When variables in time series context are non-negative, such as for volatility, survival
time or wave heights, a multiplicative autoregressive model of the type Xt = Xα
t−1Vt ,
0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper,
we study the properties of such models and propose methods for parameter estimation.
Explicit solutions of the model are obtained in the case of gamma marginal distribution
Description:
Statistics and Probability Letters 82 (2012) 1530–1537
In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.
The average availability of a repairable system is the expected proportion of time that the system is operating in the interval [0, t]. The present article discusses the nonparametric estimation of the average availability when (i) the data on 'n' complete cycles of system operation are available, (ii) the data are subject to right censorship, and (iii) the process is observed upto a specified time 'T'. In each case, a nonparametric confidence interval for the average availability is also constructed. Simulations are conducted to assess the performance of the estimators.
We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.
The standard models for statistical signal extraction assume that the signal and noise are
generated by linear Gaussian processes. The optimum filter weights for those models are
derived using the method of minimum mean square error. In the present work we study
the properties of signal extraction models under the assumption that signal/noise are
generated by symmetric stable processes. The optimum filter is obtained by the method of
minimum dispersion. The performance of the new filter is compared with their Gaussian
counterparts by simulation.