Fitting Weibull ACD Models to High Frequency Transactions Data: A Semi-parametric Approach based on Estimating Functions

Autoregressive conditional duration (ACD) models play an important role in financial modeling. This paper considers the estimation of the Weibull ACD model using a semi-parametric approach based on the theory of estimating functions (EF). We apply the EF and the maximum likelihood (ML) methods to a data set given in Tsay (2003, p203) to compare these two methods. It is shown that the EF approach is easier to apply in practice and gives better estimates than the MLE. Results show that the EF approach is compatible with the ML method in parameter estimation. Furthermore, the computation speed for the EF approach is much faster than for the MLE and therefore offers a significant reduction of the completion time.Volatility, Option pricing, Volatility of volatility, Forecasting

Modelling and forecasting with financial duration data using non-linear model

The class of autoregressive conditional duration (ACD) models plays an important role in modelling the duration data in economics and finance. This paper presents a non-linear model to allow the first four moments of the duration to depend nonlinearly on past information variables. Theoretically the model is more general than the linear ACD model. The proposed model is fitted to the data given by the 3534 transaction durations of IBM stock on five consecutive trading days. The fitted model is found to be comparable to the Weibull ACD model in terms of the in-sample and out-of-sample mean squared prediction errors and mean absolute forecast deviations. In addition, the Diebold-Mariano test shows that there are no significant differences in forecast ability for all models

Bond option pricing under the CKLS model

Consider the European call option written on a zero coupon bond. Suppose the call option has maturity T and strike price K while the bond has maturity S T . We propose a numerical method for evaluating the call option price under the Chan, Karolyi, Longstaff and Sanders (CKLS) model in which the increment of the short rate over a time interval of length dt , apart from being independent and stationary, is having the quadratic-normal distribution with mean zero and variance dt. The key steps in the numerical procedure include (i) the discretization of the CKLS model; (ii) the quadratic approximation of the time-T bond price as a function of the short rate rT at time T; and (iii) the application of recursive formulas to find the moments of r(t+dt) given the value of r(t). The numerical results thus found show that the option price decreases as the parameter in the CKLS model increases, and the variation of the option price is slight when the underlying distribution of the increment departs from the normal distribution

Efficient estimation in ZIP models with applications to count data

Estimating functions have been used in estimating parameters of many continuous time series models. However, this method has not been applied to models involving count data. In this paper, we use quadratic estimating functions (QEF) to derive estimators for the joint estimation of the conditional mean and variance parameters of count data models, specifically the basic zero-inflated Poisson (ZIP) model, ZIP regression model and integer-valued generalized autoregressive heteroscedastic model with ZIP conditional distribution. Results show that the estimators derived from QEF method, which uses information from combined estimating functions, is more informative than linear estimating functions (LEF) method that only uses information from component estimating functions. Finally, we also fit the real data sets using the ZIP models via QEF, LEF and maximum likelihood methods, and in so doing, demonstrate the superiority of the QEF method in practice

Predicting automobile insurance fraud using classical and machine learning models

Insurance fraud claims have become a major problem in the insurance industry. Several investigations have been carried out to eliminate negative impacts on the insurance industry as this immoral act has caused the loss of billions of dollars. In this paper, a comparative study was carried out to assess the performance of various classification models, namely logistic regression, neural network (NN), support vector machine (SVM), tree augmented naïve Bayes (NB), decision tree (DT), random forest (RF) and AdaBoost with different model settings for predicting automobile insurance fraud claims. Results reveal that the tree augmented NB outperformed other models based on several performance metrics with accuracy (79.35%), sensitivity (44.70%), misclassification rate (20.65%), area under curve (0.81) and Gini (0.62). In addition, the result shows that the AdaBoost algorithm can improve the classification performance of the decision tree. These findings are useful for insurance professionals to identify potential insurance fraud claim cases

Volatility modelling using range-based measures and weighted exogenous threshold CARR model

Three volatility measures including the squared returns and range based Parkinson and Garman Klass were applied to estimate the financial volatility. These measures are then fitted to conditional autoregressive range (CARR) models and its weighted exogenous threshold extensions using generalised Beta type two distribution. The daily All Ordinaries index is studied by fitting the three volatility measures to the two types of CARR models and compare their model performances. Results show that the Garman Klass measure fitted to weighted exogenous threshold CARR model gives the best in-sample model fit based on Akaike information criterion. Different levels of value-at-risk are also provided

CHANGE POINT DETECTION OF ROBUST INDIVIDUALS CONTROL CHART

Crucial part in the inference of industrial process change point detection is that once a suspected change point is detected, statistical test needs to be carried out to ensure the significance of the change. Conventional test statistics such as Maximum-Type testing method is very sensitive to outliers as the formulation of estimator is lack of robustness. In addition, oftentimes, evidence of larger shifts could be mistakenly downweighted or rejected stemming from these outliers and also due to the designated score function. The proposed robust individuals control chart adopting the HMT testing method is based on a well-motivated Huber score function, which appears to provide protection against this complication. Extensive numerical simulation studies were carried out to assess the performance of the proposed procedure with its counterparts.  Taking a real data set from industry, we illustrate the usefulness and applicability of the proposed chart in practice

Change point detection in process control with robust individuals control chart

It is crucial to realize when a process has changed and to what extent it has changed, then it would certainly ease the task. On occasion that practitioners could determine the time point of the change, they would have a smaller search window to pursue for the special cause. As a result, the special cause can be discovered quicker and the necessary actions to improve quality can be triggered sooner. In this paper, we had demonstrated the use of so-called exploratory data analysis robust modified individuals control chart incorporating the M-scale estimator and had made some comparisons to the existing charts. The proposed modified robust individuals control chart which incorporates the M-scale estimator in order to compute the process standard deviation offers substantial improvements over the existing median absolute deviation framework. With respect to the application in real data set, the proposed approach appears to perform better than the typical robust control chart, and outperforms other conventional charts particularly in the presence of contamination. Thus, it is for these reasons that the proposed modified robust individuals control chart is preferred especially when there is a possible existence of outliers in data collection process

Moment Properties And Quadratic Estimating Functions For Integer-Valued Time Series Models

Recently, there has been a growing interest in integer-valued volatility models. In this paper, using a martingale transformation, a general theorem on moment properties of a class of integer-valued volatility models is given with simpler proof. We show that the first two moments obtained in the recent literature are special cases. In addition, we also derive the closed form expressions of the kurtosis and skewness formula for the models. The results are very useful in understanding the behaviour of the process and in estimating the parameters of the models using quadratic estimating functions method. Specifically, we derive the optimal function of INGARCH(1,1) and obtain the estimated parameters of interest via simulation. We show that the performance of the quadratic estimating functions method is superior compared to maximum likelihood and least square methods. For illustration, we fit the INGARCH(1,1) on 108 monthly strike data from January 1994 to December 2002 from Jung et al. (2005)

On the speculative nature of cryptocurrencies: A study on Garman and Klass volatility measure

We propose to measure volatilities of 102 active cryptocurrencies using Garman and Klass (GK) volatility measures and model the measures using asymmetric bilinear Conditional Autoregressive Range (ABL-CARR) model. Results reveal volatility persistence and leverage effects which can improve the predictability of volatility, reduce risk and hence lessen the level of speculation in cryptocurrency market. We further relate volatility features for the top five cryptocurrencies to their time of development and transaction speed and recommend investors to distinguish between long-term or short-term speculation in their investment profile. © 2018 Elsevier Inc