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

Applications of recursive estimation methods in statistical process control

In recent years there has been a growing interest in recursive estimation techniques as applied to statistical process control (SPC). In cases where prior information about the processes are available, it is shown that procedures based on the “optimal” smoothing can be superior to the classical procedures like Shewhart’s CUSUM control charts (see, for instance, Thavaneswaran, McPherson and Abraham (1998)). This paper reviews the recursive algorithms based on EWMA (exponentially weighted moving average), DLM (dynamic linear modeling), KF (Kalman filtering) and OS (optimal smoothing) in statistical process control with correlated data. We also discuss various relationships among the asymptotic mean square errors (MSE) of these procedures in SPC

Forecasting the Volatility of Cryptocurrencies in the Presence of COVID-19 with the State Space Model and Kalman Filter

During the COVID-19 pandemic, cryptocurrency prices showed abnormal volatility that attracted the participation of many investors. Studying the behaviour of volatility for the prices of cryptocurrency is an interesting problem to be investigated. This research implements the state space model framework for volatility incorporating the Kalman filter. This method directly forecasts the conditional volatility of five cryptocurrency prices (Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), Litecoin (LTC) and Bitcoin Cash (BCH)) for 10,000 consecutive hours, i.e., approximately 417 days during the COVID-19 pandemic from 26 February 2020, 00:00 h until 18 April 2021, 00:00 h. The performance of this model is compared to the GARCH (1,1) model and the neural network autoregressive (NNAR) based on root mean square error (RMSE), mean absolute error (MAE) and the volatility plot. The autocorrelation function plot, histogram and the residuals plot are used to examine the model adequacy. Among the three models, the state space model gives the best fit. The state space model gives the narrowest confidence interval of volatility and value-at-risk forecasts among the three models

Measures of kurtosis and skewness of INGARCH model

Recently there has been a growing interest in time series of counts/integer-valued time series. The time series under the hypothesis of homogeneous variance becomes unrealistic in many situations because the variance tend to change with level. Important models such as ACP (autoregressive conditional Poisson ) models and integer valued GARCH models have been proposed in the literature. Ghahramani and Thavaneswaran [1] studied the moment properties of ACP models using martingale transformation. However the forecasting for count process has not been studied in the literature. Using a martingale transformation, Thavaneswaran et al. [2] studied the volatility forecasts for GARCH models. In this paper, first we derive closed form expressions for skewness and kurtosis for count processes via martingale transformation then we study the joint forecasts for integer-valued count models with errors following Poisson