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1.INTRODUCTIONTime series forecasting method is a basic forecasting method with a long history and vitality. Its basic idea is to reveal the law of demand value changing with time through the historical data of time series, and extend this law to the future, so as to predict the future. Time series forecasting method has attracted extensive attention because it only needs to use past records, easy data collection, low cost, simple calculation and easy execution [1][2]. 2.ANALYSIS OF INFLUENCING FACTORS OF TIME SERIES2.1Time levelThe time level affects the forecasting method in three aspects: first, select the appropriate forecasting method according to the future time span. Generally speaking, qualitative methods are generally used for long-term forecasting, while quantitative forecasting methods are mostly used for medium-term and short-term situations; The second is the historical data required by a forecasting method. Some forecasting methods need little historical data, while others must ensure a certain amount of historical data, otherwise the forecasting method cannot run; Finally, the effective forecasting length of one method. Some forecasting methods can predict one or two time cycles in the future, while others can predict multiple cycles. The basic demand conditions and application scope of the main forecasting methods are shown in Table 1[6]. Table 1.Comparison between traditional statistical method and gray forecasting method
2.2Data typeSome data series may contain both seasonal type and trend type, or consist of simple mean and random disturbance, or periodic type. Because different forecasting methods have different forecasting abilities for different data types, it is particularly necessary to predict different data types with appropriate forecasting methods. 2.3Forecasting accuracyThe first-line indicator closely related to the forecasting method is the forecasting accuracy. For some cases, the forecasting accuracy of 10% is enough, while for some precision industries, the accuracy of 0.2% will be far lower than the use requirements. Other influencing factors such as ease of use and availability of relevant software can be used as indicators to evaluate the advantages and disadvantages of a forecasting method. Nevertheless, the most important indicator is the forecasting accuracy mentioned above. The forecasting problem based on time series is studied for two problems: firstly, the spare parts demand time series is preprocessed, and then the corresponding mathematical model is established for the processed time series, and the forecasting analysis is carried out. 3.TIME SERIES CHARACTERISTIC ANALYSISThe assumption that the future “looks like the past” is a very important assumption in time series analysis, which is called stationarity. However, time series variables become unstable in various ways, two of which are particularly relevant to the regression analysis of time series data [7]:
These deviations from stationarity will endanger the forecasting and inference based on time series. Fortunately, however, we have statistical methods to find trends and mutations. Once these situations are found, we can adjust the setting form of the model. The main methods of time series forecasting include exponential smoothing method, regression analysis method, regression method, ARMA method and Gray forecasting method. The research on the characteristics of time series by these methods mainly includes: stability detection, sequence analysis, and the selection of trend items. The following mainly studies the spare parts demand forecasting method based on ARMA model. 4.SPARE PARTS DEMAND FORECAST BASED ON ARMA MODELIn the actual use of equipment, the obtained spare parts demand data is usually non-stationary. How to reasonably predict the future spare parts demand according to the non-stationary data sequence. ARMA model forecasting requires that the sequence must be stable, that is, the influencing factors of the research object must be basically the same within the research time range. If the given sequence is not a stationary sequence, the given sequence must be preprocessed to stabilize it, and then modeled with ARMA model. The modeling steps are shown in Figure 1. Time series analysis is an effective modeling method, which requires that the observation data samples should not be less than 30, and the test time should be equal. However, in engineering practice, due to the constraints of various factors, there are often less than 30 observation data samples with different time intervals. Therefore, it is particularly important to study the time series data processing method of small samples. Some literates use SVM to model and predict small sample data, but how to reasonably define the model is very difficult[8]. The process of spare parts demand forecasting method is as follows: firstly, obtain the historical demand data sequence of equipment spare parts, preprocess the demand data sequence, test the stability of the sequence, and finally select the forecasting method to predict and analyze the future demand of spare parts. 4.1Data preprocessingBefore establishing the time series model, the data must be preprocessed to eliminate those abnormal samples that do not comply with the statistical law, and the basic statistical characteristics of these samples must be tested to ensure the reliability and confidence of the time series model and meet certain accuracy requirements. For the original data sequence of spare parts demand X = {x1, x2,⋯,xt,⋯}, t = 1, 2,⋯,n, there are generally the following two characteristics:
Therefore, the test data must be preprocessed before statistical analysis. Firstly, the values with obvious errors, that is, the possible outliers in the original data, are eliminated. At the same time, in order to ensure the integrity and continuity of data, the eliminated data are interpolated; Then, in order to ensure the equal interval of the test data, the original data is interpolated and supplemented again[9]. The stationarity of time series is an important prerequisite for time series modeling. The purpose of stationarity test is to determine whether there is a random trend or determine the trend in the sequence, otherwise there will be a pseudo regression problem[10]. Stationarity test mainly includes parameter test method, non-parametric test method and sequence diagram test method[11]. After the stationarity detection of the time series, according to the detection results, if it is a stationary series, it is directly predicted by ARMA model. If it is a non-stationary series, the series is processed by difference until it is stable, and then it is modeled by ARMA model and predicted by correlation analysis. 4.2ARMA model order determinationParameter estimation and model order determination are important contents of establishing spare parts consumption forecasting model, which affect each other. Based on the above model identification, the unknown parameters of ARMA (P, q) model, namely autoregressive coefficient, moving average coefficient and white noise variance, are estimated by using sample moment estimation method, least square estimation method or maximum likelihood estimation method and got Table 2Discriminant principles of ARMA (p, q) model
Box Jenkins proposed to use the truncation of sample auto-correlation function Order determination, parameter estimation and test are combined step by step. For the above preliminary determination MA(q0) and AR(p0) by truncation, the corresponding order shall also be determined through white noise test. The order of ARMA model is mainly determined by F-test, FPE, AIC and BIC order determination criteria. For specific methods, refer to literature [11]. 4.3Model adaptability testAfter the identification, order determination and parameter estimation of the model, the remaining problem is to judge whether the model is appropriate to describe the time series, that is, the adaptability test of the model. The adaptability of the model refers to the degree to which a time series model explains the dynamics of the system (that is the correlation of data series). The suitable model of a time series {at} should completely or basically explain the dynamics of the system (that is the correlation of data series), so the residual sequence {at} in the model should be a white noise sequence. In essence, the adaptability test of the model is to test whether the sequence is white noise sequence. The most important one is the independence test of sequence {at}. The progress of computer technology has greatly promoted the development of time series analysis. At present, many statistical software can be used for time series analysis. Commonly used software mainly includes S-PLUS, MATLAB, Gauss, TSP, Eviews and SAS software[14]. This paper mainly studies the characteristic form of time series through Eviews analysis software. Eview is the abbreviation of economic views. It is an econometric software package launched by GMS company[15]. The original intention of the software is to analyze the quantitative law of socio-economic relations and economic activities by using econometric methods and techniques. The core of econometric research is to design models, collect data, estimate models, test models, use models to predict, solve models and use models. Eview is an indispensable tool to complete the above tasks. 5.CASE ANALYSISIn the actual use of equipment, the obtained spare parts demand data is usually non-stationary. How to reasonably predict the future spare parts demand according to the non-stationary data sequence. ARMA model forecasting requires that the sequence must be stable, that is, the influencing factors of the research object must be basically the same within the research time range. If the given sequence is not a stationary sequence, the given sequence must be preprocessed to stabilize it, and then modeled with ARMA model. The modeling steps are shown in Figure 1. Now, the statistical sequence of spare parts used for an equipment from the first quarter of 2006 to the first quarter of 2014 is as follows (the unit of spare parts demand sequence is calculated quarterly (0 means lack of statistical data)):43,42,47,45,46,43,0,43,47,48,46,42,49,48,46,42,47,45,49,47,48,41,0,46,48,43,49,42,48,23,41,44,46。 In order to verify the forecasting effectiveness of the model, the first 32 data in the series are selected for modeling and analysis. It can be seen from the above statistical data that the spare parts demand sequence of the system {xt} is a stationary random demand sequence. The number of samples {xt} is 33, greater than 30, does not belong to small sample series, so statistical methods can be used to analyze the series. For the data shown above, the Pauta criterion is applied to calculate the mean value In addition, the time series analysis requires equal intervals. As can be seen from the above table, the statistics of spare parts in the third quarter of 2007 and the second quarter of 2010 are missing in the series {xt}, mainly because the detachment performed ocean training tasks in the third quarter of 2007 and the second quarter of 2010 respectively, resulting in the lack of equipment support and maintenance records. After the Lagrange interpolation polynomial is used to interpolate and supplement it, x7 =44.75. Considering that the actual demand for spare parts cannot be non integer, the value x7 is 45, x14 is obtained as 46 by the same method, that is, the latest correction sequence {xt} is:43,42,47,45,46,43,45,43,47,48,46,42,49,48,46,42,47,45,49,47,48,41,46,46,48,43,49,42,48,44,41,44。 For the spare parts demand series {xt}, it can be seen from the figure above that the series is stable. According to the above figure, AR (1), MA (1), ARMA (1,1) and other models can be used for continuous fitting and comparison. Due to the space relationship, only the correlation analysis diagram of ARMA (1,1) is given here. The relevant information of ARMA (1,1) can be obtained through software analysis, as shown in Figure 3. For model comparison and model selection, it is often not to simply look at a certain index, but to comprehensively consider all aspects of the situation, make a comprehensive judgment and select an optimal model. The following factors are generally considered:
According to the above analysis results, the overall accuracy of multi sample spare parts demand forecasting based on ARMA model meets the error requirements. With the increase of sample data, the forecasting results will be more accurate. This must be paid attention to when applying ARMA model to predict the demand for spare parts. According to the forecasting model, the demand for spare parts in the first quarter of 2014 is predicted, and the predicted value is 45.3249, rounded to 46. It is consistent with the actual demand value of spare parts, which verifies the effectiveness of the model. 6.CONCLUSIONThe forecasting error of ARMA model is small, and the forecasting effect meets the needs of the actual situation. It can better solve the problem that the demand for ship equipment spare parts can not be accurately predicted, and has good engineering application value. It is more convenient and intuitive to study the historical demand sequence through relevant statistical software. This method also has important reference significance for the life forecasting of other complex systems and has broad application prospects. REFERENCESWang Naichao, Kang Rui,
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