Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China

Transcription

1 Journal of Integrative Agriculture 2012, 11(4): April 2012 RESEARCH ARTICLE Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China LI Gan-qiong 1, XU Shi-wei 1, LI Zhe-min 1, SUN Yi-guo 2 and DONG Xiao-xia 1 1 Agricultural Information Institute, Chinese Academy of Agricultural Sciences/Key Laboratory of Agri-information Service Technology, Ministry of Agriculture/Key Laboratory of Digital Agricultural Early Warning Technology and System, Chinese Academy of Agricultural Sciences, Beijing , P.R.China 2 Department of Economics, University of Guelph, Ontario N1G2W1, Canada Abstract This paper studies how the price movements of pork, chicken and egg respond to those of related cost factors in short terms in Chinese market. We employ a linear quantile approach not only to explore potential data heteroscedasticity but also to generate confidence bands for the purpose of price stability study. We then evaluate our models by comparing the prediction intervals generated from the quantile regression models with in-sample and out-of-sample forecasts. Using monthly data from January 2000 to October 2010, we observed these findings: (i) the price changes of cost factors asymmetrically and unequally influence those of the livestock across different quantiles; (ii) the performance of our models is robust and consistent for both in-sample and out-of-sample forecasts; (iii) the confidence intervals generated from 0.05th and 0.95th quantile regression models are good methods to forecast livestock price fluctuation. Key words: cost factors, agricultural products, forecasting, price movements, quantile regression model INTRODUCTION Since 1949 the Chinese agricultural products market has experienced three stages such as a planned economy, the coexistence of the planned economy and a marketoriented economy, and the transition from the planned economy to the market-oriented economy. In a perfectly market-oriented economy, the type and amount of agricultural products produced by farmers are jointly determined with market price signals. However, in the current Chinese agriculture industry, the lack of advisable market information analysis makes it difficult for Chinese farmers to form sensible prior decision. Consequently, it is not surprising to see a roller-coaster kind of price movements of agriculture products repeating in recent years, which has severely distorted the agriculture industry and incurred significant loss of consumer welfare in China, and the current high-inflation environment makes the situation even worse. Understanding the price spillover effects from one agriculture product to another one becomes prerequisite for policymakers to lay down any price control policy in agricultural product markets and subsidy policy in consumer consumption. Therefore, this paper tends to study the price influence factors of four commonly consumed agriculture products such as pork, chicken, egg, and milk. Specifically, we investigate how the changes of livestock feed prices spread to the price movements of Received 27 July, 2011 Accepted 16 January, 2012 LI Gan-qiong, Tel: , lgqxjf@caas.net.cn; Correspondence XU Shi-wei, Tel: , xushiwei@mail.caas.net.cn

2 Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China 675 these four agriculture food products in short terms. Traditional regression analysis focuses on conditional mean function m (x) that has been applied widely in the social sciences. Generally conditional mean model summarizes the relationship between one or more covariate X and the conditional mean of a response variable Y given X=x (Yu and Jones 1998). Under ideal conditions, the approach can provide a complete and parsimonious description of the relationship between the independent variables and the dependant variable. However, the conditional mean regression model has some limitations (Hao and Naiman 2007). First, it can not be readily extended to tail locations where social science research is often of interest. Second, the conditional mean model is heavily influenced by outliers. Nevertheless, heavytailed distributions often occur in the real world. Third, this approach easily steers attention away from the properties of the whole distribution of the response variable that is how changes in the independent variables affect the shape of response variable distribution. There is an alternative to conditional mean model. The quantile regression model was introduced by Koenker and Bassett (1978), which models the relationship between predictor X and the conditional quantiles of Y given X=x. The linear quantile regression model complements the linear mean regression model if the error terms in the mean regression model are heteroscedastic. Therefore, by examining the results estimated from both the quantile and mean regression models, we are able to explore more useful information from the data. One important application of a quantile regeression method is to construct 95% confidence intervals for fitted dependent variables or forecast values. Recent 10 yr there is a rapidly expanding empirical quantile regression literature in economics such as forecasting, consumption, education, risk evaluation, finance, etc. In forecasting application, Taylor and Bunn (1999) used quantile regression approach to generate prediction intervals and results indicated this method was useful for various forecasting applications. Koenker and Hallock (2001) used quantile regression to analyze the relationship between household food expenditure and household income and the results revealed that the conditional distribution of food expenditure was skewed to the left. Matthys et al. (2004) presentd an extreme quantile estimator for heavy-tailed distributions. Gustavsen and Rickertsen (2006) used censored quantile regression to analyze vegetable demand. Taylor (2007) used exponentially weighted quantile regression to construct interval forecasts for daily supermarket sales and results showed it was better than point forecasting by traditional methods. Cai (2007) fitted a quantile selfexciting threshold autoregressive time series model to forecast the growth rate of US GNP and the results showed that the method worked very well in practice. Clements et al. (2008) used this method to forecast daily exchange rate returns. Ma and Pohlman (2008) showed that under mild conditions quantile regression approach could provide more accurate forecasts and potentially higher value-added portfolios than classical conditional mean model. In consumption study, Koenker and Hallock (2001) used quantile regression to analyze the relationship between household food expenditure and household income. Chen et al. (2008, 2009) employ quantile regression to analyze Chinese resident s consumption. Chen et al. (2009) use local quantile regressions to analyze relations between health care expenditure and income. In risk evaluation, Wu and Ma (2006) introduce quantile regression method to estimate extreme behaviour models. Banachewicz and Lucas (2008) employed quantile forecasting for credit risk management. Li (2010) re-examined the risk return relationship in the banking industry using quantile regression. In education fields, Liu (2008) uses quantile regression and censored quantile regression to analyze influences of education and experience on Chinese residents. In finance study, Lai and Lai (2008) use quantile regression to explain the determinants of capital structure. Li and Dong (2008) employs quantile regression to analyze relationship between volatility and trading volume of Chinese stock market. Findings from existing literature, most studies on agricultural products market forecasts are involved in conditional mean regression model (Ma et al. 2007; Li 2010; Xie 2010), time series model (Fu et al. 2008; Liu and Li 2009; Dong et al. 2010), artificial neural network (Wang 2008; Ping et al. 2010), etc. Typically, the accuracy of these methods could reach more than 80% when we employed them to forecast short term market price. However, the results are not very satisfactory when extreme conditions occur. In addition, the point forecasting is difficult to ensure accurate prediction when the uncertainty of future situation increases, especially for agricultural products.

3 676 LI Gan-qiong et al. The objective of this paper focuses on introducing the quantile regression approach to model price movements of pork, egg, chicken, and milk and analyzes short term impacts of cost factors on livestock s price fluctuation. We observe that the price changes of cost factors asymmetrically and unequally influence those of the livestock across different quantiles. To our interesting, the confidence intervals generated from 0.05th and 0.95th quantiles regression model are a good method to forecast livestock price fluctuation, and the performance of our models is robust and consistent for both in-sample and out-of-sample forecasts. All the estimation and tests are obtained by the usage of R package named quanreg. The remainder of the paper is set out as follows. In section of MODELLING PRICE MOVEMENTS OF AGRICULTURAL PRODUCTS: AN EMPIRICAL FRAMEWORK, we describe our empirical framework. In section of DATA DESCRIPTION, we give a brief description of the data and summary statistics of variables of interest. In section of EMPIRICAL RESULTS, we report our results, including the linear quantile regression model in-sample and out-of-sample forecasts. In section of CONCLUSION, we summarize the most important conclusions of this study and illustrate the implications of the research. MODEL LING PRICE MOVEMENTS OF AGRICULTURAL PRODUCTS: AN EMPIRICAL FRAMEWORK In this section we briefly describe our empirical framework for modelling price movements, which we apply to our data in the subsequent sections. First, we use the augmented Dickey-Fuller statistics to examine whether the time series of pork, egg, chicken, milk and related cost factors are stationary. Second, we describe the conditional quantile curves so as to explain our objective. Third, we outline the method of parametric quantile regression model. Conditional quantile curves Many studies indicated that quantile is popularly used for estimating models of conditional quantile functions. For the convenience of readers, below we give a brief introduction of the concept of conditional quantile curves. Let be an independent and identically distributed sequence, where Y takes values in R 1 and X t in R d (d 1). For 0<p<1, let Q p (x) denote the conditional pth-quantile of Y given X=x by (1) If F is absolutely continuous in y at x, then Q p (x) is the unique solution of the following equation: (2) If we know the conditional distribution function, F, Q p (x) can be inversely solved from Eq. (2). Quantile regression Without imposing any functional form on Q p (x), nonparametric kernel estimators in Chaudhuri (1991a, b) and Fan et al. (1994) are shown to be consistent under some regularity conditions. However, one often finds nonparametric approach lack of clear interpretation of the estimated quantile curves. Therefore, we aim to investigate price movements of the agriculture products via a parametric linear quantile regression approach. The linear quantile regression model considered is given by (3) Where,, and p is the probability mass of interest. X t can be a vector, i.e., multivariate quantile regression model. Then, following Konker and Basset (1978, 1982), the unknown parameter vectors appearing in Eq. (3) can be solved from the following optimization problem (4) Where is the so-called check function. In order to solve the Eq. (4), this study uses Barrodale and Roberts simplex algorithm described by Koenker and Dorey (1987). The standard errors of each coefficient are computed by a kernel estimate of the sandwich as proposed by Powell (1984). Using the above approach, the different quantile regression mod-

4 Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China 677 els of interest can be estimated. DATA DESCRIPTION The data used in this study comprises monthly observations on the prices of pork, chicken, egg, and related cost factors. For pork product and its related factors, the time series include pork price, hogfeed, hog, and piglets, and CPI. The time series for egg product and its related factors include egg price, CPI, egg-type chicks, and corn. The time series for chicken product and its related factors include chicken price, broilertype chickenfeed, broiler chicks, and live chicken. Data were abstracted from China Animal Agriculture Association ( and the sample period spans from January 2000 to October 2010, giving a total of 11 yr. In our empirical work, we carried out estimations over the period January 2000 to December 2009, reserving the last year of data for out-ofsample forecasting tests. As the time series on livestock price usually are not stationary, the raw series is transformed into growth rate to compute according to the following expression (5) Where P i, t means the price of ith series at the period of t, R i, t means growth rate of ith series at the period of t (i=1, 2, 12). Thus series R i, t not only has been stationary, but also has been kept independent each other. Table 1 gives summary statistics of the variables of interest. As seen from the Table 1, the skewness coefficients of R 1, t (pork), R 6, t (egg) series are positive, which implies a right-skewed density function. However, the skewness coefficient of R 9, t (chicken) is negative, which implies a left-skewed density function. In addition, the values of kurtosis are all overwhelmingly statistically greater than three, i.e., it means series R i, t have higher probability distributions in the vertical direction than the normal distribution probability. Table 1 also roughly reports that the average market volatility of R 1, t (pork) is higher than R 6, t (egg) and R 9, t (chicken). EMPIRICAL RESULTS Unit root test for series R i, t Table 2 reports the augmented Dickey-Fuller (ADF) statistics for series R i, t. In Table 2, the statistics indicate that the series R i, t reject the null hypothesis at 5% significance level, i.e., series R i, t are stationary. Model estimation and evaluation One important application of a quantile regression method is to construct 95% confidence intervals for fitted dependent variables or forecast values. Therefore, we choose the 0.05th quantile and the 0.95th quantile to not only analyze how the price changes of cost factors of interest influence those of the livestock across different quantiles, but also model the confidence intervals to forecast price changes of livestock. The models of pork, egg, chicken, and milk were estimated by using a linear quantile regression approach mentioned in the section of MODELLING PRICE MOVEMENTS OF AGRICUL- TURAL PRODUCTS: AN EMPIRICAL FRAMEWORK, Table 1 Summary statistics of series R Variables 1) Mean (%) Median(%) Max. (%) Min.(%) Std.Dev Skewness Kurtosis JB R 1, t R 2, t R 3, t R 4, t R 5, t R 6, t R 7, t R 8, t R 9, t R 10, t R 11, t R 12, t ) R 1, t, pork; R 2, t, hogfeed; R 3, t, hog; R 4, t, piglets; R 5, t, CPI; R 6, t, egg; R 7, t, egg-type chicks; R 8, t, corn; R 9, t, chickens; R 10, t, broiler-type chickenfeed; R 11, t, broiler chicks; R 12, t, live chicken. The same as below.

5 678 LI Gan-qiong et al. Table 2 Augmented Dickey-Fuller statistics for series R Variables 1) t-statistic Critical value (5%) (C, T, K) 2) R 1, t (0, 0, 1) R 2, t (0, 0, 1) R 3, t (0, 0, 1) R 4, t (0, 0, 1) R 5, t (0, 0, 1) R 6, t (0, 0, 1) R 7, t (0, 0, 1) R 8, t (0, 0, 1) R 9, t (0, 0, 1) R 10, t (0, 0, 1) R 11, t (0, 0, 1) R 12, t (0, 0, 1) 1) The time series R i, t (i=1, 2,, 12) reject the null hypothesis at 5% significance level. 2) C, intercept; T, trend; K, lag length. Table 3 The parametric estimates of 0.05th, 0.5th and 0.95th quantile regression models for pork 1) Variables OLSE 0.05th 0.5th 0.95th C * * * * (0.1584) (0.2689) (0.2387) (0.2639) R 2, t * * * * (0.0680) (0.1013) (0.1025) (0.1107) R 3, t * * * * (0.0475) (0.0691) (0.0759) (0.0878) R 4, t * * * * (0.0340) (0.0424) (0.0561) (0.0580) R 5, t * * * * (0.2251) (0.3069) (0.3164) (0.3617) 1) OLSE means the estimated results of OLS method. The values of brackets are the standard errors of regression coefficient estimate. *, the parameter reject null hypothesis at 5% significance level. The same as below. we describe our empirical framework. Pork quantile regression model Series R 1, t (pork) is the dependent variable. The independent variables of interest are R 2, t (hogfeed), R 3, t (hog), R 4, t (piglets), and R 5, t (CPI). In this study, we use the variable of CPI as substitute for labor wage based on two aspects. One is that the trend of CPI is very close to that of labor wage seeing from recent ten years. Another reason is that it is difficult to get monthly data of labor wage for hog production. The models were estimated as follows: R 1, t = R 2, t R 3,t R 4, t R 5, t (6) R 1, t = R 2, t R 3, t R 4, t R 5, t (7) Where Eq. (6) is 0.05th quantile regression model and Eq. (7) is 0.95th quantile regression model. The results show that the factors of R 2, t, R 3, t R 4, t and R 5, t make an important difference to pork. Among the four factors, the fluctuation of R 5, t (CPI) almost cause the same fluctuation size of pork. However, the difference of hog (R 3, t ) and piglets (R 2, t ) influence to pork are more distinct than other two factors, i.e., the price of pork will fall 0.4% if hog price goes down 1.0% in Eq. (6), and the price of pork will increase 0.9% if hog price goes up 1.0% in Eq. (7). The influence of hog in Eq. (7) is nearly more than double of that in Eq. (6). What s more, the influence of piglets (R 2, t ) to pork in 0.05th and 0.95th quantiles are exactly opposite. Table 3 reports the standard errors of each regression coefficient estimate in Eqs. (6) and (7) as well as the estimated results of OLS method. It shows that all the parameters reject null hypothesis at 5% significance level, i.e., the regression coefficient estimates are distinctly unequal to zero. Furthermore, not only the results of 0.5th quantile regression model is different from that of OLS estimation, but also the 0.05th and 0.95th quantiles regression model have significant difference from the conditional mean regression model. In addition, zero hopothesis of testing for equalities of slopes is accepted. The regression coefficient estimates of the independent variables across different quantiles compared to OLS estimation are shown in Fig. 1. The two red dashed lines are the 95% confidence intervals from the OLS estimation (the same as below). The shady area gives confidence band of coefficients estimated across different quantiles (the same as below). As seen from the Fig. 1, the influence of R 4, t (hog) to R 1, t (pork) is positive under 0.05th quantile while it is negative above 0.95th quantile, i.e., the price movement of pork responds to that of hog in the opposite direction at 0.05th and 0.95th quantiles. However, the influence of R 2, t (hogfeed) and R 5, t (CPI) to R 1, t (pork) is always positive across different quantiles respectively and their influence above 0.05th quantile is nearly the same to those under 0.05th quantile. In addition, the influence of hog (R 3, t ) to pork above 0.95th quantile is obviously stronger than that under 0.05th quantile. By the usage of Eqs. (6) and (7), we can get the fitted values in samples and forecasting performance out of samples respectively for pork. Fig. 2 shows the results of in-sample fitted values for pork between January 2000 and December Fig. 3 reports the forecasting performance out of samples from January 2010 to October The green curves are the forecasting results of 0.95th quantile regression model for pork, the blue curves are the forecasting results of 0.05th

6 Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China 679 Fig. 1 Coefficients and their confidence band estimated across different quantiles for pork model. quantile regression model, and the black curves are real observations (the same as below). It shows that the curve of real observations is overwhelmingly located between 0.05th quantile curve and 0.95th quantile curve as seen from Fig. 2 and few is outside. Furthermore, the intervals generated from 0.05th and 0.95th quantile regression model successfully predict the pork price changes out of samples as seen from Fig. 3. Egg quantile regression model R 6, t (egg) is dependent variable. The independent variables are R 5, t (CPI, the same explanation can been in pork model), R 7, t (egg-type chicks), R 8, t (corn). The models were estimated as follows: R 6, t = R 5, t R 7, t R 8, t (8) R 6, t = R 5, t R 7, t R 8, t (9) Where Eq. (8) is 0.05th quantile regression model and Eq. (9) is 0.95th quantile regression model. The results suggest that the regression coefficient estimates of R 7, t and R 8, t at the two quantiles have great changes and directions of their influencing to egg price are also completely opposite. But the influence of series R 5, t (CPI) to egg price is stronger than those of series R 7, t (egg-type chicks) and R 8, t (corn) to egg price respectively. Table 4 reports the standard errors of each regression coefficient estimate in Eqs. (8) and (9) as well as the estimated results of OLS method. It shows that all the parameters reject null hypothesis at 5% significance level. What s more, 0.5th quantile regression model Fig. 2 In-sample fitted values of pork price volatility between January 2000 and December Fig. 3 Out-of-sample forecasts for pork price volatility between January 2010 and October 2010.

7 680 LI Gan-qiong et al. has no significant difference from the results of OLS estimation as seen from the Table 4. However, the parameters at 0.05th and 0.95th quantile models are different from those estimated by conditional mean model. In addition, zero hopothesis of testing for equalities of slopes is accepted. Table 4 The parametric estimates of 0.05th, 0.5th and 0.95th quantile regression models for egg Variables OLSE 0.05th 0.5th 0.95th C * * * * (0.3414) (0.8363) (0.4183) (0.8554) R 5, t * * * * (0.4540) (0.9057) (0.5976) (0.4087) R 7, t * * * (0.0650) (0.1404) (0.1099) (0.1316) R 8, t * * * (0.1156) (0.2458) (0.1454) (0.1677) The coefficients of independent variables across different quantiles compared to OLS estimation are shown in Fig. 4. As seen from the Fig. 4, the influence of R 5, t (CPI) to R 6, t (egg) is always positive across different quantiles and its influence under 0.05th quantile is stronger than that above 0.95th quantile. However, the influence of R 7, t (egg-type chicks) and R 8, t (corn) to R 6, t (egg) become stronger with quantile increase and the regression coefficient estimates of them in the 0.05th and 0.95th quantile regression model are quite different from those of OLS estimation. By the usage of Eqs. (8) and (9), we can get insample fitted values and out-of-sample forecasts for egg respectively. Fig. 5 shows the results of fitted values in samples between January 2000 and December Fig. 6 reports the forecasting performance out of samples from January 2010 to October In Fig. 5 it shows that the curve of real observations is overwhelmingly located between 0.05th quantile curve and 0.95th quantile curve and few is outside. Furthermore, the intervals generated from 0.05th and 0.95th quantile regression model successfully predict the egg price movements out of samples as seen from Fig. 6, i.e., real observations out of samples did not go beyond the intervals. But at the same time, we also can find that the cures of 0.05th quantile model and 0.95th quantile model sometimes have a certain distance from that of observations. Chicken quantile regression model R 9, t (chicken) is dependant variable. The independent variables are R 10, t (broiler-type chickenfeed), R 11, t (broiler chicks) and R 12, t (live chicken). The models were estimated as follows: R 9, t = R 10, t R 11, t R 12, t (10) R 9, t = R 10, t R 11, t R 12, t (11) Where Eq. (10) is 0.05th quantile regression model and Eq. (11) is 0.95th quantile regression model. As seen from Eqs. (10) and (11), it is obvious to find that the influence of broiler-type chickenfeed (R 10, t ) to chicken price is more distinct. The regression coefficient estimate of broiler-type chickenfeed in Eq. (10) is 0.81, but it is only negative 0.02 in Eq. (11). Table 5 reports the standard errors of each regression coefficient estimate in Eqs. (10) and (11) as well as the estimated results of OLS method. It shows that Fig. 4 Coefficients and their confidence band estimated by different quantiles for egg model.

8 Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China 681 Table 5 The parametric estimates of 0.05th, 0.5th and 0.95th quantile regression models for chicken Variables OLSE 0.05th 0.5th 0.95th C * * * * (0.1857) (0.3456) (0.1478) (0.6196) R 10, t * * * * (0.1249) (0.1779) (0.0861) (0.3520) R 11, t * * * * (0.0253) (0.0277) (0.0143) (0.0465) R 12, t * * * * (0.0628) (0.0761) (0.0322) (0.2225) Fig. 5 In-sample fitted values of egg price volatility between January 2000 and December Fig. 6 Out-of-sample forecasts for egg price volatility between January 2010 and October all the parameters reject null hypothesis at 5% significance level, i.e., the regression coefficient estimates are distinctly unequal to zero. Furthermore, the 0.05th and 0.95th quantile regression model are significantly different from the conditional mean regression model. In addition, zero hopothesis of testing for equalities of slopes is accepted. The regression coefficient estimate of R 10, t (broilertype chickenfeed), R 11, t (broiler chicks) and R 12, t (live chicken) across different quantiles compared to linear mean regression can be seen in Fig. 7. As seen from the Fig. 7, the coefficients of R 12, t (live chicken) is positive across different quantiles and is significantly different from results of OLS estimation. However, the influence of R 10, t (broiler-type chickenfeed) and R 11, t (broiler chicks) are quite different from R 12, t (live chicken) at 0.05th and 0.95th quantiles. The influence of R 10, t and R 11, t under 0.05th quantile is stronger than that above 0.95th quantile. The influence of R 12, t above 0.95th quantile is stronger than that under 0.05th quantile. By the usage of Eqs. (10) and (11), we can get fitted values in samples and forecasting performance out of samples respectively for chicken. Fig. 8 shows the results of fitted values in samples between January 2000 and December Fig. 9 reports the forecasting performance out of samples from January 2010 to October It shows that the curve of real observations is located between 0.05th quantile curve and 0.95th quantile curve seen from Fig. 8. The intervals Fig. 7 Coefficients and their confidence band at different quantiles for chicken model.

9 682 LI Gan-qiong et al. generated from 0.05th and 0.95th quantile regression model successfully predict chicken price movements out of samples as seen from Fig. 9, and the real curve is nearly in the middle of the intervals. CONCLUSION Models of livestock price movements with monthly data are assessed using a linear quantile regression approach. In general, the empirical results provide evidence in favor of the price changes of cost factors asymmetrically and unequally influence those of the livestock across different quantiles. Our study suggests that for pork model the influence of R 4, t (piglets) to R 1, t (pork) is positive under 0.05th quantile while it is negative above 0.95th quantile, i.e., the regression coefficient estimate of R 4, t is 0.20 in 0.05th quantile regression model and is in 0.95th quantile regression model. However, the influence of R 2, t (hogfeed), R 3, t (hog) and R 5, t (CPI) to R 1, t (pork) is positive across different quantiles. What s more, hog s influence above 0.95th quantile is obviously stronger than that under 0.05th quantile. For example, the regression coefficient estimate of R 3, t (hog) is 0.9 in 0.95th quantile regression model and it is more than double of that in 0.05th quantile regression model. The same conclusions are also found in egg model and chicken model. We also evaluate the performance of quantile regression models in forecasting and draw the same conclusion that using quantile regression approach to generate prediction intervals is useful for various forecasting applications (Taylor and Bunn 1999). The evidence we document suggests that the intervals generated from the 0.05th and 0.95th quantiles regression model can be seen as possible price fluctuation range of pork, egg and chicken. The economic value of forecasting using quantile regression is that it not only help analyze the cost factors influencing and improve the accuracy of prediction, but also benefit to risk management of agricultural product market. Understanding the price spillover effects from one agriculture product to another one becomes prerequisite for policymakers to lay down any price control policy in agricultural product markets. Acknowledgements This work was supported by the Key Project of National Key Technology R&D Program of China (2009BADA9B01). Fig. 8 In-sample fitted values of chicken price volatility between January 2000 and December Fig. 9 Out-of-sample forecasts for chicken price volatility between January 2010 and October References Banachewicz K, Lucas A Quantile forecasting for credit risk management using possibly misspecified hidden markov models. Journal of Forecasting, 27, Cai Y Z A quantile approach to US GNP. Economic Modelling, 24, Chaudhuri P. 1991a. Global nonparametric estimation of conditional quantile functions and their derivatives. Journal of Multivariate Analysis, 39, Chaudhuri P. 1991b. Nonparametric estimates of regression quantiles and their local Bahadur representation. The Annals of Statistics, 19, Chen J, Lin L, Ye A Z A quantile regression analysis on Chinese resident s consumption. The Journal of Quantitative and Technical Economics, 26, (in Chinese) Chen J B, Du X M, Dong H L Empirical analysis of Chinese residents income and consumption based on quantile regression. Statistics and Information Forum, 24, (in Chinese) Chen M Y, Lin F L, Chang C K Relations between

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