Temporal -Spatial dependencies ENhanced deep learning model TSEN for household leverage series forecasting Hu Yang1 Yi Huang1 Haijun Wang2 and Yu Chen3

2025-05-02 0 0 1.56MB 26 页 10玖币
侵权投诉
Temporal-Spatial dependencies ENhanced deep learning model
(TSEN) for household leverage series forecasting
Hu Yang1,§, Yi Huang1, Haijun Wang2,*, and Yu Chen3
(1 School of Information, Central University of Finance and Economics, Beijing, 100081, China; 2
School of Economics, Beijing Wuzi University, Beijing, 102600, China; 3 School of Public
Finance and Taxation, Central University of Finance and Economics, Beijing, 100081, China)
Corresponding authors
:
*
Haijun Wang (wanghaijun2005@126.com),
§
Hu Yang (hu.yang@cufe.edu.cn)
Abstract
Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time
series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series
from different locations often have distinct patterns; and for the same time series, patterns may vary
as time goes by. Inspired by the successful applications of deep learning, we propose a new model
to resolve the issues of forecasting household leverage in China. Our solution consists of multiple
RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal
pattern of a specific series with multivariate exogenous series, and then the attention layer learns
the spatial correlative weight and obtains the global representations simultaneously. The results
show that the new approach can capture the temporal-spatial dynamics of household leverage well
and get more accurate and solid predictive results. More, the simulation also studies show that
clustering and choosing correlative series are necessary to obtain accurate forecasting results.
Keywords: Financial Time Series, Forecasting, Temporal-Spatial dynamics, Deep learning
Acknowledgment
HY was supported by grants from the National Natural Science Foundation for Distinguished
Young Scholars of China (71701223), the National Statistical Science Foundation of China
(2018LZ08), the Central University of Finance and Economics Young Talents Training Support
Project (QYP2014), and Fundamental Research Funds for the Central Universities (China): the
Central University of Finance and Economics Scientific Research and Innovation Team Support
Project. YC was supported by grants from the National Social Science Foundation (20BGL066) and
the "Young Talents" Cultivation and Support Program of the Central University of Finance and
Economics.
Temporal-Spatial dependencies ENhanced deep learning model
(TSEN) for household leverage series forecasting
Abstract
Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time
series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series
from different locations often have distinct patterns; and for the same time series, patterns may vary
as time goes by. Inspired by the successful applications of deep learning, we propose a new model
to resolve the issues of forecasting household leverage in China. Our solution consists of multiple
RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal
pattern of a specific series with multivariate exogenous series, and then the attention layer learns
the spatial correlative weight and obtains the global representations simultaneously. The results
show that the new approach can capture the temporal-spatial dynamics of household leverage well
and get more accurate and solid predictive results. More, the simulation also studies show that
clustering and choosing correlative series are necessary to obtain accurate forecasting results.
Keywords: Household leverage, Forecasting, Temporal-spatial dynamics, Deep learning
1 Introduction
Time series forecasting (TSF) is imperative to a wide range of financial forecasting problems that
have a temporal pattern. For instance, with the help of forecasting tools, if the governors of a country
can foresee that their nation might suffer from financial risk in the next couple of months, they will
make a good fiscal policy that allocates sufficient resources to hedge against market risks and
optimize investments in advance. Such financial risks may be caused by the rapid raising household
debt, which always amplifies downturns, weakens recoveries, and serves as the fuse for an outbreak
of financial crisis (Clarke, 2019; Mian, Sufi, & Verner, 2017), or the drastic fluctuating international
exchange rate(Ca’Zorzi & Rubaszek, 2020). Due to the complex and continuous fluctuation of
impacting factors, real-world time series tend to be extraordinarily non-stationary, which exhibit
diverse dynamics. For example, the household debt (Verner & Gyngysi, 2020) of a certain region is
largely affected not only by exogenous variables, but also by the location of the region. The location
is representing the spatial pattern, where similar series could have similar trends, variations, and
uncertainty. Another example is the international exchange rate (Ca’Zorzi & Rubaszek, 2020), which
is influenced by both the domestic economy and economies of many associated countries. It also
has diverse dynamical patterns: the temporal pattern within a specific series and the spatial
correlation pattern among the target series and its associated series. In this work, we will study
multiple multi-variate time series forecasting: multi-variate time series evolve with time; and, they
are spatially correlated.
Many traditional statistical-based models and machine learning models have been developed for
computers to model and learn the trend and seasonal variations of the series and also the correlation
between observed values that are close in time. For instance, the autoregressive integrated moving
average (ARIMA) (Saboia, 1977; Tsay, 2000), as a classical linear model in statistics, is an expert
in modeling and learning the linear and stationary time dependencies with a noise component (De
Gooijer & Hyndman, 2006), the multivariate autoregressive time series models (MAR) (Fountis &
Dickey, 1989) that can learn time series patterns accompanied by explanatory variables. Moreover,
several statistical methods have been developed to extract the nonlinear signals from the series, such
as the bilinear model (Poskitt & Tremayne, 1986), the threshold autoregressive model (Stark, 1992),
and the autoregressive conditional heteroscedastic (ARCH) model (Engle, 1982). However, these
models have a rigorous requirement of the stationarity of a time series, which encounters severe
restrictions in practical use if most of the impacting factors are unavailable.
Since the time series prediction is closely related to regression analysis in machine learning,
traditional machine learning models (MLs), such as decision tree (DT) (Galicia, Talavera-Llames,
Troncoso, Koprinska, & Martínez-Álvarez, 2019; Lee & Oh, 1996), support vector machine (SVM),
and k nearest neighbor (kNN), can be used for time series forecasting (Galicia, et al., 2019). Inspired
by the notable achievements of deep learning (DL) in natural language processing (Devlin, Chang,
Lee, & Toutanova, 2018), image classification (Krizhevsky, Sutskever, & Hinton, 2012), and
reinforcement learning (Silver, et al., 2016), several artificial neural network (ANN) algorithms
have drawn people’s attention and become strong contenders along with statistical methods in the
forecasting community with their better prediction accuracies (Zhang, Patuwo, & Hu, 1998).
Significantly, different from MLs that require hand-crafted features, DLs have a great potential to
learn complex non-linear temporal feature interactions among multiple series. Because DLs
automatically learn complex data representations of an MTS, they alleviate the need for manual
feature engineering and model design (Bengio, Courville, & Vincent, 2013; Lim & Zohren, 2021).
Moreover, DLs can learn the linear and nonlinear patterns of data better.
Initially, most DLs are developed to model and learn the temporal dependency of time series. For
instance, the simplest DL, the recurrent neural network (RNN), can store a lot of information about
the past and it allows updates of its hidden state dynamically (Rumelhart et al. 1986; Werbos 1990;
Elman 1990). To address the weakness of RNNs in managing long-term dependencies, the long-
short term memory (LSTM) (Hochreiter & Schmidhuber, 1997), a variant of RNN capable of
learning long-term dependence, has also been employed for series forecasting (Gers, Schmidhuber,
& Cummins, 2000). LSTM comprises a separate autoencoder and forecasting sub-models. LSTM
has an RNN architecture but it is different from RNN, whereas it can solve the problem of vanishing
gradient. The Gate Recurrent Unit (GRU) (Dey & Salem, 2017) is also an important variant of RNN,
where its basic idea of learning long-term dependence is consistent with LSTM; however, it only
uses a reset gate and an update gate. The long- and short-term time-series network (LSTNet) (Lai,
Chang, Yang, & Liu, 2018) is designed specifically for MTS forecasting with up to hundreds of time
series. LSTNet uses CNNs to capture short-term patterns and LSTM (Hochreiter & Schmidhuber,
1997) or GRU (Dey & Salem, 2017) for memorizing relatively long-term patterns. Besides, the
attention mechanism (Bahdanau, Cho, & Bengio, 2014; Luong, Pham, & Manning, 2015), originally
utilized in encoder-decoder networks (Krizhevsky, et al., 2012), somewhat solves the problem of
integrating correlative unites, and thus increases the effectiveness of RNNs (Lai, et al., 2018). The
temporal pattern attention reviews the information at each stage and selects relevant information to
help to generate the outputs (Shih, Sun, & Lee, 2019). Recent studies demonstrate how both the
automatic feature learning capabilities of LSTMs and their ability to handle input sequences can be
harnessed in an end-to-end model that can be used to drive demand forecasting (Hu & Zheng, 2020).
Besides learning the dynamics of temporal dependence, time series that exhibit spatial
dependencies are also important information of time series. The spatio-temporal (ST) properties are
commonly observed in various fields, such as transportation (Shao, Salim, Gu, Dinh, & Chan, 2017),
social science (Kupilik & Witmer, 2018), and criminology (Rumi, Luong, & Salim, 2019). Some
researchers have made efforts to utilize spatial correlation of multiple target time series to realize
accurate forecasting. In statistics, the fully Spatio-temporal MAR (ST-MAR) model is developed
within the framework of functional data analysis to utilize both the linear temporal patterns of the
series itself and the linear spatial patterns of its neighbors (Valdes-Sosa, 2004). Although ST-MAR
is doing well in the inclusion of spatial information, ST-MAR has the same problems while
analyzing nonlinear and non-stationary time series similar to MAR. Similarly, spatio-temporal
modeling has seldom been taken into account in the DLs, and DLs models consist of two
components: one is for capturing the spatio-temporal dynamical pattern of the series; and the other
one is for decoding these latent states and translating them into actual series observations. Based on
the design, models can capture the dynamics and correlations in multiple series at the spatial and
temporal levels (Ziat, Delasalles, Denoyer, & Gallinari, 2017). For instance, PV energy production
prediction (Ceci, Corizzo, Fumarola, Malerba, & Rashkovska, 2016), traffic time series forecasting
(Cirstea, Yang, Guo, Kieu, & Pan, 2022), covid-19 forecasting (Kapoor, et al., 2020), and brain-
computer interface (BCI) (Topic & Russo, 2021), all of which are both spatial and temporal
dependencies. Therefore, they demonstrate good performance on forecasting tasks.
Although DLs are state-of-art techniques and good for modeling and learning the nonlinear and
non-stationary time series with spatial patterns, implementation of DLs in forecasting financial time
series projects would not provide significant improvement in forecasting. On the one hand, while
DLs were successful in some instances, where the series being extrapolated are often numerous and
long, in typical time series forecasting, where data is insufficient and the regressor is unavailable,
the performance of DLs algorithms tends to be under expectations (Makridakis, Spiliotis, &
Assimakopoulos, 2018). For instance, some finance time series, like household debt, are short in
time with limited observations. On the other hand, both the spatial proximity and the long-term
temporal correlations of the data are usually complex and hard to be captured. Moreover, previous
spatial-temporal methods assume neighboring individuals interfere with each other, so they learn the
representation of spatial correlation based on the given graph structure. For instance, the neighbor
pixels usually have similar RGB values in image and video (Topic & Russo, 2021), and adjacent
nodes in the road may cause congestion one after the other (Cirstea, Yang, Guo, Kieu, & Pan, 2022).
However, in financial time series, the structural relationship between any two individual time series is
uncertain. Meanwhile, a series spatially depends on which time series is also unknown. These factors
would impede the way of utilizing spatial patterns to enhance the performance of the forecasting
models.
With the recent advancements in DLs techniques, we are now capable of handling complex
dynamics as a single unit, even without any additional impact factors. In this paper, we study
forecasting models in both a short series and a long series in finance – focusing on the key example
of the household debt and international exchange rate – in a data-rich environment, where our data
includes not only conventional multi-variate series but also multiple target time series. We find that
our forecasts are either superior to or as good as those benchmark DLs. This is the case when (a) we
compare our approach with the CNN, LSTM, and GRU in terms of forecasting the series of
household debt and the series of international exchange rates or (b) we compare our approach with
other models in the artificial data. The former is a comparison of different methods, whereas the
latter reveals under which conditions the model could perform well. In addition, we also conduct
statistical testing to evaluate the difference between the new method and previous DLs.
We make several novel contributions to the new model to achieve our goal. (1), a new method,
the Temporal-Spatial dependencies ENhanced deep learning model (TSEN), is proposed to forecast
the short and long financial time series. The method consists of two components: one captures new
representations of spatio-temporal dynamics of the series, and another one decodes these
representations into target series observations. It is finally used to forecast the household leverage
in multiple regions and the international exchange rate of multiple countries simultaneously. (2) The
accuracy and robustness of the proposed approach are validated through applications of forecasting
multiple MTS. (3) The model is also validated by simulated datasets to explain under which
conditions it could outperform previous DLs.
The rest of the paper is organized as follows. Section 2 presents the related studies on time series
analysis. Section 3 presents the issue and notations of our studies. In section 4, we describe the
framework of the Temporal-Spatial dependencies ENhanced deep learning model (TSEN). Section
5 describes two financial time series and the way of generating artificial data. Section 6 elaborates
on the experimental results of forecasting time series in the previous section. Finally, we provide
the concluding remarks in Section 7.
2. Preliminary
The goal of time series forecasting is to predict its value at based on available observations
from a time series at time . Suppose if there is only one single time-dependent variable is available,
the problem can be studied using univariate time series (UTS) analysis methods, formulated as
 
where  refers to time series data points, are the parameters such as
autoregression coefficients,  is the forecasting values at , is the number of inputs, and
 is any positive integer. For instance, ARIMA and its variants can model and learn
stationary UTS well. With some exogenous time series data, the problem of financial time series
forecasting turns into multivariate time series (MTS) analysis, which can be formulated as
 
where  refers to the target time and  is the
exogenous MTS whose item is  for  . Financial time
series forecasting is a type of MTS analysis, which can be implemented by both traditional methods
and state-of-art deep learning methods, such as RNN (Rumelhart et al. 1986; Werbos 1990; Elman
1990), LSTM (Hochreiter & Schmidhuber, 1997), GRU (Dey & Salem, 2017), and so on.
However, in practical circumstances, such as household debt(Verner & Gyngysi, 2020),
international exchange rate(Ca’Zorzi & Rubaszek, 2020), cryptocurrency(Chen, Xu, Jia, & Gao, 2021),
retail sales(Rafiei & Adeli, 2016), and energy consumption(Deb, Zhang, Yang, Lee, & Shah, 2017),
datasets are collected as spatially indexed MTS and are often spatially correlated because of their
similar location, or economic structures, or development levels. This fact indicates that the variances
of a target series may be influenced by others. The inclusion of spatial dependencies in the
forecasting model may enhance the performance of the model. We use  to denote a MTS
for the jth region or nation, where  and is the number of regions or nations we have
observed. Thus, the problem of modeling multiple MTSs 
to forecast multiple target
time series is formulated as
摘要：

Temporal-SpatialdependenciesENhanceddeeplearningmodel(TSEN)forhouseholdleverageseriesforecastingHuYang1,§,YiHuang1,HaijunWang2,*,andYuChen3(1SchoolofInformation,CentralUniversityofFinanceandEconomics,Beijing,100081,China;2SchoolofEconomics,BeijingWuziUniversity,Beijing,102600,China;3SchoolofPublicFi...

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