TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY LINEAR ERRORS-IN-VARIABLES MODEL

The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.

High dimensional cross-sectional dependence test under arbitrary serial correlation

In panel data analysis,the cross-sectional dependence(CD)test has been extensively used to test the cross-sectional dependence.However,this traditional CD test does not take serial correlation into consideration,which commonly occurs in many fields.To solve this problem,we propose an adjusted CD test which is able to effectively handle serial correlation.More specifically,the serial correlation can be of arbitrary form in our work.Furthermore,we establish the theoretical properties of the proposed adjusted CD test.Our extensive Monte Carlo experiments show that the traditional CD test cannot work well under serial correlation,while the proposed adjusted CD test does provide rather satisfactory performance.

Consistent Estimation of Order for Regression in the Presence of Serial Correlation and Heteroscedasticity

In this paper, we consider a multiple regression model in the presence of serial correlation and heteroscedasticity. We establish the convergence rate of an efficient estimation of autoregressive coefficients suggested by Harvey and Robison (1988). We propose a method to identify order of serial correlation data and prove that it is of strong consistency. The simulation reports show that the method of identifying order is available.

Testing for Serial Correlation in Three-dimensional Panel Data Models

This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial autoregression modeled by centering and differencing residuals. The test can be shown to asymptotically chisquare distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects. Monte Carlo simulations are carried out for illustration.

Testing Serial Correlation in Semiparametric Varying-Coefficient Partially Linear EV Models

This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.

ZERO FINITE-ORDER SERIAL CORRELATION TEST IN A PARTIALLY LINEAR SINGLE-INDEX MODEL

The purpose of this paper is to test the underlying serial correlation in a partially linear single-index model. Under mild conditions, the proposed test statistics are shown to have standard chi- squared distribution asymptotically when there is no serial correlation in the error terms. To illustrate their finite sample properties, simulation experiments, as well as a real data example, are also provided. It is revealed that the finite sample performances of the proposed test statistics are satisfactory in terms of both estimated sizes and powers.

A Modified Residual-based Test for Serial Correlation in Linear Panel Data Models

This paper suggests a modified serial correlation test for linear panel data models, which is based on the parameter estimates for an artificial autoregression modeled by differencing and centering residual vectors. Specifically, the differencing operator over the time index and the centering operator over the individual index are, respectively, used to eliminate the potential individual effects and time effects so that the resultant serial correlation test is robust to the two potential effects. Clearly, the test is also robust to the potential correlation between the covariates and the random effects. The test is asymptotically chi-squared distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The finite sample properties of the test are investigated by means of Monte Carlo simulation experiments, and a real data example is analyzed for illustration.

Evaluation of Rainfall Tendency for the Twentieth Century over Indira Sagar Region in Central India

The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource development, and hydropower system reliability in the region rely heavily on monsoon rainfall. Monthly rainfall data from three stations (East Nimar, Barwani, and West Nimar) were analyzed. Initially, the pre-whitening method was applied to eliminate serial correlation effects from the rainfall data series. Subsequently, statistical trends in annual and seasonal rainfall were assessed using both parametric (student-t test) and non-parametric tests [Mann-Kendall, Sen’s slope estimator, and Cumulative Sum (CUSUM)]. The magnitude of the rainfall trend was determined using Theil-Sen’s slope estimator. Spatial analysis of the Mann-Kendall test on an annual basis revealed a statistically insignificant decreasing trend for Barwani and East Nimar and an increasing trend for West Nimar. On a seasonal basis, the monsoon season contributes a significant percentage (88.33%) to the total annual rainfall. The CUSUM test results indicated a shift change detection in annual rainfall data for Barwani in 1997, while shifts were observed in West and East Nimar stations in 1929. These findings offer valuable insights into regional rainfall behavior, aiding in the planning and management of water resources and ecological systems.

Influence of non-stationarity and auto-correlation of climatic records on spatio-temporal trend and seasonality analysis in a region with prevailing arid and semi-arid climate,Iran

Trend and stationarity analysis of climatic variables are essential for understanding climate variability and provide useful information about the vulnerability and future changes,especially in arid and semi-arid regions.In this study,various climatic zones of Iran were investigated to assess the relationship between the trend and the stationarity of the climatic variables.The Mann-Kendall test was considered to identify the trend,while the trend free pre-whitening approach was applied for eliminating serial correlation from the time-series.Meanwhile,time series stationarity was tested by Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests.The results indicated an increasing trend for mean air temperature series at most of the stations over various climatic zones,however,after eliminating the serial correlation factor,this increasing trend changes to an insignificant decreasing trend at a 95%confidence level.The seasonal mean air temperature trend suggested a significant increase in the majority of the stations.The mean air temperature increased more in northwest towards central parts of Iran that mostly located in arid and semiarid climatic zones.Precipitation trend reveals an insignificant downward trend in most of the series over various climatic zones;furthermore,most of the stations follow a decreasing trend for seasonal precipitation.Furthermore,spatial patterns of trend and seasonality of precipitation and mean air temperature showed that the northwest parts of Iran and margin areas of the Caspian Sea are more vulnerable to the changing climate with respect to the precipitation shortfalls and warming.Stationarity analysis indicated that the stationarity of climatic series influences on their trend;so that,the series which have significant trends are not static.The findings of this investigation can help planners and policy-makers in various fields related to climatic issues,implementing better management and planning strategies to adapt to climate change and variability over Iran.

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr TypeⅫdistribution

Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.

Assessing the Response of Seasonal Variation of Net Primary Productivity to Climate Using Remote Sensing Data and Geographic Information System Techniques in Xinjiang

Net primary productivity （NPP） is a key component of energy and matter transformation in the terrestrial ecosystem, and the responses of NPP to global change locally and regionally have been one of the most important aspects in climatevegetation relationship studies. In order to isolate causal climatic factors, it is very important to assess the response of seasonal variation of NPP to climate. In this paper, NPP in Xinjiang was estimated by NOAA/AVHRR Normalized Difference Vegetation Index （NDVI） data and geographic information system （GIS） techniques. The impact of climatic factors （air temperature, precipitation and sunshine percentage） on seasonal variations of NPP was studied by time lag and serial correlation ageing analysis. The results showed that the NPP for different land cover types have a similar correlation with any one of the three climatic factors, and precipitation is the major climatic factor influencing the seasonal variation of NPP in Xinjiang. It was found that the positive correlation at 0lag appeared between NPP and precipitation and the serial correlation ageing was 0 d in most areas of Xinjiang, which indicated that the response of NPP to precipitation was immediate. However, NPP of different land cover types showed significant positive correlation at 2 month lag with air temperature, and the impact of which could persist 1 month as a whole. No correlation was found between NPP and sunshine percentage.

OPTIMAL INVESTMENT WITH NOISE TRADING RISK

This paper investigates the optimal dynamic investment for an investor who maximizes constant absolute risk aversion （CARA） utility in a discrete-time market with a riskfree bond and a risky stock. The risky stock is assumed to present both the dividend risk and the price risk. With our assumptions, the dividend risk is equivalent to fundamental risk, and the price risk is equivalent to the noise trading risk. The analytical expression for the optimal investment strategy is obtained by dynamic programming. The main result in this paper highlights the importance of differentiating between noise trading risk and fundamental risk for the optimal dynamic investment.

Truncated Estimator of Asymptotic Covariance Matrix in Partially Linear Models with Heteroscedastic Errors

A partially linear regression model with heteroscedastic and/or serially correlated errors is studied here. It is well known that in order to apply the semiparametric least squares estimation （SLSE） to make statistical inference a consistent estimator of the asymptotic covariance matrix is needed. The traditional residual-based estimator of the asymptotic covariance matrix is not consistent when the errors are heteroscedastic and/or serially correlated. In this paper we propose a new estimator by truncating, which is an extension of the procedure in White. This estimator is shown to be consistent when the truncating parameter converges to infinity with some rate.