate of change in daily losses. We finally express our proposed hybrid for extreme return losses as r t ∼ SARI MA(p, d, q) × (P, D, Q) − MS(k) − EGARCH(p, q) − GEVD(xi, µ t , σ t ).…”

Section: Methodsmentioning

confidence: 99%

“…According to Maposa et al (2016), a 100(1 − α)% Bayesian credible set C (or, in particular, credible interval) is a subset of the space parameter Θ, such that…”

Section: Bayesian Markov-chain-monte-carlo Frameworkmentioning

confidence: 99%

Predicting Extreme Daily Regime Shifts in Financial Time Series Exchange/Johannesburg Stock Exchange—All Share Index

Makatjane

Moroke

2021

IJFS

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During the past decades, seasonal autoregressive integrated moving average (SARIMA) had become one of a prevalent linear models in time series and forecasting. Empirical research advocated that forecasting with non-linear models can be an encouraging alternative to traditional linear models. Linear models are often compared to non-linear models with mixed conclusions in terms of superiority in forecasting performance. Therefore, the aim of this study is to build an early warning system (EWS) model for extreme daily losses for financial stock markets. A logistic model tree (LMT) is used in collaboration with a seasonal autoregressive integrated moving average-Markov-Switching exponential generalised autoregressive conditional heteroscedasticity-generalised extreme value distribution (SARIMA-MS-EGARCH-GEVD) estimates. A time series of the study is a five-day financial time series exchange/Johannesburg stock exchange-all share index (FTSE/JSE-ALSI) for the period of 4 January 2010 to 31 July 2020. The study is set into a two-stage framework. Firstly, SARIMA model is fitted to stock returns in order to obtain independently and identically distributed (i.i.d) residuals and fit the MS(k)-EGARCH(p,q)-GEVD to i.i.d residuals; while, in the second stage, we set-up an EWS model. The results of the estimated MS(2)-EGARCH(1,1) -GEVD revealed that the conditional distribution of returns is highly volatile giving the expected duration to approximately 36 months and 4 days in regime one and 58 months and 2 days in regime two. We further found that any degree losses above 25% implies that there will be no further losses. Using the seven statistical loss functions, the estimated SARIMA(2,1,0)×(2,1,0)240−MS(2)−EGARCH(1,1)−GEVD proved to be the most appropriate model for predicting extreme regimes losses as it was ranked at 71%. Finally, the results of EWS model exhibit reasonably an overall performance of 98%, sensitivity of 79.89% and specificity of 98.40% respectively. The model further indicated a success classification rate of 89% and a prediction rate of 95%. This is a promising technique for EWS. The findings also confirmed 63% and 51% of extreme losses for both training sample and validation sample to be correctly classified. The findings of this study are useful for decision makers and financial sector for future use and planning. Furthermore, a base for future researchers for conducting studies on emerging markets, have been contributed. These results are also important to risk managers and and investors.

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“…A substantial part of the variability in the data can probably be explained by a systematic variation in rainfall over the years. One way of capturing this trend is by allowing the GEVD location and scale parameters to vary with time [40]. From Figure 2 a simple linear trend in time seems plausible for our annual maximum rainfall X t , and we can use the model…”

Section: Non-stationary Gevd Modelling Of Annual Block Maxima Rainfall Datamentioning

confidence: 99%

Modelling Long-Term Monthly Rainfall Variability in Selected Provinces of South Africa: Trend and Extreme Value Analysis Approaches

Masingi

Maposa

2021

Hydrology

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Extreme rainfall events have made significant damages to properties, public infrastructure and agriculture in some provinces of South Africa notably in KwaZulu-Natal and Gauteng among others. The general global increase in the frequency and intensity of extreme precipitation events in recent years is raising a concern that human activities might be heavily disturbed. This study attempts to model long-term monthly rainfall variability in the selected provinces of South Africa using various statistical techniques. The study investigates the normality and stationarity of the underlying distribution of the whole body of rainfall data for each selected province, the long-term trends of the rainfall data and the extreme value distributions which model the tails of the rainfall distribution data. These approaches were meant to help achieve the broader purpose of this study of investigating the long-term rainfall trends, stationarity of the rainfall distributions and extreme value distributions of monthly rainfall records in the selected provinces of South Africa in this era of climate change. The five provinces considered in this study are Eastern Cape, Gauteng, KwaZulu-Natal, Limpopo and Mpumalanga. The findings revealed that the long-term rainfall distribution for all the selected provinces does not come from a normal distribution. Furthermore, the monthly rainfall data distribution for the majority of the provinces is not stationary. The paper discusses the modelling of monthly rainfall extremes using the non-stationary generalised extreme value distribution (GEVD) which falls under the block maxima extreme value theory (EVT) approach. The maximum likelihood estimation method was used to obtain the estimates of the parameters. The stationary GEVD was found as the best distribution model for Eastern Cape, Gauteng, and KwaZulu-Natal provinces. Furthermore, model fitting supported non-stationary GEVD model for maximum monthly rainfall with nonlinear quadratic trend in the location parameter and a linear trend in the scale parameter for Limpopo, while in Mpumalanga the non-stationary GEVD model with a nonlinear quadratic trend in the scale parameter and no variation in the location parameter fitted well to the monthly rainfall data. The negative values of the shape parameters for Eastern Cape and Mpumalanga suggest that the data follow the Weibull distribution class, while the positive values of the shape parameters for Gauteng, KwaZulu-Natal and Limpopo suggest that the data follow the Fréchet distribution class. The findings from this paper could give information that can assist decision makers establish strategies for proper planning of agriculture, infrastructure, drainage system and other water resource applications in the South African provinces.

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Modelling non-stationary annual maximum flood heights in the lower Limpopo River basin of Mozambique

Cited by 13 publications

References 13 publications

Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood Heights Time Series Models in the Lower Limpopo River Basin of Mozambique

Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood Heights Time Series Models in the Lower Limpopo River Basin of Mozambique

Predicting Extreme Daily Regime Shifts in Financial Time Series Exchange/Johannesburg Stock Exchange—All Share Index

Modelling Long-Term Monthly Rainfall Variability in Selected Provinces of South Africa: Trend and Extreme Value Analysis Approaches

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