Abstract: The paper evaluates several hundred one-day-ahead
VaR forecasting models in the time period between the years 2004
and 2009 on data from six world stock indices - DJI, GSPC, IXIC,
FTSE, GDAXI and N225. The models model mean using the ARMA
processes with up to two lags and variance with one of GARCH,
EGARCH or TARCH processes with up to two lags. The models are
estimated on the data from the in-sample period and their forecasting
accuracy is evaluated on the out-of-sample data, which are more
volatile. The main aim of the paper is to test whether a model
estimated on data with lower volatility can be used in periods with
higher volatility. The evaluation is based on the conditional coverage
test and is performed on each stock index separately. The primary
result of the paper is that the volatility is best modelled using a
GARCH process and that an ARMA process pattern cannot be found
in analyzed time series.
Abstract: This paper studies ruin probabilities in two discrete-time
risk models with premiums, claims and rates of interest modelled by
three autoregressive moving average processes. Generalized Lundberg
inequalities for ruin probabilities are derived by using recursive
technique. A numerical example is given to illustrate the applications
of these probability inequalities.
Abstract: The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL0). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL1) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL0) and (ARL1) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL1).