JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI)
Year:2009 | Volume:6 | Issue:1|Papers Count:7

Air pollution is one of the major problems of Tehran metropolis. Regarding the fact that Tehran is surrounded by Alborz NIountains from three sides, the pollution due to the cars traffic and other polluting means causes the pollutants to be trapped in the city and have no exit without appropriate wind guff. Carbon monoxide (CO) is one of the most important sources of pollution in Tehran air ...

In general case, Chambers et al. (1976) introduced the following algorithm for simulating any stable random variables X ~ S (a, b, g, d), with four parameters. They use a nonlinear transformation of two independent uniform random variables for simulating an stable random variable …

The extension of classical analysis to time series data is the basic problem faced in many fields, such as engineering, economic and medicine. The main objective of discriminant time series analysis is to examine how far it is possible to distinguish between various groups. There are two situations to be considered in the linear time series models. Firstly when the main discriminatory information contained in mean function and secnodly when the mean functions are equal and discriminotary information is in the autocovariance functions. The latter case is more interested because the the first case is well documnted.The classical method for discrimation of time series is based on likelihood ratio approach. Using this approach the vector x has to be allocated to H1 or H2 leads to the discriminant function dQ (x) = x' (R2-1 - R1-1) x (Shumway and Stoffer, 2006) in where x is the the R1 and R2 are the covariance matrices under and models, respectively.Another approach is based on assessing distance between models.Two important and common distance measuers, Kullback-Leibler information measure, KL, and Chernoff information measure, CH. In this case x is allocated to H1 or H2 depending on disparity measure between the sample spectrum of and two models (H1 or H2), (see Kakizawa et al., 1998).In this article KL and CH have been adopted to both autoregressive models and moving average models.Three methods, classical method (call Shumway method) has been compared with KL and CH criterions.The peformance of method has been carried out using a numerical study. One hundred time series each of length two hundred points simulated from the first model, say H1, and subjected to the discrimination criterion obtained from Kullback-Leibler, KL, and Chernoff, CH, crierions. The number of series that were misclassified out of hundred was noted.The results showed that three method work well for both autoregressive or order of one and moving average order of one models. The miscllasifican rate decreases when the distance between two populations increases. However, the performance of KL method is superior than both CH and Shumway methods.

Time series and their methods of analysis are important subjects in statistics. Most of time series have a linear behavior and can be modelled by linear ARIMA models. However, some of realized time series have a nonlinear behavior and for modelling them one needs nonlinear models. For this, many good parametric nonlinear models such as bilinear model, exponential autoregressive model, threshold autoregressive model and GARCH model are commonly used.On analysis of nonlinear time series, when there is no priori information, identification of a parametric nonlinear model, due to expanded nonlinear relation, is very difficult. A suitable substitution for parametric nonlinear models is the use of nonparametric models and their methods of analysis. In this direction various models and methods of analysis are introduced. One of the most important of such models is the functional-coefficient autoregressive (FAR) model. Flexibility of FAR models on fitting to real observation makes this model very useful as an applied methods in modelling economic survey, hydrology, and other related subjects. Many parametric models such as autoregressive model, threshold autoregressive model and exponential autoregressive model may be obtained as special cases of FAR models.In this paper, using Chen and Tsay (1993) and Cai et al. (2000), we introduce FAR model and a method for fitting this model. Also, some methods for prediction of future of the time series using the fitted model are presented.Specially, a bootstrap predictive method for prediction of m-steps ahead of the time series is introduced. Using the bootstrap method point, interval and distribution of predictions are obtained.We use FAR model for modelling of Iranian heavy crude oil price from July 1994 to December 2007. For this aim, using average prediction error criteria we identify a FAR (2, 1) model with smoothing parameter h=1.3. This model is fitted using locally linear regression with Epanechnikov kernel. Examination of ability of prediction of the model and performance of the bootstrap prediction show that the fitted model has good performance. We finally use fitted model and bootstrap method for prediction of the first 3 months of 2008 of Iranian heavy crude oil price.Comparesion of these predictions with their real values shows a maximum of absolute differences of $4.75. This was related to March 2008 and it had a relative error of %5 with respect to the real value.

Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets.On one hand, most of real world time series data display a time-varying second order structure.On the other hand, wavelets are well situated for forecasting non-stationary time series since wavelets are local which is very important property to analyze non-stationary time series.To extend stationary processes, slow changes are allowed over time of the second order structure of time series or equivalently the amplitude in spectral representation is allowed to depend on time the spectral representation.Dahlhaus (1997) proposes a minimum distance estimation procedure for non-stationary time series models. Ombao et al. (2002) defined non-stationary processes by changing covariance stationary processes over time.Instead of using windowed Fourier transform (as in Priestley 1965), Nason et al. (2000) introduce the Locally Stationary Wavelet (LSW) processes, using the (non-decimated) wavelet transform and the rescaled time principle.Fryzlewicz et al. (2003) suggest an algorithm to predict LSW processes. This algorithm was used by Van Bellegem and Von Sachs (2002) to model financial log-return series.Forecasting LSW processes arrives to a generalization of the Yule-Walker equations, which can be solved numerically by matrix inversion or standard iterative algorithms such as the innovations algorithm. In the stationary case, these equations reduced to ordinary Yule-Walker equations.In all the above articles, the point wise prediction of discrete time series has been considered, but functional prediction (prediction of an interval) of time series can be considered instead of a point wise prediction since for continuous time series, interval prediction is more suitable than point wise prediction. Antoniadis et al. (2006) propose functional wavelet-kernel smoothing method. This method uses interpolating wavelet transform which is not most popular wavelet transform.The predictor may be seen as a weighted average of the past paths, associating more weight on those paths which are more similar to the present one. Hence, the similar blocks  are to be found.To summarize, this method is performed in two following steps: We should find within the past paths the ones that are similar or close to the last observed path. This determines the weights; then we use locally weighted average using obtained weights to predict time series.In this article, after describing mentioned methods, we suggest some extensions to the functional wavelet-kernel method to forecast time series by means of wavelets and then we compare that with several prediction methods. We propose to use two different types of wavelet transform instead of interpolating wavelet transform: discrete wavelet transform (DWT) and non-decimated wavelet transform (NDWT). The first one is an orthogonal wavelet transform while the second one is a redundant transform. These transformations are applied more than interpolating wavelet transform and can be used easily in most of mathematical programming software as S-Plus and MATLAB.We consider the following methods: the methods proposed by Fryzlewics et al.(2003) and Antoniadis et al. (2006), the classical autoregressive model and our two proposed methods. Then, we compare these methods by simulation and real data. We simulate the data from AR (7) (stationary data) and AR (7) contaminated by a sinusoid (non stationary data). We also consider two real data set; Electricity Paris Consumption and El-Nino data. In our comparison, our methods give better results than other compared methods.In this paper we also show that mean square prediction error converges to zero under some conditions when the sample size is large.

Understanding dependence structure and relationship between two sets of variables is of main interest in statistics. When encountering two large sets of variables, a researcher can express the relationship between the two sets by extracting only finite linear combinations of the original variables that produce the largest correlations with the second set of variables.When data are continuous functions of another variable (generally time), the methods of multivariate analysis cannot be applied to the data. Therefore, some theoretical justification is needed to provide the required definitions and concepts regarding the essential nature of the data. This leads to difining canonical correlation for pairs of random functions called functional canonical correlation (FCCA).If the data related to functional phenomena, are observed discretely, the first task is to convert these observations to appropriate curves. This is due to functional nature of the phenomena that the data related to. On the other hand, the functional quantity of interest may be measured with error. In such cases, we should first remove the observational error bay taking a smoothing procedure to account. In this paper, Iranian weather data, collected in 2006, are treated by using FCCA. The data set contains discret measurment’s of three phenomena: temperature, humidity and precipitation and was collected from 102 weather stations. we have fitted continuous curves to the original data, and then extrated the correlation patterns between each pair of the three phenomena.

A number of nonparametric methods exist when studying the population and its parameters in the situation when the distribution is unknown. Some of them such as "resampling bootstrap method" are based on resampling from an initial sample ...