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# 统计代写|时间序列和预测代写Time Series & Prediction代考|QMS517 Experimental Modality and Results

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## 统计代写|时间序列和预测代写Time Series & Prediction代考|Policies Adopted

The close price data for both main factor and secondary factors are obtained for the period 1990-2004 from the website [56]. The training session was fixed for 10 months: January 1 to October 31 of each year on all trading days. In case all the trading days of secondary factors do not coincide with those of the main factor, we adopt two policies for the following two cases. Let Set $\mathrm{A}$ and $\mathrm{B}$ denote the dates of trading in main and secondary factors respectively. If $\mathrm{A}-\mathrm{B}(\mathrm{A}$ minus $\mathrm{B})$ is a non-null set, then the close price of previous trading days in secondary factor has to be retained over the missing (subsequent) days. If $\mathrm{B}-\mathrm{A}$ is non-null set, then we adopt the following policies. First, if the main factor has missing trading days due to holidays and/or other local factors, then no training is undertaken on those days.
Second, in the trading of next day of main factor, we consider the influence of the last day of trading in secondary closing price. After the training is over, the following items including prediction rules (also called Fuzzy Logic Implications (FLI)) and secondary to main factor variation groups are saved for the subsequent prediction phase. The prediction was done for each trading day during the month of November and December. Comparison of the results of prediction with those of Chen et al. [47] is given in authors’ webpage [53], and is not given here for space restriction. The results of prediction (November-December, 2003) with and without adaptation of parameters (standard deviations) of MFs are given in Fig. $2.8$ along with the actual close price.

## 统计代写|时间序列和预测代写Time Series & Prediction代考|MF Selection

Experiments are performed with both Gaussian and triangular T1 MFs. The UMF (LMF) of the IT2FS is obtained by taking maximum (Minimum) of the T1 MFs describing the same linguistic concept obtained from different sources. Figure 2.2 respectively provides the construction of IT2FS from triangular and Gaussian T1 MFs, following the steps outlined in Sect. 2.3. The relative performance of triangular and Gaussian MFs is examined by evaluating RMSE of the predicted close price with respect to its actual TAIEX values. In most of the test cases, prediction of close price is undertaken during the months of November and December of any calendar year between 1999 and 2004.

The RMSE plots shown in Fig. $2.8$ reveal that triangular MFs yield better prediction results (less RMSE) than its Gaussian counterpart. For example, the RMSE for TAIEX for the year 2003 using triangular and Gaussian MFs are respectively found to be $37.123$ and $47.1108$ respectively, justifying the importance of triangular MFs over Gaussian ones in the time-series prediction.

The training algorithm is run with the close price time-series data from January $1 \mathrm{st}$ to October 31st on all trading days. For tuning the T1 MFs (before IT2FS construction) for qualitative prediction, the adaption algorithm is run for the period of September 1st to October 31st for the subsequent prediction of November. After the prediction of November month is over, the adaption procedure is again repeated for the month of October 1st to November 30th in order to predict the TAIEX close price in December. Such adaption over two consecutive months is required to track any abnormal changes (such as excessive level shift) in the time-series.

The improvement in performance due to inclusion of adaptation cycles is introduced in Fig. $2.8$ (see [53] for precision), obtained by considering Gaussian MFs. It is apparent from Fig. 2.8a that in presence of adaptation cycles, the RMSE appears to be $47.1108$, while in absence of adaptation, RMSE is found to be $52.771$. The changes in results (RMSE) in presence of adaptation cycles due to use of triangular MFs are illustrated in Fig. 2.8b. Both the realizations confirm that adaptation has merit in the context of prediction, irrespective of the choice of MFs.

## 统计代写|时间序列和预测代写TIME SERIES \& PREDICTION代 考|POLICIES ADOPTE

$$56$$
. 培训期固定为 10 个月：每年1月1日至 10 月31日所有交易日。如果次要因拜的所有交易日与主要因筰的交易日不重合，我们对以下两种情况采取两种策略。让集A 和B分别表示主要和次要因嫊的交易日期。如果 $\mathrm{A}-\mathrm{B}(\mathrm{A}$ 減 $\mathrm{B})$ 是一个非空集，则次要因子中前几个交易日的收盘价必须保留在缺失的subsequent天。如果 $\mathrm{B}-\mathrm{A}$ 是非空集，那么我们采用以下策䀩。首先，如果主要因筰由于节假日和/或其他当地因债而缺少交易日，那么这些日子就不会进行培训。

alsocalledFuzzyLogicImplications $(F L I)$ 和次要的主要因䋤变化组被保存用于后续预测阶段。预测是针对 11 月和 12 月的每个交易日进行的。与 Chen 等人预 测结果的比较。
47

## 统计代写|时间序列和预测代写TIME SERIES \& PREDICTION代 考|MF SELECTION

RMSE 图如图 1 所示。2.8揭示三角形 MF 产生更好的预测结果lessRMSE比它的高斯对应物。例如，使用三角和高斯 MF 的 2003 年 TAIEX的 RMSE 分别被发现是 $37.123$ 和 $47.1108$ 分别证明了三角 MF 在时间序列预测中相对于高斯 MF 的重要性。

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。