We examine the joint time series of option prices and returns on the S&P 500 index and a set of stocks drawn from the index with a new arbitrage-free multivariate stochastic volatility model that captures a market effect. The preliminary results show that the new model fits well for all the marginal time series for different periods of time. The price of volatility risk is estimated from option...

Time series data measure phenomena when there are dependencies over time between prior and current values of the observations. This chapter provides a brief introduction to the standard (linear autoregressive moving-average) time series models including how such models are identified and fitted to the data. A review of more generalized models follows. This includes bilinear models which are use...

Overview In contrast to the classical linear regression model, in which the components of the dependent variable vector y are not identically distributed (because its mean vector varies with the regressors) but may be independently distributed, time series models have dependent variables which may be identically distributed, but are typically not independent across ovbservations. Such models ar...

1 Trend and Cycle Decomposition y t = t + t where y t is an n 1 vector and t and t represent trend and cycle components respectively. This decomposition into components is not unique. Beveridge and Nelson (1981) and Stock and Watson (1988) derive the following decomposition: y t = C(L)" t = C(1)" t + (1 L)C (L)" t Integrating up gives: y t = C(1) 1 X i=0 " ti | {z } + C (L)" t | {z } trend cycl...

We review regression models for count time series. We discuss the approach which is based on generalized linear models and the class of integer autoregressive processes. The generalized linear models framework provides convenient tools for implementing model fitting and prediction using standard software. Furthermore, this approach provides a natural extension to the traditional ARMA methodolog...

The point-valued time series (PTS) is simply about one value in each or period of the data, but when data have two values at time, suitable called interval-valued (ITS). An example ITS daily close and open stock prices. If are typed linguistic for example, “low increase”, “medium increase” “high a fuzzy-valued being well-known as fuzzy (FTS). aim this study to compare PTS FTS models forecasting...