本科毕业设计（论文）

外文翻译

用于股指预测的适应性波转换、长期短期记忆和 ARIMA-GARCH 系列模型的混合方法

作者：Zolfaghari Menhdi-Gholami Samad

国籍：伊朗

出处：Expert Systems.With Applications

中文译文：

摘要：对学者和从业人员来说，股价的建模和预测都是金融研究的一个重要领域。这项研究旨在通过使用混合模型预测股指和波动性以及结合财务变量来确定是否可以实现改进。我们应用混合模型，将自适应波转换 （AWT）、长期短期记忆 （LSTM） 和 ARIMAX-GARCH 家族模型相结合，以预测股指并结合 AWT，从而扩展了股市预测文献， LSTM 和实现波动性 （HAR-RV） 模型的异质自动反向模型，用于预测美国股市两大指数（包括道琼斯工业平均指数 （DJIA） 和纳斯达克综合指数 （IXIC） 的股票波动性。结果表明，使用AWT-LSTM-ARMAX-FIEGARCH模型与学生指数的预测总体上有所改进t与基准模型相比的分布。强大的测试证明，该模型在预测两个股指的不同时间范围（1-、10、15、20、30和60天）方面具有更高的预测准确性。此外，AWT-LSTM 提高了 HAR （3） X-RV 模型在预测上述时间范围内实现的库存波动性的能力。

关键字：股指预测；长期内存；自适应波转换；FIGARCH 和 FIEGARCH 模型

一、介绍

对不同金融资产收益进行建模和预测，是经济和金融研究中一个被广泛研究的课题。在金融文献中，提出了广泛的模型来预测回报和波动性，但最受欢迎的模型是具有通用自动回归条件异质性 （GARCH） 模型（阿内里奇和波克列波维奇，2016年）的自动回归综合移动平均值 （ARIMA）。然而，通常很难预测使用传统GARCH模型的回报和波动性，因为该系列受不同特征的影响，如非静止行为、有条件方差的高持久性、不对称行为和非线性（Zolfaghari amp; Sahabi，2017）。由于传统GARCH的实际局限性，在文献中引入了一系列补充模型，捕捉了时间系列的更多特征。GARCH 家族模型分析时间系列数据的最重要特征和优势在表 1中进行了总结。

除了用于建模长内存的 FIGARCH 和 FIEGARCH 模型外，Corsi 还于 2009年推出了实现波动性的异质自动反动模型 （HAR-RV），以考虑长期内存属性来建模和预测时间系列波动性（不返回）。ARIMA-GARCH家族模型中财务时间系列的非静止和非线性特征，近年来许多学者应用了人工智能（AI）方法。相关文献中提出了基于人工智能的技术模型，如深度学习网络（DLN）、模糊神经网络（FNN）、支持矢量机（SVM）和基于知识的专家系统算法，用于时间系列预测。在最近的研究中，第二组通常由模拟非线性关系的DLN代表，并且从培训示例（Voulodimos等人，2018年，哈佳波托拉比等人，2019年）中获取。DNS分为几个类别，人工神经网络（ANN）在过去几年被广泛应用于财务数据的预测（卡瓦克利奥卢等人，2009年，查，佐尔法加里和萨哈比，2019年）。然而，由于过去信息的时间影响没有被ANN考虑用于预测时间系列（Thi Kieu Tran， 李，申，金，卡姆鲁扎曼，2020年），专家研究人员最近一直在开发其他DLN的类别，特别是经常性神经网络（RNN），而不是等，2015年，Rout等人，2017年，贝拉迪和拉扎尔，2019年，崔等人，2020年，图博等人，x）。RNN 主要用于时间系列分析，因为它们的架构中提供反馈连接。在最近的研究（如比安科菲奥雷等人，2017年，哈佳波托拉比等人，2019年，范德卢格特和感觉，2019年），比较这两个预测因素（ANN和RNN），所有的发现都表明RNN模型在传统的神经网络（如ANN）中占优势。RNN，特别是具有长期短期内存（LSTM）的变种，最近被证明是涉及顺序数据的广泛应用中的一个高效模型。LSTM 被公认为 RNN 的一大变种模型，它能够应用历史数据在时间系列分析中享受高水平的适应性（彼得森、罗德里格斯和佩雷拉，2019年）。但是，LSTM 无法显示时间系列的多频特性。因此，无法对数据的频率域进行建模。为了解决这一限制，张，阿加瓦尔和齐（2017年）建议富利埃转换（FT）提取时间频率信息。此外，他们将其与神经网络相结合进行预测：但建议的模型是相互排斥的，这意味着频率域中没有时间域信息，时间域中也未包含频率域信息。与英国《金融时报》不同，波波转换（WT）通过表示翻译和可变比例因素，有效地消除了上述问题。

WT 可以通过在许多方面进行缩放和移动来改进多个尺度的时间系列，以实现频率分割的最终目标。WT 和 LSTM（以下简称 WT-LSTM）的组合能够充分提取数据的时间-频率信息，并改进时间系列频率模型。最近，有少数研究应用WT-LSTM预测股指（李和谭，2017年，斯凯欣等人，2018年，哈佳波托拉比等人，2019年，梁等人，2019年，邱等人，2020年）。但是，由于各种序列取决于不同的频率模式，预测性能不能最佳，WT 和 LSTM 不能专注于主频率组件。事实上，在分解输入系列后，每个细节部分都放入输出结果的预测模型中，而该模型没有考虑到它们之间的相似复杂性和相关性，从而降低了准确性和效率。为了解决这个问题，在这项研究中，我们提供了一组自适应层（从1到3）与WT-LSTM（以下简称AWT-LSTM）结构中具有多种激活功能，因为不同的权重设置为不同的频率组件，根据频率域之间的重要关系捕捉股指时间序列的频率模式。根据建议的模型，WT 用于分解股票市场指数中的时间频率，并改进其多个维度，以完全提取高频和低频数据。然后，LSTM 应用于数据频率域的建模和预测。同时，为

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1. Introduction

Modelling and forecasting the different financial assetsrsquo; returns constitute a widely-studied topic in economic and financial research. In the financial literature, a wide range of models have been proposed to predict return and volatility, but the most popular ones is autoregressive

integrated moving average (ARIMA) with generalized autoregressive conditional heteroskedasticity (GARCH) model (Arneriacute;c amp; Poklepoviacute;c, 2016). However, it is often difficult to forecast return and volatility applying traditional GARCH model because the series is influenced by different features like nonstationary behavior, high persistence in the conditional variance, asymmetric behavior, and nonlinearity (Zolfaghari amp; Sahabi, 2017). Due to the practical limitations of the traditional GARCH, a range of complementary models have been introduced in the literature which capture more characteristics of time series. The most important characteristics and advantages of the GARCH family models to analyze the time series data are summarized in Table 1. In addition to FIGARCH and FIEGARCH models for modelling the long memory, Corsi, 2009 introduced the heterogeneous autoregressive model of realized volatility (HAR-RV) to model and forecast the time series volatility (not return) with consideration of the long-term memory attributes.

Due to lack of enough ability to capture nonstationary and nonlinearity characteristics of financial time series in ARIMA-GARCH family

models, many scholars have applied artificial intelligence (AI) approaches in recent years. The AI technique-based models like deep learning networks (DLNs), fuzzy neural networks (FNNs), support vector machine (SVM) and knowledge-based expert system algorithms have been proposed in the related literature for time series prediction. Among recent studies, the second group is generally represented by the DLNs that model nonlinear relationships and are accessible from the supply of training examples (Voulodimos, Doulamis, Doulamis, amp; Protopapadakis, 2018; Hajiabotorabi, Kazemi, Samavati, amp; Ghaini, 2019). DLNs are divided into several categories which artificial neural networks (ANNs) have been widely applied for prediction of financial data in last years (Kavaklioglu, Ceylan, Ozturk, amp; Canyurt, 2009; Cha abane, 2014;

Zolfaghari amp; Sahabi, 2019). However, since the temporal influence of past information is not considered by ANNs for forecasting time series (Thi Kieu Tran, Lee, Shin, Kim, amp; Kamruzzaman, 2020), expert researchers recently have been developing other DLNsrsquo; categories, especially the recurrent neural networks (RNNs) (Rather, Agarwal, amp; Sastry, 2015; Rout, Dash, Dash, amp; Bisoi, 2017; Berradi amp; Lazaar, 2019; Cui, Ke, Pu, amp; and Wang, 2020; Toubeau et al., xxxx). RNNs are primarily used for time series analysis because of the feedback connection available in their architecture. In recent studies (e.g. Biancofiore et al., 2017; Hajiabotorabi et al., 2019; van der Lugt amp; Feelders, 2019) that compare these two predictors (ANN and RNN), all findings indicate the predominance of RNN models over conventional neural networks (such as ANN). RNN and specifically a variant with long short-term memory(LSTM), have been lately proven to be an efficient model in a wide range of applications involving sequential data. LSTM is recognizedas a great variant model of RNN which is able to apply historical data to enjoy a high level of adaptability in time series analysis (Petersen, Rodrigues, amp; Pereira, 2019). However, LSTM cannot show the multi-frequency features of time series. So, modeling the frequency domain of the data is not possible. To address this limitation, Zhang, Aggarwal, and Qi (2017)

suggested Fourier transform (FT) for extracting time frequency information. Moreover, they combined it with neural network for forecasting; but the proposed model is mutually exclusive, which means, here is no information of time domain in the frequency domain, and no

information of frequency domain is included in the time domain. Unlike the FT, wavelet transform (WT) effectively obviates the afore-mentioned problem by representing translation and variable scale factors. WT can refine time series at multiple scales by scaling and shifting in

many respects to achieve the final goal of frequency segmentation. The combination of WT and LSTM (hereinafter referred to as the WT-LSTM) is capable of fully extracting the time–frequency information of data and refining a model for time series frequency. Recently, a limited number of studies have applied WT-LSTM to forecast stock index (Li amp; Tam, 2017;

Skehin, Crane, amp; Bezbradica, 2018; Hajiabotorabi et al., 2019; Liang, Ge, Sun, He, amp; Chen, 2019; Qiu, Wang, amp; Zhou, 2020).

However, since various sequences depend on different frequency patterns, the prediction performance could not be optimal and WT and LSTM cannot concentrate on main frequency components. In fact, after decomposing the input series, each detail part is put into a forecasting model for the output results, which does not take into account the similar complexity and correlation among them resulting in lower accuracy and efficiency.

To solve this problem, in this research, we offer a set of adaptive layers

(from 1 to 3) with a variety of activation functions in structure of WTLSTM (hereinafter referred to as the AWT-LSTM) because different weights are set for different frequency components to capture the frequency pattern of stock index time series according to the important

relationship between frequency domains. According to the proposed model, WT is utilized to decompose the time–frequency in stock market index and refine numerous dimensions of it to completely extract both the high-frequency and low-frequency data. Then, LSTM is applied for modeling and predicting the data frequency domain.

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