The capital asset pricing model has been one of the most prevalent models in assessing investors’ expected rate of return. Provided that it is likely that the residuals of the estimated regression of this model resemble conditional Heteroscedasticity, this paper aims to test the predictive power of standard CAPM and CAPM based on symmetric and asymmetric conditional Heteroscedasticity. For this purpose, the expected returns during the time period of the rese(ARCH) have been estimated based on three existing models. The findings were compared with obtained returns and mean squared error index was utilized for measurement of the predictive power of those models. The models were compared using Diebold-Mariano test on mean squared error index. The findings indicated that, with respect to the CAPM model, the consideration of the conditional Heteroscedasticity (symmetric and asymmetric) can stimulate predictive power of the obtained return.

In this paper, an approximate mathematical expression is proposed for the residual variance of Auto-Regressive (AR) estimation in the case where the AR estimation method is Least-Squares- Forward (LSF), using statistical arguments and approximations as well as Hilbert space concepts. This expression approximates the statistical behavior of the residual variance. While its validity is tested through simulations. This important formula can be employed to propose various AR order selection methods. Such as the method proposed in this paper which is an iterative algorithm. The performance of this algorithm is compared with other existing order selection methods using simulations. The results of which demonstrate that in spite of the information criteria, the overestimation probability of the proposed algorithm does not increase in short data record cases.

Summary:The main purpose of exploration seismology is data gathering, data processing, and finally obtaining an interpretable image of subsurface layers. Sometimes, because of problems such as undesirable area topography, instrument defects, and environmental constraints, we have data with missing spatial samples. Reconstruction and recovery of the missing data can be carried out using interpolation and reconstruction methods. There are many reconstruction and interpolation methods. One of the most useful methods to reconstruct missing data is the Auto-Regressive model. This method refers to the techniques that model the evolution of a signal as a function of its past/future samples(Lau et al., 2002; Takalo et al., 2005). Also, it has a wide range of applications in signal processing including noise suppression (Canales, 1984), parametric spectral analysis (Marple, 1987), and signal interpolation and reconstruction (Sacchi and Ulrych, 1996; Porssani, 1999; Spits, 1991; Naghizade and Sacchi, 2007). The AutoRegressive reconstruction methods were introduced by Spitz (1991). Spitz (1991) proposed computing prediction filters (AutoRegressive operators) from low frequencies to predict interpolated traces at high frequencies. This methodology is applicable only if the original seismic section is regularly sampled in space. Conversely, irregularly sampled data can be reconstructed using Fourier methods. In this case, the Fourier coefficients of the irregularly sampled data are retrieved by inverting the inverse Fourier operator with a band limiting and/or a sparsity constraint (Sacchi et al., 1998; Zwartjes and Gisolf, 2006). In this paper, a reconstruction method has been introduced that combines a Fourier-based method and an Auto-Regressive model to reconstruct the missing data. The method includes a two-stage algorithm. The first step of the proposed algorithm involves the reconstruction of the irregularly missing spatial data on a regular grid at low frequencies using a Fourier-based algorithm called the minimum-weighted norm (Liu and Sacchi, 2004) method. Fourier reconstruction methods are well suited to reconstruct seismic data in the low-frequency (non-aliased) portion of the Fourier spectrum. The reconstruction problem is well-conditioned at low frequencies where only a few wavenumbers are required to honor the data. This makes the problem well-posed; therefore, it is quite easy to obtain a low frequency spatial reconstruction of the data. Seismic data at low frequencies are band-limited in the wavenumber domain. Due to the band-limited nature of the wavenumber spectra at low frequencies, this portion of the data can be reconstructed with high accuracy (Duijndam et al., 1999). Then, prediction filter components are computed for all frequency bands from the low-frequency portion of the reconstructed data using the Auto-Regressive method. Finally, these prediction filters are used to reconstruct the missing data. The basic equations for computing the prediction filter components (Auto-Regressive operators) and reconstructing the missing data are as follows:xn(f)=åLj=1Pj(af)xn-aj(f),¬ forward & xn*(f)= åLj=1Pj(af)xn+ aj(f), ¬ backwardn=aL+1, …, N, n=1, …, N-aLThe aforementioned equations show that one can predict the data samples using past/future samples (forward/backward equations). It is important to stress that the technique presented in this paper can only be used to reconstruct data that live on a regular grid with missing observations. The results of the application of the algorithm on both synthetic and real seismic data showed and confirmed the performance of the method.

A detector for the case of a radar target with known Doppler and unknown complex amplitude in complex Gaussian noise with unknown parameters has been derived. The detector assumes that the noise is an Auto-Regressive (AR) process with Gaussian Autocorrelation function which is a suitable model for ground clutter in most scenarios involving airborne radars. The detector estimates the unknown parameters by Maximum Likelihood (ML) estimation for the use in the Generalized Likelihood Ratio Test (GLRT). By computer simulations, it has been shown that for large data records, this detector is Constant False Alarm Rate (CFAR) with respect to AR model driving noise variance. Also, measurements show the detector excellent performance in a practical setting. The detector’s performance in various simulated and actual conditions and the result of comparison with Kelly’s GLR and AR-GLR detectors are also presented.

The main purpose of this paper is using the probablity models, Auto Regressive Moving Average (ARMA) in order to modeling of daily position time series of permanent GPS station. The daily position time series of LLAS site in Southern California region from SCIGN array that were active during January 1,2000 to Dec 30, 2006 are evaluated for analysis and determinig of daily position time series. According of daily position time series, a site motion model is used to estimate simultaneously geodetic parameters such as: linear trend, annual harmonics, semi annual harmonics and offsets. In each daily position time series, model parameters are estimated using weighted least squares. In this study, Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) are used as study tools for identification of behavior of daily position time series of permanent GPS station. These functions provide consideration of correlations between daily positions of daily time series. Moreover, Akaike Information Criterion is used to identify model orders, because some kind of ARMA model may appropriate for a daily position time series of GPS station. In this study, some numerical results shows that a model order from (1, 1) is appropriate for direction N of permanent GPS station. Probabality model of ARMA (2, 1) is best model for direction E and a model order from (1, 1) is suitable for direction U. In the final step, a daily position time series of LLAS permanent station were predicted for seasonal component.

Rural inhabitants’ perception of better life changes when observing the success of other people, and hope to emulate their success. They know that University degree can lead to a higher expected income. In fact urbanism has some benefits but the costs (pollution, congestion, and crime) are also pervasive in developing countries. In order to better understand the problem, and examine policy measures for controlling its negative externalities, it is of importance to study and analyze the factors which may affect migration. Therefore, in this study we investigated this important issue with emphasis on the effect of rural literacy level on rural-urban migration by using an Auto-Regressive Distributed Lag (ARDL) model utilizing time-series data related to the years 1959-2005 in Iran. Results indicate that in long term, rural literacy level has the most effect on this function. It was also found that, 1% increase in rural wage, urban wage, rural value added and rural literacy level can cause 0.25% decrease, 0.32% increase, 0.16% decrease and 0.32% increase in migrant’s number, respectively.

River flow modeling has special importance in water resources management. Since the actual river flow data are often low and they correlate and depend yearly and monthly, making the data similar to historical data is so difficult and complex. In this study, 50 year data and Seasonal Auto Regressive Moving Average (SARMA) and Clayton and Frank Copulas which are the prediction and simulation methods of the river flow molding, were used to generate random flow data of Helmand River. Results show, SARMA model forecasts minimum river flow data very good, but the generated data hasn’t correlation of historical data and usually the maximum river flow is greater than real data. Otherwise, Copula preserved concordance of real data and make the data that are similar to real river flow. Also Root Mean Square Error of Copula method was 0.3 that is was less than SARMA method (0.4). Therefore Copulas are good methods for Helmand river flow modeling.

This Paper investigates impacts of macroeconomic variables on the demand for money in Iranian economy using an Auto Regressive distributed lag model (ARDL) and the data for the period 1340-1382. The results indicate that there is a unique cointegrated and stable long-run equilibrium relationship between the real demand for money and its determinants such as: real GDP, interest rate, and inflation rate. These results reveal that the demand for money in Iranian economy is more sensitive to the real GDP than to the other macroeconomic variables (long term interest rate and inflation rate). Moreover, the long-term income and inflation elasticity of money demand is 2.620 and 0.038, respectively. This shows that money demand function is more elastic with respect to long-term income and inelastic with respect to price level. Also, adjustment coefficient for money demand is estimated to be 0.19. This means that the adjustment process for money demand would take 5 years.