Predicting Rainfall in the Context of Rainfall Derivatives Using Genetic Programming

Rainfall is one of the most challenging variables to predict, as it exhibits very unique characteristics that do not exist in other time series data. Moreover, rainfall is a major component and is essential for applications that surround water resource planning. In particular, this paper is interested in the prediction of rainfall for rainfall derivatives. Currently in the rainfall derivatives literature, the process of predicting rainfall is dominated by statistical models, namely using a Markov-chain extended with rainfall prediction (MCRP). In this paper we outline a new methodology to be carried out by predicting rainfall with Genetic Programming (GP). This is the first time in the literature that GP is used within the context of rainfall derivatives. We have created a new tailored GP to this problem domain and we compare the performance of the GP and MCRP on 21 different data sets of cities across Europe and report the results. The goal is to see whether GP can outperform MCRP, which acts as a benchmark. Results indicate that in general GP significantly outperforms MCRP, which is the dominant approach in the literature

A Comparison between Wavelet Networks and Genetic Programming in the Context of Temperature Derivatives

The purpose of this study is to develop a model that accurately describes the dynamics of the daily average temperature in the context of weather derivatives pricing. More precisely we compare two state of the art machine learning algorithms, namely wavelet networks and genetic programming, against the classic linear approaches widely used in the pricing of temperature derivatives in the financial weather market and against various machine learning benchmark models such as neural networks, radial basis functions and support vector regression. The accuracy of the valuation process depends on the accuracy of the temperature forecasts. Our proposed models are evaluated and compared in-sample and out-of-sample in various locations where weather derivatives are traded. Furthermore, we expand our analysis by examining the stability of the forecasting models relative to the forecasting horizon. Our findings suggest that the proposed nonlinear methods significantly outperform the alternative linear models, with wavelet networks ranking first, and can be used for accurate weather derivative pricing in the weather market

New Genetic Programming Methods for Rainfall Prediction and Rainfall Derivatives Pricing

Rainfall derivatives is a part of an umbrella concept of weather derivatives, whereby the underlying weather variable determines the value of derivative, in our case the rainfall. These financial contracts are currently in their infancy as they have started trading on the Chicago Mercantile Exchange (CME) since 2011. Such contracts are very useful for investors or trading firms who wish to hedge against the direct or indirect adverse effects of the rainfall. The first crucial problem to focus on in this thesis is the prediction of the level of rainfall. In order to predict this, two techniques are routinely used. The first most commonly used approach is Markov chain extended with rainfall prediction. The second approach is Poisson-cluster model. Both techniques have some weakness in their predictive powers for rainfall data. More specifically, a large number of rainfall pathways obtained from these techniques are not representative of future rainfall levels. Additionally, the predictions are heavily influenced by the prior information, leading to future rainfall levels being the average of previously observed values. This motivates us to develop a new algorithm to the problem domain, based on Genetic Programming (GP), to improve the prediction of the underlying variable rainfall. GP is capable of producing white box (interpretable, as opposed to black box) models, which allows us to probe the models produced. Moreover, we can capture nonlinear and unexpected patterns in the data without making any strict assumptions regarding the data. The daily rainfall data represents some difficulties for GP. The difficulties include the data value being non-negative and discontinuous on the real time line. Moreover, the rainfall data consists of high volatilities and low seasonal time series. This makes the rainfall derivatives much more challenging to deal with than other weather contracts such as temperature or wind. However, GP does not perform well when it is applied directly on the daily rainfall data. We thus propose a data transformation method that improves GP's predictive power. The transformation works by accumulating the daily rainfall amounts into accumulated amounts with a sliding window. To evaluate the performance, we compare the prediction accuracy obtained by GP against the most currently used approach in rainfall derivatives, and six other machine learning algorithms. They are compared on 42 different data sets collected from different cities across the USA and Europe. We discover that GP is able to predict rainfall more accurately than the most currently used approaches in the literature and comparably to other machine learning methods. However, we find that the equations generated by GP are not able to take into account the volatilities and extreme periods of wet and dry rainfall. Thus, we propose decomposing the problem of rainfall into 'sub problems' for GP to solve. We decompose the time series of rainfall by creating a partition to represent a selected range of the total rainfall amounts, where each partition is modelled by a separate equation from GP. We use a Genetic Algorithm to assist with the partitioning of data. We find that through the decomposition of the data, we are able to predict the underlying data better than all machine learning benchmark methods. Moreover, GP is able to provide a better representation of the extreme periods in the rainfall time series. The natural progression is to price rainfall futures contracts from rainfall prediction. Unlike other pricing domains in the trading market, there is no generally recognised pricing framework used within the literature. Much of this is due to weather derivatives (including rainfall derivatives) existing in an incomplete market, where the existing and well-studied pricing methods cannot be directly applied. There are two well-known techniques for pricing, the first is through indifference pricing and the second is through arbitrage free pricing. One of the requirements for pricing is knowing the level of risk or uncertainty that exists within the market. This allows for a contract price free of arbitrage. GP can be used to price derivatives, but the risk cannot be directly estimated. To estimate the risk, we must calculate a density of proposed rainfall values from a single GP equation, in order to calculate the most probable outcome. We propose three methods to achieve the required results. The first is through the procedure of sampling many different equations and extrapolating a density from the best of each generation over multiple runs. The second proposal builds on the first considering contract-specific equations, rather than a single equation explaining all contracts before extrapolating a density. The third method is the proposition of GP evolving and creating a collection of stochastic equations for pricing rainfall derivatives. We find that GP is a suitable method for pricing and both proposed methods are able to produce good pricing results. Our first and second methods are capable of pricing closer to the rainfall futures prices given by the CME. Moreover, we find that our third method reproduces the actual rainfall for the specified period of interest more accurately

Feature Engineering for Improving Financial Derivatives-based Rainfall Prediction

Rainfall is one of the most challenging variables to predict, as it exhibits very unique characteristics that do not exist in other time series data. Moreover, rainfall is a major component and is essential for applications that surround water resource planning. In particular, this paper is interested in extending previous work carried out on the prediction of rainfall using Genetic Programming (GP) for rainfall derivatives. Currently in the rainfall derivatives literature, the process of predicting rainfall is dominated by statistical models, namely using a Markov-chain extended with rainfall prediction (MCRP). In this paper we further extend our new methodology by looking at the effect of feature engineering on the rainfall prediction process. Feature engineering will allow us to extract additional information from the data variables created. By incorporating feature engineering techniques we look to further tailor our GP to the problem domain and we compare the performance of the previous GP, which previously statistically outperformed MCRP, against our new GP using feature engineering on 21 different data sets of cities across Europe and report the results. The goal is to see whether GP can outperform its predecessor without extra features, which acts as a benchmark. Results indicate that in general GP using extra features significantly outperforms a GP without the use of extra features

A Genetic Decomposition Algorithm for Predicting Rainfall within Financial Weather Derivatives

Regression problems provide some of the most challenging research opportunities, where the predictions of such domains are critical to a specific application. Problem domains that exhibit large variability and are of chaotic nature are the most challenging to predict. Rainfall being a prime example, as it exhibits very unique characteristics that do not exist in other time series data. Moreover, rainfall is essential for applications that surround financial securities such as rainfall derivatives. This paper is interested in creating a new methodology for increasing the predictive accuracy of rainfall within the problem domain of rainfall derivatives. Currently, the process of predicting rainfall within rainfall derivatives is dominated by statistical models, namely Markov-chain extended with rainfall prediction (MCRP). In this paper, we propose a novel algorithm for decomposing rainfall, which is a hybrid Genetic Programming/Genetic Algorithm (GP/GA) algorithm. Hence, the overall problem becomes easier to solve. We compare the performance of our hybrid GP/GA, against MCRP, Radial Basis Function and GP without decomposition. We aim to show the effectiveness that a decomposition algorithm can have on the problem domain. Results show that in general decomposition has a very positive effect by statistically outperforming GP without decomposition and MCRP

Stochastic model genetic programming: Deriving pricing equations for rainfall weather derivatives

Rainfall derivatives are in their infancy since starting trading on the Chicago Mercantile Exchange (CME) in 2011. Being a relatively new class of financial instruments there is no generally recognised pricing framework used within the literature. In this paper, we propose a novel Genetic Programming (GP) algorithm for pricing contracts. Our novel algorithm, which is called Stochastic Model GP (SMGP), is able to generate and evolve stochastic equations of rainfall, which allows us to probabilistically transform rainfall predictions from the risky world to the risk-neutral world. In order to achieve this, SMGP's representation allows its individuals to comprise of two weighted parts, namely a seasonal component and an autoregressive component. To create the stochastic nature of an equation for each SMGP individual, we estimate the weights by using a probabilistic approach. We evaluate the models produced by SMGP in terms of rainfall predictive accuracy and in terms of pricing performance on 42 cities from Europe and the USA. We compare SMGP to 8 methods: its predecessor DGP, 5 well-known machine learning methods (M5 Rules, M5 Model trees, k-Nearest Neighbors, Support Vector Regression, Radial Basis Function), and two statistical methods, namely AutoRegressive Integrated Moving Average (ARIMA) and Monte Carlo Rainfall Prediction (MCRP). Results show that the proposed algorithm is able to statistically outperform all other algorithms

Spectrometer Scan Mechanism for Encountering Jovian Orbit Trojan Asteroids

This paper describes the design, testing, and lessons learned during the development of the Lucy Ralph (L'Ralph) Scan Mirror System (SMS), composed of the Scan Mirror Mechanism (SMM), Differential Position Sensor System (DPSS) and Mechanism Control Electronics (MCE). The L'Ralph SMS evolved from the Advanced Topographic Laser Altimeter System (ATLAS) Beam Steering Mechanism (BSM), so design comparisons will be made. Lucy is scheduled to launch in October 2021, embarking upon a 12-year mission to make close range encounters in 2025 and 2033 with seven Trojan asteroids and one main belt asteroid that are within the Jovian orbit. The L'Ralph instrument is based upon the New Horizons Ralph instrument, which is a panchromatic and color visible imager and infrared spectroscopic mapper that slewed the spacecraft for imaging. The L'Ralph SMM is to provide scanning for imaging to eliminate the need to slew the spacecraft. One purpose of this paper is to gain understanding of the reasoning behind some of the design features as compared with the ATLAS BSM. We will identify similarities and differences between the ATLAS BSM and the L'Ralph SMM that resulted from the latter's unique requirements. Another purpose of this paper is to focus upon "Lessons Learned" that came about during the development of the L'Ralph SMM and its MCE, both mechanism engineering issues and solutions as well as Ground Support Equipment (GSE) issues and solutions that came about during the validation of requirements process. At the time of this writing, the L'Ralph SMM has been flight qualified and delivered to the project

Decomposition Genetic Programming: An Extensive Evaluation on Rainfall Prediction in the Context of Weather Derivatives

Regression problems provide some of the most challenging research opportunities in the area of machine learning, where the predictions of some target variables are critical to a specific application. Rainfall is a prime example, as it exhibits unique characteristics of high volatility and chaotic patterns that do not exist in other time series data. Moreover, rainfall is essential for applications that surround financial securities, such as rainfall derivatives. This paper extensively evaluates a novel algorithm called Decomposition Genetic Programming (DGP), which is an algorithm that decomposes the problem of rainfall into subproblems. Decomposition allows the GP to focus on each subproblem, before combining back into the full problem. The GP does this by having a separate regression equation for each subproblem, based on the level of rainfall. As we turn our attention to subproblems, this reduces the difficulty when dealing with data sets with high volatility and extreme rainfall values, since these values can be focused on independently. We extensively evaluate our algorithm on 42 cities from Europe and the USA, and compare its performance to the current state-of-the-art (Markov chain extended with rainfall prediction), and six other popular machine learning algorithms (Genetic Programming without decomposition, Support Vector Regression, Radial Basis Neural Networks, M5 Rules, M5 Model trees, and k-Nearest Neighbours). Results show that the DGP is able to consistently and significantly outperform all other algorithms. Lastly, another contribution of this work is to discuss the effect that DGP has had on the coverage of the rainfall predictions and whether it shows robust performance across different climates

An extensive evaluation of seven machine learning methods for rainfall prediction in weather derivatives

Regression problems provide some of the most challenging research opportunities in the area of machine learning, and more broadly intelligent systems, where the predictions of some target variables are critical to a specific application. Rainfall is a prime example, as it exhibits unique characteristics of high volatility and chaotic patterns that do not exist in other time series data. This work’s main impact is to show the benefit machine learning algorithms, and more broadly intelligent systems have over the current state-of-the-art techniques for rainfall prediction within rainfall derivatives. We apply and compare the predictive performance of the current state-of-the-art (Markov chain extended with rainfall prediction) and six other popular machine learning algorithms, namely: Genetic Programming, Support Vector Regression, Radial Basis Neural Networks, M5 Rules, M5 Model trees, and k-Nearest Neighbours. To assist in the extensive evaluation, we run tests using the rainfall time series across data sets for 42 cities, with very diverse climatic features. This thorough examination shows that the machine learning methods are able to outperform the current state-of-the-art. Another contribution of this work is to detect correlations between different climates and predictive accuracy. Thus, these results show the positive effect that machine learning-based intelligent systems have for predicting rainfall based on predictive accuracy and with minimal correlations existing across climates