Time series properties of the class of generalized first-order autoregressive processes with moving average errors

A new class of time series models known as Generalized Autoregressive of order one with first-order moving average errors has been introduced in order to reveal some hidden features of certain time series data. The variance and autocovariance of the process is derived in order to study the behaviour of the process. It is shown that in special cases these new results reduce to the standard ARMA results. Estimation of parameters based on the Whittle procedure is discussed. We illustrate the use of this class of model by using two examples

Approximate asymptotic variance-covariance matrix for the whittle estimators of GAR(1) parameters

Generalized Autoregressive (GAR) processes have been considered to model some features in time series. The Whittle's estimates have been investigated for the GAR(1) process by a simulation study by Shitan and Peiris (2008). This article derives approximate theoretical expressions for the enteries of the asymptotic variance-covariance matrix for those estimates of GAR(1) parameters. These results are supported by a simulation study

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

GARMA, HAR and rules of thumb for modelling realized volatility

This paper features an analysis of the relative effectiveness, in terms of the Adjusted R-Square, of a variety of methods of modelling realized volatility (RV), namely the use of Gegenbauer processes in Auto-Regressive Moving Average format, GARMA, as opposed to Heterogenous Auto-Regressive HAR models and simple rules of thumb. The analysis is applied to two data sets that feature the RV of the S&P500 index, as sampled at 5 min intervals, provided by the OxfordMan RV database. The GARMA model does perform slightly better than the HAR model, but both models are matched by a simple rule of thumb regression model based on the application of lags of squared, cubed and quartic, demeaned daily returns

Comparison of Alternative ACD Models via Density and Interval Forecasts: Evidence from the Australian Stock Market

In this paper a number of alternative ACD models are compared using a sample of data for three major companies traded on the Australian Stock Exchange. The comparison is performed by employing the methodology for evaluating density and interval forecasts, developed by Diebold, Gunther and Tay (1998) and Christoffersen (1998), respectively. Our main finding is that the generalized gamma and log-normal distributions for the error terms have similar performance and perform better that the exponential and Weibull distributions. Additionally, there seems to be no substantial difference between the standard ACD specification of Engle and Russel (1998) and the log-ACD specification of Bauwens and Giot (2000).ACD models, Density forecasts Acknowledgements: This paper forms part of an ARC Linkage Grant research project, ÃModelling stock market liquidity in Australia and the Asia Pacific RegionÓ. We are grateful to the Australian Research Council for financial support. The financial data has been graciously provided by the Securities Research Institute (SIRCA) which is our industry partner.

Finite Sample Properties of the QMLE for the Log-ACD Model: Application to Australian Stocks

This paper is concerned with the finite sample properties of the Quasi Maximum Likelihood Estimator (QMLE) of the Logarithmic Autoregressive Conditional Duration (Log-ACD) model. Although the distribution of the QMLE for the log-ACD model is unknown, it is an important issue as it is used widely for testing various market microstructure models and effects. Knowledge of the distribution of the QMLE is crucial for purposes of valid inference and diagnostic checking. This paper investigates the structural and statistical properties of the log-ACD model by establishing the relationship between the log-ACD model and the Autoregressive-Moving Average (ARMA) model. The theoretical results developed in the paper are evaluated using Monte Carlo experiments. The experimental results also provide insights into the finite sample properties of the log-ACD model under different distributional assumptions.Conditional duration, Asymmetry, ACD, Log-ACD, Monte Carlo simulation Acknowledgement: The authors are grateful for the financial support of the Australian Research Council.

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

In recent years fractionally differenced processes have received a great deal of attention due to their exibility in nancial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. Forestimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the rst step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the nite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory

Volatility and irregularity Capturing in stock price indices using time series Generative adversarial networks (TimeGAN)

This paper captures irregularities in financial time series data, particularly stock prices, in the presence of COVID-19 shock. We conjectured that jumps and irregularities are embedded in stock data due to the pandemic shock, which brings forth irregular trends in the time series data. We put forward that efficient and robust forecasting methods are needed to predict stock closing prices in the presence of the pandemic shock. This piece of information is helpful to investors as far as confidence risk and return boost are concerned. Generative adversarial networks of a time series nature are used to provide new ways of modeling and learning the proper and suitable distribution for the financial time series data under complex setups. Ideally, these traditional models are liable to producing high forecasting errors, and they need to be more robust to capture dependency structures and other stylized facts like volatility in stock markets. The TimeGAN model is used, effectively dealing with this risk of poor forecasts. Using the DAX stock index from January 2010 to November 2022, we trained the LSTM, GRU, WGAN, and TimeGAN models as benchmarks and forecasting errors were noted, and our TimeGAN outperformed them all as indicated by a small forecasting error.Comment: 36 page

Some statistical models for durations and their applications in finance

This paper considers a new class of time series models called Autoregressive Conditional Duration (ACD) models. Various statistical properties of this class of ACD models are given. A minimum mean square error (mmse) forecast function is obtained as it plays an important role in many practical applications. The theory is illustrated using a potential application based on financial data

Generalized moving average models and applications in high frequency data

This paper considers a new class of first order moving average type time series model with index δ (\u3e 0) to describe some hidden features of a time series. It is shown that this class of models provides a valid, simple solution to a new direction of time series modelling. In particular, for suitably chosen parameters (coefficient β and index δ) this type of models could be used to describe data with low or high frequency components. Various new results associated with this class are given in a general form. A simulation study is carried out to justify the theory. We justify the importance of this class of models in practice using a set of real time series data