In this article it is proved that the stationary Markov sequences generated by minification models are ergodic and uniformly mixing. These results are used to establish the optimal properties of estimators for the parameters in the model. The problem of estimating the parameters in the exponential minification model is discussed in detail.
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
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.
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.