1 Introduction
Due to its high nutritional value, mutton is gradually regarded as one of the important meat consumer goods. As the main mutton producing and consuming area in China, the mutton price of Xinjiang has a direct impact on the national mutton price. At the same time, the mutton price is affected by the relationship between supply and demand and external factors. According to the related statistical data, the mutton price increased from 27.63 Yuan/Kg at the beginning of 2008 to 63.52 Yuan/Kg in June 2013 and then decreased to 41.33 Yuan/Kg in 2016. This sharp fluctuation of mutton price in Xinjiang will produce huge economic losses and increase the economic burden of farmers and herdsmen. Therefore, the monitoring and risk early warning of mutton price fluctuation is particularly important.
In the volatility process of mutton price, the price changes from peak to trough in the price curve, and then from trough to the next peak, which is called a fluctuation cycle. Similarly, from trough to peak, and then from peak to next trough is also called a fluctuation period. Thus, the fluctuation characteristic in this paper is analyzed from the perspective of the fluctuation cycle. For this purpose, this paper will analyze the length of the fluctuation cycle and the change frequency within a certain cycle and meantime analyze the future fluctuation trend of mutton price to better monitor and make risk warnings for mutton price volatility.
In recent years, some scholars have conducted a lot of related studies on the fluctuation characteristics of the price of livestock products. These studies can be classified into two categories: one is the analysis of periodic and seasonal characteristics of single time series and the other is the linkage analysis of the price fluctuation among different livestock products in Xinjiang. Regrettably, there are few studies about the volatility characteristics of mutton price in Xinjiang in the existing literature.
For the study of mutton price in a single time series, the monthly mutton price time series often contains four different components: long-term trend component (T), cycle component (C), seasonal component (S), and irregular component (Ⅰ). Among them, the long-term trend component and cycle component analyze the price change from a long-term perspective. The seasonal component mainly focuses on the annual circular fluctuation. The change of irregular components has no rules to follow, and they are the response to the impact of emergencies. Usually, seasonal and irregular components often cover up the objective changes in market price fluctuations and interfere with the analysis of price fluctuations. For this purpose, these two components are often eliminated through seasonal adjustment methods such as the X-12 Seasonal Adjustment Method
[1] before analyzing price fluctuations. Therefore, the adjusted information only contains trend and cycle components. To make a better analysis, it is necessary to decompose the data and divide the two components from the data. Common trend decomposition methods include regression analysis
[2], moving average method
[3], Hodrick Prescott (HP) Filtering Method
[1], and empirical mode decomposition (EMD) method
[4]. In fact, for complex problems, the idea of divide and conquer can better solve complex problems and extract important information. Among the uncertain components, it is mainly affected by weather conditions, policy factors, and transportation costs. Therefore, HP filtering and EMD methods can better decompose signals and uncertainty terms with different frequencies, and then explore the impact of various factors on mutton price fluctuation.
Numerous factors influence the prices of agricultural and livestock products, including mutton. Existing literature often focuses on examining the impact of a single or limited number of factors on prices, but has not yet successfully identified the primary factors driving price fluctuations from a broad array of diverse influencing elements using an appropriate methodology. Addressing the gaps in existing literature, this paper makes two key contributions.
Firstly, it unveils the spatio-temporal evolution patterns of mutton price in Xinjiang. Secondly, it provides a systematic examination of the mechanisms driving these price fluctuations. To achieve these two objectives, this paper employs the HP filtering method to analyze the long-term trends and cyclical behaviors of mutton price fluctuations in Xinjiang. It also investigates the spatial characteristics of mutton price fluctuations across different regions in Xinjiang through statistical descriptions and heatmap analyses. Additionally, the Threshold Autoregression (TAR) model is used to assess the interactive relationships between mutton prices and those of beef and other livestock products, thereby elucidating the underlying mechanisms of mutton price volatility in the region.
The rest of this paper are organized as follows. Section 2 provides a comprehensive literature review about the factors of price volatility of agricultural and livestock products. In Section 3, the analytical methodology is described in detail. Section 4 presents the data sources for analysis. In Section 5, patiotemporal evolution analysis of mutton price in Xinjiang are investigated and the linkage analysis between the price of mutton and beef in Xinjiang are given in Section 6. Finally, the concluding remarks are included in Section 7.
2 Literature Review
Most existing studies have focused on the price fluctuations in agricultural and livestock products and has conducted in-depth discussions about the topic. This paper reviews and summarizes the factors affecting the price fluctuations of agricultural and livestock products from three levels: macro policies, macroeconomic financial fluctuations, and the prices and production of related micro and meso-level products.
In terms of macro policy factors, this paper primarily examines the impact of trade policies, agricultural policies, and banking loan policies on the price fluctuations of agricultural and livestock products. Sun, et al.
[5] used bootstrap full-sample and subsample rolling-window Granger causality tests to explore the impact of trade policy uncertainty (TPU) on agricultural product prices (ACP). Anderson and Nelgen
[6] argued that trade barriers are a significant factor affecting price stability, specifically including international agricultural trade policies, and standards and methods for agricultural product quality testing. Pop and Mihuţ
[7] studied different stabilization mechanisms implemented throughout the history of the Common Agricultural Policy (CAP) for three major agricultural commodities: wheat, sugar, and milk, finding that different policy approaches often lead to varying results in market volatility correlations and price processes. Burakov
[8] investigated the long-term and short-term direct and indirect impacts of oil price changes (including impacts on exchange rates) and banking loan policies (interest rate channels) on the prices of six types of Russian agricultural products: buckwheat, potatoes, oats, wheat, rye, and barley.
Regarding broader macroeconomic and financial volatility factors, some studies has investigated the impacts of international trade, economic development, and financial markets on the price fluctuations of agricultural and livestock products. Zhou
[9] found that the real effective exchange rate of the Renminbi affects agricultural product prices and is a cause of price increases. Rezitis
[10] observed that, in the long term, changes in the U.S. dollar exchange rate negatively affect agricultural product prices. Alexandratos
[11] analyzed and suggested that the main risk factors for food prices include agricultural futures prices, international financial markets, prices of related products (prices of substitutes and inputs), population, economic growth rate, and national policies. Hao, et al.
[12] used a panel structure vector autoregression econometric approach to capture market interdependencies, and the possibility of heterogeneous and dynamic responses in developing countries. Gohin and Cordier
[13] developed a theoretical model to explain the behaviors of speculators and producers in futures and spot markets, finding that positions taken before price spikes stimulated production and inventory, helping to mitigate food price volatility.
More specifically, focusing on the micro and meso-levels, prior research has mainly examined the impact of related product prices and their production on the price fluctuations of agricultural and livestock products. This includes some factors such as international grain prices, regional market wholesale and retail price fluctuations, biofuel production, and oil prices. Byerlee, et al.
[14] noted that international grain prices are a significant reason affecting domestic food prices, and emphasized that the degree and scope of this impact are closely related to the specific food consumption habits of different countries. Kavoosi-Kalashami, et al.
[15] used Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to examine the spillover effects of wholesale and retail price fluctuations in a specific region's rice market in Iran. Paris
[16] argued that the development of biofuels leads to an increased impact of oil prices on agricultural product prices, meaning that the growth in biofuel production causes agricultural product prices to rise. Ma, et al.
[17] found that the response curve of oil price shocks on agricultural product prices is not significant, and in the long term, agricultural product prices are neutral to changes in oil prices.
In summary, existing studies has explored the price fluctuations of agricultural and livestock products from multiple perspectives and aspects. However, most studies have focused on investigating the factors influencing these fluctuations and analyzing causes and effects, with less attention given to the inherent characteristics of the price fluctuations themselves and their interconnected relationships. For this purpose, this paper employs the Hodrick-Prescott (HP) filter method to analyze the long-term trends and cyclical characteristics of mutton prices in Xinjiang, explores the spatial evolution characteristics of mutton price fluctuations across different regions of Xinjiang, and uses a threshold autoregressive (TAR) model to analyze the interlinkages between mutton prices and the prices of other livestock products.
3 Methodology
3.1 Fluctuation Analysis Methods
Considering that the X-12 Seasonal Adjustment Method, HP filtering method, and EMD decomposition method are classical models, the steps and contents of these three methods are briefly introduced below.
3.1.1 X-12 Seasonal Adjustment Method
The X-12 Seasonal Adjustment Method is an extended model based on the X-11 Seasonal Adjustment Method, which can be completed by the following steps when using addition rule for seasonal fluctuation analysis.
Firstly, the analysis method of the X-12 Seasonal Adjustment Method is determined according to the analyzed data and objectives. The X-12 Seasonal Adjustment Method decomposed the time series fluctuation into three different fluctuation factors, the basic formula of which is , with Trend , Seasonal factor , and Irregular factor . Trend variation factor reflects the trend of time series over a long time, while irregular variation factor is the influence of random factors on the original time series data. And the seasonal variation factor is the variation factor with an annual cycle.
Then, the trend variable factor and the irregular variable factor are stripped from the original time series. The trend factor was measured by the central moving average method. For the monthly data, 12 moving average items were first carried out, followed by 2 average items of the 12 2 moving average method.
Thus, and .
Finally, the irregular components are separated. The number of moving average items should not be too large, the moving average method is often used.
Therefore, we can get
Thus, the seasonal fluctuation component is .
3.1.2 HP Filtering Analysis Method
The HP filtering method is often used to decompose the long-term trend of economic time series, mainly by increasing the cycle frequency of time series to weaken the cycle fluctuation, and then highlight the trend of economic time series. It has gained wide attention in business cycle analysis. Its mathematical formula is expressed as follows.
Assume is a seasonally adjusted time series and it has removed seasonal fluctuation and irregular components. Accordingly only trend and cyclical components are included into the time series. Assume is a trend component, is a recurring element, we can get
HP filtering separates from , and is often defined to solve a minimization problem below:
where is the lag operator polynomial, i.e.,
After mixed calculation of the above two equations, the HP filtering problem can be obtained in the following form, i.e.,
The first part in the brackets above equation is the measurement of the fluctuation component, the second part is the measurement of the smoothness degree with control variable . Therefore, has an important influence on the results. According to experience, the value of is shown as follows. For annual data, ; for quarterly data, ; and for monthly data, .
3.1.3 Empirical Mode Decomposition (EMD)
In addition to the HP filter method, from the perspecitve of mode decomposition for non-stationary time series, empirical mode decomposition (EMD) is a competitive solution. Usually, the EMD decomposition is used as a result of several cycles of different simple time series and a residual series. Through a specific algorithm, some simple components (i.e., the intrinsic Modal functions (IMF)) are separated from the original time series. Among the remaining residual items, IMF should meet two requirements. First, in the complete interval, the difference between the number of zeros through which the function passes and the number of its extreme points is 1. Second, the function defined by the local maximum values of the envelope and demarcated by the local minima envelope of the mean to 0. The first IMF of EMD decomposition results is the shortest cycle for the IMF, and finally to the longest period of the lowest frequency component and the last remaining residual item. The specific extraction process follows the following four main steps.
1) Calculate all the maxima and minima of the original time series , and construct the upper envelope for the maxima , and the lower envelope for all minima by cubic spline interpolation.
2) Calculate the difference between the original time series and the mean value of the upper and lower envelope, i.e.,
3) If the meet the IMF's two requirements, thus the is the IMF, surplus is the new .
4) Repeat the above process until the new IMF component cannot be decomposed, at which point the residual is denoted as .
3.2 Linkage Analysis Methods
For the study of the fluctuation characteristics of mutton price, from the perspective of mutton price and the price of other livestock products, the econometric model is used to find the decisive factors of price fluctuation. Accordingly, the threshold autoregressive (TAR) model
[18], vector autoregressive (VAR) model
[19, 20], ARCH model
[21] and multiple regression model
[2] analyzed price fluctuation and explored the influence of product substitutes on price fluctuation. In this paper, the threshold autoregressive model and vector autoregressive model are introduced for linkage anlayisis, which are elaborated below.
3.2.1 Threshold Auto-regressive (TAR) Model
The TAR model was able to explain the nonlinear characteristics of data in a better way. The basic theory of the TAR model was that the motion form of sequences changed from one mode to another mode at a certain time point, and the two modes were discontinuous discrete. The basic idea of the TAR model is shown as follows.
Set threshold values within the value range of observed time series. The timeline is divided into sections, and different TAR models in different intervals are fitted. The TAR model for time series can be expressed as
where , .
In the above formula, represents the threshold value, , ; represents the number of threshold intervals, represents the number of threshold values; represents a threshold variable; is a white noise sequence with the mean of 0 and a variance of ; is the th autoregressivn coefficient of the model in the th threshold interval.
The above model can be expressed as , where represents the order of TAR model in the stage.
3.2.2 Vector Autoregressive (VAR) Model
The VAR model transforms the autoregressive model of a single variable into an autoregressive model of multiple time series variables by portraying each endogenous variable in the system as a function of the lag value of all endogenous variables. VAR models are often used to explain the effects of economic variables. Its mathematical expression is given by
where is the column vector of endophytic variable, is the column vector of dimensional exogenous variables, is the lag order, is the number of samples, and is the coefficient matrix to be estimated, is the error disturbance vector.
In the VAR model, for non-smooth time series, it is necessary to change into smooth time series by using differential method. However, with the development of cointegration theory, for non-smooth time series, as long as there is a cointegration relationship between variables, the VAR model can be built directly.
4 Data Sources
This paper mainly studies the analysis of the fluctuation characteristics of mutton prices, the analysis of the time and space characteristics and evolution of prices, the interaction between mutton and other livestock products, and the analysis of the influencing factors of mutton prices. For the mutton price and the number of variables affecting the price of mutton and different sources. The main data sources for this study are shown as follows.
National Bureau of Statistics: Statistics on the production of livestock products such as mutton, price information statistics, and agricultural economic statistics can be obtained from the National Bureau of Statistics. Such as Data on consumer price indices, and complementary or alternative livestock products are also available. In particular, pork, beef, and mutton production refers to the weight of the carcass. Information related to the price of mutton in Xinjiang can also be obtained For example, mutton production, mutton production as a proportion, per capita household mutton consumption, import and export amount, import and export volume, urban residents per capita disposable income, as well as the production of mutton and mutton consumption in various regions of Xinjiang, meat and sheep out of the column rate.
China Livestock Information Network: China Livestock Information Network covers the annual local price trend chart, in addition to Xinjiang bone-bone mutton prices, bone-meat mutton prices, mutton feed prices (take corn, bran, and soybean meal average price as mutton feed prices), pork, beef, chicken and fish prices are also available from the China Livestock Information Network.
FAO Statistical Database: To better reflect the changing relationship between mutton prices in Xinjiang and mutton prices in other regions, world mutton price data were downloaded from the FAO Statistical Database. It includes the meat and sheep stock, mutton production, carcass weight, import and export quantity, and import and export value.
National Agricultural Product Business Information Public Service Platform: To better capture the uncertain factors in the fluctuation of mutton price, policies and regulations exogenous variables affect the fluctuation of mutton price. The National Agricultural Product Business Information Public Service Platform can obtain accurate policy and regulation information. And can also get some livestock products and other related price information.
Compilation of Cost-Benefit Data of Agricultural Products: The unit production cost of sheep is calculated according to the production cost of 50 kg sheep in the "Cost-benefit Data Collection of Agricultural Products".
5 Spatiotemporal Evolution Analysis of Mutton Price in Xinjiang
In recent years, Xinjiang's economy has been developing rapidly, and people's demand for mutton is also increasing. Meanwhile, mutton prices in Xinjiang have continued to rise since 2003. Throughout the development history of the Xinjiang mutton sheep industry in recent years, the Xinjiang mutton sheep industry has not developed under relatively stable market conditions, and the fluctuation of mutton prices is also obvious. Based on this, the purpose of this chapter is to summarize the fluctuation rule of mutton market price in the Xinjiang region based on literature research and theoretical analysis, to lay a good foundation for explaining the reasonable fluctuation of the mutton market price. Mutton has become an important part of China's national consumption at the present stage. In recent years, the frequent fluctuation of mutton price has intensified the risk degree of the market, which will have an important impact on production behavior and consumer behavior, which also constitutes an important realistic starting point for empirical research in this chapter.
In this chapter, the HP filter is used to analyze the periodicity and long-term trend of mutton price in Xinjiang. The spatial characteristics of mutton price in Xinjiang were analyzed by comparing the difference of mutton price in different regions with the help of the thermal map. Based on the analysis results of the time and space characteristics of mutton price in the Xinjiang region, the paper further summarizes the time and space characteristics and discusses the evolution law of the time and space characteristics.
5.1 Temporal Evolution Characteristics of Mutton Price
HP filter is an analysis method of time series in state space, which can separate trend factors and fluctuation factors in time series. Therefore, based on the factor decomposition idea of time series, this chapter uses the HP filtering method to decompose the Xinjiang mutton retail price through filtering processing, obtains its periodicity part and trend part, and then analyzes its periodicity characteristics and long-term trend.
5.1.1 Descriptive Analysis
The monthly retail price of mutton (yuan/kg) in Xinjiang from January 2010 to August 2019 is shown in
Figure 1. As can be seen from the figure, the price of mutton fluctuates greatly on the whole, showing a trend of rising at first, remaining stable after reaching a certain extent, declining, and then rising, with a rise or fall of 46.15%. It can be divided into four stages.
Figure 1 Monthly price trend of mutton in Xinjiang |
Full size|PPT slide
First of all, the first stage is from January 2010 to May 2013, lasting 41 months, the price of mutton keeps rising, showing an upward trend, a rise and fall of 45.47%; In particular, from December 2012 to May 2013, the price of mutton grew rapidly, and the fluctuation increased significantly, with a rise and fall of 20.37% at one time The second stage lasted for 13 months from June 2013 to June 2014. The trend chart showed that the overall price of mutton was relatively stable, with an average value of 61.33 yuan/kg and a standard deviation of 0.51. From the perspective of data, the fluctuation range of mutton price in this stage was relatively flat and stable The third stage was from July 2014 to December 2015, which lasted for 18 months. The price of mutton showed an obvious downward trend, with a decrease rate of 33.86%. The fourth stage is from January 2016 to August 2019, lasting 44 months. It can be seen from the figure that although the price of mutton decreased to some extent in some months of this stage, it still showed an overall upward trend, with a rise or fall of 33.45%. Compared with the trend of the first stage, the price of mutton rose relatively slowly
5.1.2 HP Filtering Analysis
In this section, based on the analysis of the original data, HP filter will be used to analyze the retail price of mutton in Xinjiang. Using Eviews
11.0 measurement analysis software, the monthly mutton retail price from January
2010 to August
2019 was decomposed by HP filter. According to the experience of monthly data analysis,
was set as
14400 to obtain the periodic component and long-term trend of Xinjiang mutton retail price. The monthly data of mutton retail price after HP filter decomposition is shown in
Figure 2.
Figure 2 HP filter decomposition diagram of mutton retail price sequence |
Full size|PPT slide
In
Figure 2, the Cycle curve shows the part of Cycle variation obtained from the decomposition of mutton price series, that is, the components with high frequency are separated, that is, the components with medium and short-term fluctuations in mutton price series. It can be seen from this curve that the variation range of mutton price series is consistent with the original sequence of mutton price. Fluctuates around 0, and the fluctuation range is relatively severe, especially during the period from
2012 to
2016, the fluctuation is most obvious and violent. Meanwhile, from
2016 to
2019, although the fluctuation amplitude decreased compared with the previous period, the fluctuation frequency increased.
In addition, the Trend curve represents the long-term Trend sequence derived from the decomposition of the mutton price sequence, that is, the components with lower frequency separated. As shown in
Figure 2, during the period from January
2010 to August
2019, the Trend curve showed an upward trend at first, then a downward Trend, and then an upward Trend, which can be divided into three periods. As shown in
Table 1, first of all, the first cycle is from January
2010 to January
2014, a total of
49 months. During this period, the overall price of mutton has a rising trend, with a fluctuation range of
59.84% and a rise or fall of 77.85% within the cycle. Then, the second cycle was from February 2014 to December
2015, a total of
23 months. During this cycle, the price of mutton showed a downward trend, with a fluctuation range of
40.18% and a rise or fall of
−32.78% within the cycle. Finally, there is the third cycle, which spans from January
2016 to August
2019, a total of
44 months. In this cycle, the price of mutton is still on the rise, with a fluctuation of
43.63% and a rise or fall of
33.45% within the cycle. Comparing the results of the three cycles, the fluctuation range in cycle 1 is larger than that in cycle
2 and cycle
3. At the same time, the rise and fall of cycle 1 is higher than the other two cycles, and the price of mutton changes the most.
Table 1 Long-term trend period of mutton price decomposed by HP filtering method |
| period | Fluctuation period (month) | fluctuation range | rise and down within the period |
| period one | 2010.1–2014.1 (49) | 59.84% | 77.85% |
| period two | 2014.2–2015.12 (23) | 40.18% | 32.78% |
| period three | 2016.1–2019.8 (44) | 43.63% | 33.45% |
According to the above analysis, although the price of mutton in Xinjiang decreased to a certain extent in 2014 and 2015, it still showed an overall upward trend. Moreover, in recent years, the fluctuation cycle composition is relatively complex, the fluctuation is more and more frequent, and the fluctuation frequency is gradually accelerating, but there is no obvious periodicity.
Comparing the data of mutton price in Xinjiang in January and February 2009, it can be seen from the color of the thermal map that the mutton price in February as a whole rose compared with January, with an average increase of 1.8 yuan/kg in each region. Meanwhile, according to the results of two months, the price of mutton in Xinjiang in January and February 2009 showed a decreasing trend from the south to the north, with higher price of mutton in the south and lower price of mutton in the north. The main cause of this phenomenon is the southern border region is the other inland provinces and regions in our country, the northern border is neighboring countries more, more international supply and transport, domestic transportation more convenient and international supply problems such as export tax, causing demand is relatively higher in the north and south so south of mutton price higher than the northern. In addition, from February 2009 to January, the highest price of mutton region from Aksu, Kizilsu Kirgiz Autonomous Region and Kashi into Hotan region, the price increased by 12.5%; The regions with the lowest mutton prices changed from Altay to Tacheng and Boltala Mongol Autonomous Prefecture, with the price increasing by 17.39%.
It can be concluded that the spatial characteristics of mutton price in Xinjiang are mainly as follows: The price of mutton in the southern region is higher, while the price of mutton in the northern region is lower, showing a decreasing trend from south to north on the whole.
5.2 Spatiotemporal Evolution Analysis of Mutton Price
Based on the time fluctuation trend of mutton price data, mutton price fluctuates greatly on the whole, showing a trend of rising first, then stable, then falling, and then rising. Specifically divided into four stages. The first stage was from January 2010 to May 2013, lasting for 41 months. The price of mutton kept rising, presenting an upward trend. The second stage lasted for 13 months from June 2013 to June 2014, during which the overall price of mutton was relatively stable. The third stage was from July 2014 to December 2015, which lasted for 18 months. The price of mutton showed an obvious downward trend. The fourth stage lasted 44 months from January 2016 to August 2019, with an overall upward trend. However, compared with the first stage, the price of mutton rose relatively slowly.
HP filter method was used to analyze the periodicity and long-term trend of mutton price in Xinjiang. The results showed that mutton price increased first, then decreased, and then increased. In addition, from 2012 to 2016, the price fluctuation of mutton was the most obvious and severe; From 2016 to 2019, although the fluctuation range decreased compared with the previous period, the fluctuation frequency of mutton price increased. Therefore, although the price of mutton in Xinjiang decreased to a certain extent in 2014 and 2015, it still showed an overall upward trend. In recent years, the fluctuation cycle composition is relatively complex, with more and more frequent fluctuations and gradually accelerating frequency, but there is no obvious periodicity.
5.3 Spatial Evolution Characteristics of Mutton Price
As the largest province in China, Xinjiang Uygur Autonomous Region has a vast area and complex and changeable geographical environment. Therefore, the climatic conditions and resource environments in various regions in Xinjiang are different. These spatial factors also affect the spatial change law of mutton price to a certain extent, resulting in different mutton prices in different regions. This chapter analyzes the spatial characteristics of mutton price in Xinjiang by taking the mutton price in January 2009 and February 2009 as an example.
5.3.1 Descriptive Statistical Comparison
To better compare the differences of mutton prices in various regions of Xinjiang in January and February 2009, first, descriptive statistics are made on the overall situation of mutton prices in Xinjiang in the two months in combination with indicators such as mean, standard deviation, skewness and kurtosis. The results are shown in
Table 2. In addition, the price of mutton in various regions of Xinjiang is shown in
Figure 3.
Table 2 Descriptive statistics of mutton prices in January and February 2009 |
| time | mean | standard deviation | maximum | minimum value | range | kurtosis | Partial degrees |
| 2009.01 | 28.143 | 2.852 | 32.000 | 23.000 | 9.000 | −0.866 | −0.098 |
| 2009.02 | 29.867 | 2.416 | 36.000 | 27.000 | 9.000 | 1.733 | 1.196 |
Figure 3 Mutton prices in Xinjiang in January and February 2009 |
Full size|PPT slide
From
Figure 3 and
Table 2, for the mutton prices in various regions of Xinjiang in January and February 2009, on the whole, the mutton prices in February in most regions are higher than that in January, and the average value in February is 29.867 yuan/kg, higher than 28.143 yuan/kg in January, which also shows this problem. From the perspective of fluctuation, the standard deviation of mutton price in February is lower. Although the maximum and minimum values in February are higher than those in January, they have the same range. Therefore, the mutton price in various regions of Xinjiang fluctuated more in January 2009. In terms of kurtosis, the kurtosis value in January is less than 0, indicating that the data distribution of mutton price in January is more flat than the normal distribution; The kurtosis value in February is greater than 0, indicating that the data distribution of mutton price in February is steeper than the normal distribution. In terms of skewness, the skewness value in January is less than 0, indicating that the distribution of mutton price data in January is left skewed, and the price data are more concentrated on smaller values; The skewness value in February is greater than 0, indicating that the distribution of mutton price data in February is right skew, and the price data is more concentrated on larger values.
5.3.2 Analysis of Thermodynamic Diagram Results
Considering the mutton price data of 15 regions in Xinjiang in January 2009, the spatial characteristics of mutton price fluctuation in Xinjiang are studied with the help of the thermal map, as shown in
Figure 4.
Figure 4 Heat map of mutton price in various regions of Xinjiang in January 2009 |
Full size|PPT slide
As can be seen from
Figure 4, except for the lack of mutton price data in the three regions, on the whole, mutton prices show a downward trend from southwest to northeast, with a decrease of 28.13%. Specifically, the price of mutton in Northern Xinjiang is low, and the price of mutton in Altay, the northernmost region, is the lowest, 23 yuan/kg; The price of mutton in Southwest China is the highest, especially in Aksu, Kizilsu, Kirgiz Autonomous Region and Kashgar, with the highest price of 32 yuan/kg.
Considering the mutton price data of 15 regions in Xinjiang in February 2009, the spatial characteristics of mutton price fluctuation in Xinjiang are studied with the help of the thermal map, as shown in
Figure 5.
Figure 5 Heat map of mutton price in Xinjiang in February 2009 |
Full size|PPT slide
As can be seen from
Figure 5, except for the lack of mutton price data in the three regions, on the whole, the mutton price still shows a downward trend from southwest to northeast, with a decrease of 25%. The price of mutton in Northern Xinjiang is low, and the price of mutton in Tacheng and Bortala Mongolian Autonomous Prefecture is the lowest, 27 yuan/kg; The price of mutton in the south is the highest, especially in Hotan, which is 36 yuan/kg.
For the price of mutton in January and February of 2009 in Xinjiang, on the whole, the price of mutton in February in most regions was higher than that in January, and the price of mutton in various regions of Xinjiang in January was more volatile. In addition, the data distribution of mutton price in January is flatter, and the data are more concentrated on smaller values. Compared with the normal distribution, the data distribution of mutton price in February is steeper, and the data are more concentrated on larger values.
In using a heat map in the Xinjiang region under the condition of mutton price difference, analysis results show that the mutton prices overall in February from January have increased, and the results of two months of Xinjiang region mutton prices are from the south to the north of present decreasing trend, south mutton prices higher, northern mutton prices lower. In addition, compared with January, the regions with the highest mutton price in February 2009 changed from Aksu, Kizilsu Kirgiz Autonomous Region, and Kashi to Hotan region; The lowest price of mutton from Altay region to Tacheng and Bortala Mongol autonomous prefecture region. Therefore, the spatial characteristics of mutton price in Xinjiang are mainly as follows: the price of mutton in the south is higher, and the price of mutton in the north is lower, showing a decreasing trend from south to north on the whole.
6 Linkage Analysis between the Price of Mutton and Beef in Xinjiang
Xinjiang is an area inhabited by ethnic minorities. Compared with other livestock products (such as pork and chicken, etc.), beef and mutton are the main meat consumer goods for local urban and rural residents
[22]. According to the "14th Five-year Development Plan of Animal Husbandry in Xinjiang Uygur Autonomous Region", during the 14th Five-year plan period, At the same time, animal husbandry is an important basis and economic source for the district animal husbandry will adhere to the direction of ecological development, the combination of agriculture and animal husbandry, the matching of grass and livestock, steadily develop animal husbandry in pastoral areas, and highlighting the development of animal husbandry in agricultural areas, expanding beef cattle and sheep industry, developing dairy industry and other characteristic industries. At the meantime, animal husbandry also is an important basis and economic source for the subsistence and development of farmers and herdsmen, especially minority herdsmen. Therefore, the linkage analysis of the price fluctuation of beef and mutton is helpful in promoting the development of animal husbandry in Xinjiang and has important research significance for Xinjiang's economic development and rural revitalization. Therefore, this section mainly takes beef price as the linkage analysis object of Xinjiang mutton price fluctuation, conducting statistical analysis, comparative analysis, and linkage analysis on beef price, to observe the impact of beef price on mutton price.
6.1 Fluctuation Analysis of Beef Price
The data in this study are derived from relevant statistical yearbooks over the years, including China Animal Husbandry Yearbook and Xinjiang Statistical Yearbook. Based on the availability and missing degree of data, the data sample is the monthly beef price (yuan/kg) of Xinjiang province from January 2010 to August 2019, and there are 116 samples.
Figure 6 shows the fluctuation trend of beef price. As can be seen from
Figure 6, beef price shows the obvious non-linear fluctuation characteristics and strict statistical test and analysis will be conducted below.
Figure 6 Xinjiang beef monthly price fluctuation chart |
Full size|PPT slide
Firstly, descriptive statistical analysis is conducted on the price of beef and mutton.
Table 3 lists the related results.
Table 3 Statistical analysis table of monthly price of beef and mutton in Xinjiang |
| | Mean | Variance | Maximum | Minimum | Skewness | Kurtosis |
| Mutton | 50.90 | 8.00 | 64.81 | 34.90 | 0.07 | −1.29 |
| Beef | 52.81 | 10.29 | 65.00 | 33.10 | −0.66 | −1.11 |
For Xinjiang beef and mutton monthly prices, combined with the mean, skewness, kurtosis, and other indicators, descriptive statistical analysis. The average price of beef was higher, at 52.81 yuan/kg, indicating that beef was more expensive than mutton from 2010 to 2019. In terms of fluctuation, the range and variance of beef are higher than that of mutton, which indicates that the price of beef in Xinjiang fluctuates greatly and presents irregular characteristics. Compared with mutton, beef prices are more active. From the perspective of skewness and kurtosis, the skewness value of mutton price is greater than 0, the kurtosis value is less than 0, and the overall distribution is right skewness, that is, the price of Mutton in Xinjiang is more concentrated on smaller values. However, the skewness value and kurtosis value of beef price are less than 0 and the overall distribution is left skewness, namely, the beef price in Xinjiang is more concentrated on smaller values, and the data distribution is flatter than the normal distribution.
To test the stationarity of beef price time series, the ADF test is mainly used in this paper to test the stationarity of beef price before the analysis of fluctuation characteristics. The original hypothesis is that the tested sequence has a unit root, that is, a non-stationary sequence, and the alternative hypothesis is that the tested sequence does not have a unit root, namely, a stationary sequence.
Table 4 lists the test results. In
Table 4,
represents the price of beef, and
represents the first-order difference of variable
.
Table 4 ADF test results of beef price |
| Test sequence | ADF statistic | Mackinnon critical value |
| 1% | 5% | 10% |
| −1.556964 | −3.489117 | −2.887190 | −2.580525 |
| −4.474052*** | −3.489117 | −2.887190 | −2.580525 |
| Note: "*", "**" and "***" mean passing the significance test of 10%, 5%, and 1% respectively. |
As shown in
Table 4, in the case of intercept term, the beef price time series with first-order difference passes the significance test at 1% level, indicating that the series is stable, so the TAR model can be established for it.
Because the TAR model can search out the most appropriate threshold value through threshold variables, it can find the stage of sharp and gentle data fluctuation. Therefore, this study uses the TAR model to analyze the price fluctuation of beef price in Xinjiang.
In this study, the maximum lag period of beef price series is set at 14. Through the reviews software can be used to test whether there are two thresholds in beef price time series. The null hypothesis is that there is no second threshold value, and the test results show that the null hypothesis is accepted. Therefore, the threshold autoregression model of one threshold value is established. When the data is higher than the threshold value, the model builds the upper region. When the model is below the threshold value, the model builds the lower region. After the lag period of the threshold autoregression model is determined, the time series of beef price can be estimated by the TAR model through Eviews software. Based on the estimates, the sample size was reduced to 102, with the adjusted data range from March 2011 to August 2019. Meanwhile, in order to compare with the threshold regression results of beef price time series, the results of the linear autoregressive are also presented in
Table 5.
Table 5 Estimates of the TAR model of the Xinjiang beef price sequence |
| Variable | Linear self-regression | | Threshold Self-Regression (Lower Area) | | Threshold self-regression (Upper Region) |
| Coefficient | Standard Error | T-value | Coefficient | Standard Error | T-value | Coefficient | Standard Error | T-value |
| C | 1.282* | 0.701 | 1.828 | | 1.898 | 1.622 | 1.170 | | −2.807 | 3.031 | −0.926 |
| NIUROU(−1) | 1.059*** | 0.108 | 9.851 | 1.938*** | 0.189 | 10.280 | −1.489*** | 0.233 | −6.395 |
| NIUROU(−2) | 0.254 | 0.157 | 1.615 | −1.244*** | 0.404 | −3.077 | 2.045*** | 0.427 | 4.790 |
| NIUROU(−3) | −0.184 | 0.159 | −1.156 | 0.547 | 0.494 | 1.106 | −0.130 | 0.520 | −0.250 |
| NIUROU(−4) | −0.143 | 0.160 | −0.892 | −0.614 | 0.480 | −1.279 | 0.426 | 0.505 | 0.842 |
| NIUROU(−5) | 0.010 | 0.161 | 0.062 | 0.330 | 0.451 | 0.732 | −0.806* | 0.473 | −1.705 |
| NIUROU(−6) | −0.097 | 0.160 | −0.608 | 0.604 | 0.440 | 1.373 | −1.045*** | 0.460 | −2.270 |
| NIUROU(−7) | 0.054 | 0.160 | 0.336 | −0.893** | 0.438 | −2.040 | 0.923*** | 0.460 | 2.006 |
| NIUROU(−8) | 0.088 | 0.160 | 0.549 | 0.189 | 0.434 | 0.436 | 0.266 | 0.455 | 0.585 |
| NIUROU(−9) | 0.025 | 0.160 | 0.154 | 0.065 | 0.398 | 0.163 | 0.314 | 0.421 | 0.748 |
| NIUROU(−10) | −0.026 | 0.160 | −0.162 | −0.029 | 0.387 | −0.074 | −0.040 | 0.411 | −0.098 |
| NIUROU(−11) | −0.041 | 0.159 | −0.256 | 0.152 | 0.376 | 0.403 | −0.482 | 0.399 | −1.208 |
| NIUROU(−12) | −0.058 | 0.157 | −0.368 | −0.158 | 0.376 | −0.420 | −0.062 | 0.397 | −0.156 |
| NIUROU(−13) | −0.084 | 0.154 | −0.544 | −0.326 | 0.371 | −0.879 | 0.355 | 0.391 | 0.906 |
| NIUROU(−14) | 0.122 | 0.104 | 1.178 | 0.400 | 0.272 | 1.474 | −0.222 | 0.285 | −0.778 |
| -value | 455.8226 | | 388.0489 |
| -value | 0.98655 | | 0.99421 |
From
Table 5, it can be seen that the decisive coefficient R
2 value of the threshold regression model is higher than the linear self-regression, and the F statistical value is lower than the linear self-regression. In the lower area below the threshold, three of the lag items passed the significance test, and in the upper area of the threshold regression, five passed the significance test. However, in the linear model, only two have passed the significance test. It can be seen that the TAR model can better fit the change characteristics of beef price time series than the linear self-regression model, which also shows to some extent that the trend of change of beef price time series is nonlinear and the threshold regression model has advantages.
By analyzing the TAR model estimation results of the beef price index sequence, the following laws can be obtained:
1) The constant term of the upper region in the model is about 1.5 times that of the lower region. This means that when the beef price time series enters the upper region, the value of the constant item rapidly increases and the price is raised very quickly, while after entering the lower region, the constant item decreases rapidly and therefore the price falls very quickly. This indicates that beef prices fluctuate greatly.
2) Based on the estimated results of the two regions, the sum of the coefficients of the lower regional model is 2.860 and the sum of the coefficients of the upper region model is 2.754, indicating that the influence of the beef price in the lower region on the later period is greater. If the beef price is below the threshold, that is, in the lower region, under the influence of external factors, beef price fluctuates, which has a greater impact on the later price, resulting in a large fluctuation in the price of beef in the later period.
3) As can be seen from the lower region model, the lag of 12 period is significant, and the lag of 7 is also significant. This shows that beef prices are mainly affected by the early stages when they are below the threshold. In the case of the upper region, i.e. if the beef price is above the threshold, the lag of 12 and 57 is significant. In addition, the significant items are alternately presented with one positive and one negative, indicating that a period has a positive effect on beef prices, and a negative effect will occur later in the period.
6.2 Comparative Analysis of Mutton Price and Beef Price
Based on existing studies, Shi, et al.
[23] believed that there was a strong substitution between beef and mutton in China, and the regulation of a single product was bound to have a significant impact on the market of another product, and the free fluctuation of market price would also be transmitted to another market through the reaction of consumers and producers. Tang, et al.
[21] believed that the price fluctuations of beef and mutton in China were significantly cumulative, and the mutton market was not characterized by high risk and high return. Shi, et al.
[24] believed that the price fluctuation of beef and mutton had a threshold effect, and the market price would show a trend of rising in the future. Therefore, specific to Xinjiang Uygur Autonomous Region, it is also necessary to analyze the internal relationship between beef and mutton prices, which can provide an important reference for in-depth research of the industry and the introduction of relevant policies.
Figure 7 shows the comparison of monthly price fluctuations of beef and mutton in Xinjiang. From the perspective of the price trend of beef and mutton, both showed a trend of shock rising from January 2010 to May 2013, and both reached a peak in May 2013. Among them, the price of beef was 65 yuan/kg in May 2013, up 96.374% compared with January 2010. The price of mutton was 64 yuan/kg, up 83.381% from January 2010. Between January 2010 and May 2013, the price of beef was lower, but the price of beef increased significantly and reached the same level as the price of mutton in May 2013. At this stage, due to the high price of mutton, the demand for mutton decreases, and the demand for beef increases, thus causing the price of beef to rise continuously until the two prices balance. From June 2013 to July 2014, the prices of beef and mutton showed a trend of horizontal oscillation, with a limited range of overall changes.
Figure 7 Comparison of monthly price fluctuations of beef and mutton in Xinjiang |
Full size|PPT slide
After July 2014, the prices of beef and mutton in Xinjiang showed a trend of first decline and then rise, and they all turned around in October 2016. Meanwhile, it can be seen that after October 2016, the price of beef in Xinjiang was higher than that of mutton in all months. However, as the growth rate of mutton price was significantly higher than that of beef price in this stage, there was a small difference between the two prices before and after January 2019. At this stage, the high price of beef leads to a decrease in the quantity of beef and a rise in the demand for mutton, which leads to a continuous rise in the price of beef until the two prices are smooth.
From the comparison of the price of beef and mutton, in each stage of time, it has appeared with the rise and fall, or the volatility of the horizontal shock trend. Therefore, in the short term beef and mutton prices present a certain complementary relationship. However, when the price of mutton is higher than that of beef (such as in the first stage), the growth rate of beef price is higher than that of mutton, indicating that the demand for beef with lower price increases and replaces the consumption of mutton. At the same time, similar conclusions can be seen from the third stage, so the price of beef and mutton presents a substitution relationship in the long run.
In conclusion, beef and mutton prices, are complementary in the short term and substitute in the long term.
6.3 Linkage Analysis of Mutton Price and Beef Price
According to the qualitative analysis of the price of mutton and beef in Subsection 6.2, the relationship between mutton and beef is complementary in the short term and substitution in the long term. As an alternative product of mutton, the fluctuation of beef price will have a linkage relationship with mutton price to a certain extent. This section will quantitatively analyze the relationship between beef price and mutton price and how beef price affects mutton price.
First, the unit root test of mutton price and the cointegration test of mutton price and beef price are carried out. Among them, the ADF test is still used for the unit root test to judge the stationarity level of mutton price time series. EG co-integration test is used to judge whether there is a co-integration relationship between beef price and mutton price. ADF test results of mutton price are shown in
Table 6.
Table 6 ADF test results of mutton price |
| test sequence | ADF statistics | Mackinnon critical value |
| 1% | 5% | 10% |
| −0.831914 | −3.488585 | −2.886959 | −2.580402 |
| −8.426642*** | −3.488585 | −2.886959 | −2.580402 |
| Note: "*", "**" and "***" mean passing the significance test of 10%, 5% and 1% respectively. |
As can be seen from
Table 2 and
Table 4, both beef price and mutton price fail to pass the significance test level of 10%, which cannot reject the null hypothesis, that is, each time series has a unit root and is a non-stationary series. Then the two variables of first-order difference after processing, again carries on the unit root test, the price of beef and mutton price time series all through the test of significance level of 1%, the price of beef and mutton price of first order difference sequence are stationary time series, therefore, the original sequence are first-order single whole, cointegration test. Therefore, for beef price time series and mutton price time series, EG co-integration test is carried out and
Table 7 is obtained.
Table 7 Cointegration test results of beef price and mutton price |
| ADF statistical | Test threshold |
| 1% | 5% | 10% |
| −2.439576*** | −3.488585 | −2.886959 | −2.580402 |
| Note: "*", "**" and "***" mean passing the significance test of 10%, 5% and 1% respectively. |
Based on
Table 7, it can be seen that beef price and mutton price pass the significance test level of 1%. This indicates that there is a co-integration relationship between beef price time series and mutton price time series, but whether there is a causal relationship between the two in the statistical sense needs further verification. Therefore, based on the data of beef price and mutton price, the Granger causality test is conducted, and the results are shown in
Table 8.
Table 8 Granger causality test results |
| The null hypothesis | F-Statistic |
| The price of mutton is not the Granger reason for the price of beef | 0.61543 |
| Beef prices are not the original granger prices | 1246.99** |
| Note: * represents the significance level of 10%, ** represents the significance level of 5%, and *** represents the significance level of 1%. |
As can be seen from
Table 8, the test statistics of beef price passed the significance test level of 5%, rejecting the original hypothesis, indicating that there is a statistical causal relationship between beef price and mutton price. Therefore, the price of beef can be used as an influential factor to analyze the price changes of mutton.
Based on the above statistical test results, the price of beef was selected as the influencing factor for analysis. By building a VAR model, you can get the following results:
$ \begin{align*} Y_{t} & = 1.129 + 1.155Y_{t - 1} - 0.1Y_{t - 2} - 0.0310.1Y_{t - 3} - 0.04Y_{t - 4} + 0.042X_{t - 1} \notag \ & \quad + 0.122X_{t - 2} - 0.133X_{t - 3} - 0.036X_{t - 4}. \end{align*} $ Based on the above statistical test results, the price of beef was selected as the influencing factor for analysis. By building a VAR model, you can get the following results: Based on the above formula, it can be seen that in the short term, the price of mutton is positively correlated to its historical price, and the price of mutton is positively correlated to the price of beef. Among them, beef price lag data for each additional unit, mutton price will increase 0.042 yuan/kg, beef price lag two phases of data for each additional unit, mutton price will increase by 0.122 yuan/kg. In the long run, the price of mutton is negatively correlated to its historical price, and the price of mutton is negatively correlated to the price of beef. Among them, beef price lag three phases of the data for each additional unit, mutton prices will be reduced by 0.122 yuan/kg, beef prices lag four phases of data for each additional unit, mutton prices will be reduced by 0.036 yuan/kg. In addition, to understand the interaction between variables and the degree of influence, this study made a pulse response to beef price and mutton price. Figure 8 is a pulse response graph.
Figure 8 Pulse response graph |
Full size|PPT slide
Figure 8 shows the reaction of mutton prices to changes in beef prices. At first, the impact of changes in beef prices on mutton prices was 0. Therefore, in the short term, mutton and beef as complementary products, when the price of beef has a positive impact, mutton prices do not produce large fluctuations. In the long run, the increase in beef prices will have a positive effect on mutton prices, peaking in Phase 7. This suggests that mutton and beef are alternatives in the long run. The pulse response results show that without the pressure of beef price, the impact of the impact on mutton price will be 0. When a positive shock begins, the price of mutton does not fluctuate significantly in the short term. But as beef prices rise, the impact on mutton will gradually increase and reach saturation to a certain extent. Therefore, the analysis of the comprehensive VAR model and pulse response graph shows that beef and mutton are complementary in the short term, but in the long term, beef and mutton are alternative relationships. This is consistent with the qualitative analysis in Subsection 6.2.
7 Conclusions
This chapter studies the fluctuation characteristics of the price of mutton in Xinjiang, first describes the price of mutton in Xinjiang and the data sources that affect the price of mutton, and introduces several classical methods of price fluctuation analysis. Secondly, according to the analysis of the space-time characteristics and evolution laws of the price of mutton in Xinjiang, the long-term trend and cyclical characteristics of the price of mutton in Xinjiang are analyzed by the HP filtering method, and the spatial characteristics of the price fluctuation of mutton in various regions of Xinjiang are shown by statistical description and heat. Finally, the price of mutton in Xinjiang is analyzed to the price of other livestock products, the fluctuation characteristics of beef price are analyzed by the TAR model, and the interaction between the price of mutton and the price of beef in Xinjiang is analyzed based on the VAR model. The analysis of the temporal and spatial characteristics and evolutionary trends of mutton prices in Xinjiang reveals that, over time, the volatility of mutton prices shows a long-term upward trend, with the frequency of cyclical fluctuations increasing from 2010 to 2019. Spatially, mutton prices in the southern regions of Xinjiang are generally higher than those in the north. Additionally, a linkage analysis between the prices of mutton and other livestock products in Xinjiang was performed. The results show that both beef and mutton prices exhibit non-linear and non-stationary fluctuations, with a complementary relationship in the short term that evolves into a substitution relationship over the long term. To sum up, this chapter studies the characteristics of the price fluctuation of Xinjiang mutton from the single time series of the price of Xinjiang and other livestock products and paves the way for the later influence factors and the decomposition of the price sequence.
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Figure 1 Monthly price trend of mutton in Xinjiang
Table 1 Long-term trend period of mutton price decomposed by HP filtering method
