• The Korean Journal of Applied Statistics
• /
• v.29 no.1
• /
• pp.1-12
• /
• 2016

Contrasted with the standard linear ARMA models, financial time series exhibits non-standard features such as fat-tails, non-normality, volatility clustering and asymmetries which are usually referred to as "stylized facts" in financial time series context (Terasvirta, 2009). We are accordingly led to ad hoc models (apart from ARMA) to accommodate stylized facts (Andersen et al., 2009). The paper aims to give a contemporary overview on financial and special time series models based on the recent literature and on the author's publications. Various models are illustrated including asymmetric models, integer valued models, multivariate models and high frequency models. Selected statistical issues on the models are discussed, bringing some perspectives to the future works in this area.

• Communications for Statistical Applications and Methods
• /
• v.17 no.1
• /
• pp.27-37
• /
• 2010

This article concerns the forecasting in binomial AR(p) models which is proposed by Wei$\ss$ (2009b) for time series of binomial counts. Our method extends to binomial AR(p) models a recent result by Jung and Tremayne (2006) for integer-valued autoregressive model of second order, INAR(2), with simple Poisson innovations. Forecasts are produced by conditional median which gives 'coherent' forecasts, and we estimate the forecast distributions of future values of binomial AR(p) models by means of a Monte Carlo method allowing for parameter uncertainty. Model parameters are estimated by the method of moments and estimated standard errors are calculated by means of block of block bootstrap. The method is fitted to log data set used in Wei$\ss$ (2009b).

• Communications for Statistical Applications and Methods
• /
• v.17 no.3
• /
• pp.441-450
• /
• 2010

In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by McKenzie (1985) and is extended to a higher order by $Wei{\ss}$(2009). Since the binomial autoregressive model is a Markov chain, we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model. We will discuss how to compute the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$ when T periods are used in fitting. Then we obtain the maximum likelihood estimator of binomial autoregressive model and use it to derive the maximum likelihood estimator of the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$. The methodology is illustrated by applying it to a data set previously analyzed by $Wei{\ss}$(2009).

• Journal of the military operations research society of Korea
• /
• v.4 no.1
• /
• pp.113-123
• /
• 1978

Consider a series system of two units, named 1 and 2, respectively. Two units are observed at the beginning of discrete time periods t=0,1,2, $cdots$ and classified as being in one of a countable number of states. Let (i, r) be a state of the system at time t, when the state of unit 1 is i and state of unit 2 is r at time t, Under some conditions, the opportunistic replacement policy that minimizes the expected total discounted cost or the average cost of maintenance is shown to be characterized by the control limits $i^{*}(r)$ (a function of r) and $r^{*}(i)$ (a function of i) : (a) in observed state (i, r), the optimal policy for unit 1 is to replace if $i{\ge}i^{*}(r)$ and no action otherwise; (b) in observed state (i, r), the optimal policy for unit 2 is to replace if $r{\ge}r^{*}(i)$ and no action otherwise. In addition, this paper also develops optimal policy in the finite time horizon case, where time horizon is fixed or a finite integer valued r.v. with known pmf.

• Communications for Statistical Applications and Methods
• /
• v.27 no.4
• /
• pp.487-500
• /
• 2020

Insurers face increasing demands for cyber liability; entailed in part by a variety of new forms of risk of data breaches. As data breach occurrences develop, our understanding of the volatility in data breach counts has also become important as well as its expected occurrences. Volatility clustering, the tendency of large changes in a random variable to cluster together in time, are frequently observed in many financial asset prices, asset returns, and it is questioned whether the volatility of data breach occurrences are also clustered in time. We now present volatility analysis based on INGARCH models, i.e., integer-valued generalized autoregressive conditional heteroskedasticity time series model for frequency counts due to data breaches. Using the INGARCH(1, 1) model with data breach samples, we show evidence of temporal volatility clustering for data breaches. In addition, we present that the firms' volatilities are correlated between some they belong to and that such a clustering effect remains even after excluding the effect of financial covariates such as the VIX and the stock return of S&P500 that have their own volatility clustering.

• The Korean Journal of Applied Statistics
• /
• v.18 no.3
• /
• pp.639-654
• /
• 2005

The Lee and Carter method has widely used to forecast mortality because of the simple structure of model and the stable forecasting. The Lee and Carter method, however, also has limitations. The assumption of the rate of decline in mortality at each age remaining invariant over time has been violated in several decades. And, there is no way to include covariates in the model for better forecasts. Here we introduce Park, Choi and Kim method to make up for Lee and Carter's weak points by using two random processes. We discuss structural features of two methods. furthermore, for each method, we forecast life expectancy for 2005 to 2050 using South Korea data and compare the results.