Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 16, No. 2, 2024 

 

264 

Forecasting China's Consumer Price Index (CPI) Based 
on Combined ARIMA-LSTM Models 

Yu Liu 

School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, China 

 

Abstract: This study aims to construct an efficient consumer price index (CPI) forecasting model to provide policymakers, 
investors, and businesses with more accurate forecasts of future price levels and inflation trends. in this study, a combined model 

that integrates autoregressive integrated moving average (ARIMA) with long short-term memory (LSTM) networks is introduced. 

The model first captures the linear trend of CPI data using the ARIMA model, and then inputs the residuals into the LSTM 

network to predict the nonlinear part. The model is trained and tested using monthly Chinese CPI data. The findings indicate that 

the ARIMA-LSTM hybrid model outshines the single ARIMA model regarding prediction accuracy, its predicted values are 

closely aligned with the actual values, and the model residual series passes the Q-test, which suggests that the model exhibits a 

strong fitting capability. The article also introduces the evaluation indexes of the model and compares the prediction performance 

of the single ARIMA model and the ARIMA-LSTM hybrid model. Finally, the article concludes that the ARIMA-LSTM hybrid 

model has high accuracy and reliability in CPI forecasting, which provides a powerful tool for forecasting future price trends. 

Keywords: Time series forecasting, CPI, Deep learning, ARIMA-LSTM. 

 

1. Introduction 

The Consumer Price Index (CPI) is among the key 

performance metrics of changes in consumer price levels. By 

forecasting the CPI, it can help organizations, such as, central 

banks and businesses to anticipate future price levels and 

inflation trends. This is important for adjusting the economy, 

setting money, and business decision-making and planning. 

Traditional CPI forecasting methods usually rely on statistical 

and econometric techniques, which include time series 

analysis, regression modeling, seasonal adjustment, etc 

(Gautam & Kanoujiya, 2022). These methods are often based 

on historical data and predict future CPI changes by 

identifying patterns and trends in price movements. For 

example, Di Filippo (2015) used Dynamic Model Averaging 

(DMA) and Dynamic Model Selection (DMS) methods to 

forecast the CPI in the Eurozone and the U.S. Shapovalenko 

(2021) reviewed the models used by the National Bank of 

Ukraine (NBU) for predicting short-term CPI trends, 

researchers assessed the predictive precision of these models 

and provided suggestions for improving current models, 

especially in the context of data scarcity and the challenges of 

prediction in war situations. CPI price indices tend to have 

certain seasonality and trends, and ARIMA models can 

capture these linear relationships, providing forecasting 

power for long-term trends (Riofrio et al., 2023; Álvarez-Díaz 

& Gupta, 2016). Ahmar et al. (2018) used the predictive 

modeling tools in R programming language to implement the 

ARIMA method to forecast CPI data in Indonesia, both of 

which achieved good forecasting results. Shinkarenko et al. 

(2021) analyzed the time series data of CPI for Ukraine and 

constructed the ARIMA*ARIMAS model. Mohamed (2020) 

compared the performance of the ARIMA model and 

predictive analytical model with ARIMA errors in forecasting 

CPI in Somaliland.  

Machine learning methods, especially deep learning 

methods that have emerged in recent years, provide new ideas 

for CPI forecasting. These methods can handle more complex 

nonlinear relationships by automatically learning features and 

patterns from large amounts of data (Maehashi & Shintani, 

2020; Du, 2018; Samiami-Namini et al., 2018), and can 

account for long-term temporal correlations in sequential data, 

thus demonstrating higher CPI forecasting in terms of 

accuracy and adaptability (Rohmah et al., 2021; Rohmah et 

al., 2020; Wang & Fan, 2010; Feihu Qin et al., 2010). such as 

Recurrent Neural Networks (RNN) or Long Short-Term 

Memory Networks (LSTM). LSTM model is a deep learning 

model suitable for processing sequential data, which makes it 

a powerful tool within the realm of sequential data forecasting 

through its unique gating mechanism and memory units. For 

example, S. Zahara et al. (2020) combined LSTM and cloud 

computing techniques for CPI forecasting, Astrakhantseva et 

al. (2021) used an LSTM-based model and introduced a "dual 

attention" mechanism to automatically detect the effect of the 

time point on the forecasts, Reynaldo Rosado et al. (2021) 

used an LSTM-based model and introduced a "dual attention" 

mechanism to automatically detect the effect of the time point 

on the forecasts. Reynaldo Rosado et al. (2021) used different 

LSTM model architectures for forecasting CPI with good 

results. CPI price index is often affected by numerous 

elements, such as economic activity, market supply and 

demand, and changes. These factors may produce complex 

nonlinear relationships, and the LSTM model can better 

capture and predict these nonlinear trends. Combining the 

ARIMA and LSTM models, leaving the linear trends to the 

ARIMA model and the nonlinear trends to the LSTM type, 

can harness the strengths of both approaches and improve the 

model prediction accuracy. Sarveswararao and Ravi (2020) 

proposed a two-stage hybrid model and concluded that the 

Chaos and Machine Learning hybrid model outperforms the 

pure machine learning algorithm in terms of Symmetric Mean 

Absolute Percentage Error, Theil's U statistic, and directional 

statistics. D Xu et al. (2022) compared and analyzed six 

models and ARIMA-LSTM used to predict dry weather. The 

findings indicated that hybrid models outperformed 

standalone models in terms of predictive precision. 

Furthermore, the ARIMA-LSTM model achieved the greatest 

level of forecasting accuracy at 6, 12, and 24-month scales. 



 

265 

Morikawa (2022) aimed to predict in-vehicle carbon dioxide 

(CO2) concentration by ARIMA and LSTM models and to 

evaluate the comparative predictive precision of these two 

approaches. Hadwan et al. (2022) proposed a hybrid 

prediction method consisting of three models: an initial model 

grounded in ARIMA; a second model with a backpropagation 

neural network (BPNN) featuring adjustable gradient and 

momentum coefficients; and a fusion of ARIMA and BPNN 

(ARIMA/BPNN) as well as artificial neural network and 

ARIMA (ARIMA/ ANN) hybridization to obtain the 

advantages of both linear and non-linear predictive models for 

predicting CPI index. Du et al. (2014) combined the three 

methods of ARIMA, gray model, and BPNN. By improving 

the prediction method, the accuracy of sub-CPI prediction 

was improved and the method outperformed many frequently 

employed forecasting techniques regarding their precision 

and stability. 

 This literature provides specific methodological and 

empirical studies on the application of a combination of linear 

and non-linear models to sequential data forecasting. These 

studies show that forecasting accuracy can be improved, 

uncertainty can be reduced, and complex relationships in time 

series can be better captured by combining multiple models. 

Although each dataset and application scenario has own 

specific requirements, these studies provide useful guidance 

and inspiration for carrying out the practice of combining 

predictive models. 

 the remainder of the study is structured in the following 

manner: In Section 2, this study describes the suggested 

model in detail. In Section 3 gives the analytical forecasting 

process of China's CPI, i.e., the linear forecasting of the 

ARIMA model, the non-linear predictive power of the LSTM 

model, and the coupled forecasting results. In the 4 sections, 

a comparative analysis of the hybrid model versus the 

standalone models is conducted. In the 5 sections, we 

summarize the findings of the research. 

2. Relevant Theoretical Foundations 

2.1. Introduction to the ARIMA Model 

ARIMA is a frequently employed analytical tool for 

sequential data examination and forecasting. It models the 

data by considering the autocorrelation (AR, autoregressive), 

lagged difference (I, integral), and moving average (MA, 

moving average) aspects of the series. 

The general form of the ARIMA model is ARIMA (p, d, q): 

p represents the order of the autoregressive term (AR), which 

denotes the count of time lags for the linear relationship 

between the historical data and the current values in the model. 

d signifies the order of the difference (I), which refers to the 

number of differences that are applied to the original data to 

smoothen it out. q represents the order of the moving average 

term (MA), which denotes the number of lags that are 

accounted for in the model. of the mean of the prediction 

errors. 

The modeling steps for the ARIMA model are as follows: 

Determining the model order: the order parameters p , 
d,and q of the ARIMA model are determined by looking at 
the time series plot, autocorrelation function (ACF) diagram, 

and partial autocorrelation function (PACF) diagram. 

Data preprocessing: the necessary processing of the raw 

time series data, such as removing trends (using differencing 

until the series is smooth), removing seasonal effects, and so 

on. 

Fitting the model: an ARIMA model is applied to processed 

time series data using a fit function. The parameters of the 

model can be determined through maximum likelihood 

estimation or alternative techniques. 

Model checking: ensuring that the model has not been left 

out of the modeling of sequential patterns by analyzing the 

ACF diagram and PACF diagram of the model residuals and 

Q-tests, among other methods. 

Model diagnosis and improvement: If the model residuals 

show unreasonable autocorrelation or other problems, model 

improvement is needed to adjust the order, refit the model, 

and perform further diagnostics. 

Forecasting: The fitted ARIMA model is used to make 

forecasts at future points in time, and the optimal forecast 

interval can be selected. 

The mathematical expression of the model is as follows: 

𝑌𝑡 = 𝑐 + φ1 𝑌𝑡−1 + φ2𝑌𝑡−2 + ⋯ + φ𝑝𝑌𝑡−𝑝 − θ1ϵ𝑡−1 − θ2ϵ𝑡−2 − ⋯ θ𝑞 ϵ𝑡−𝑞 + ϵ𝑡                      

Where, 𝑌𝑡   is the observed value of the time series at 
moment 𝑡 ; 𝑐  is the constant term; 𝜑  is the autoregressive 
coefficient; 𝜀 is the error term (Gaussian white noise); 𝜃 is 
the moving average coefficient. The specific form of these 

equations will be adjusted according to the order of the 

particular ARIMA model. The application of the ARIMA 

model needs to be specifically analyzed and adjusted 

grounded on the corresponding time series data to ensure 

correctness and reliability. In addition, there are various 

improved and extended forms of ARIMA models, such as the 

Seasonal ARIMA (SARIMA) model, which can better handle 

time series data with specific properties. 

2.2. Introduction to the LSTM Model 

The LSTM model has a memory function to better handle 

long sequence problems (Rui Zhang et al., 2022). In LSTM, 

the flow of information is controlled by introducing gating 

mechanisms, including input gates, output gates, and 

forgetting gates, to control which information needs to be 

passed and which needs to be forgotten. These gating 

mechanisms can help LSTM models filter and store important 

information in the sequence and resist the problem of gradient 

vanishing. Therefore, LSTM is widely used in language 

modeling, natural language processing, speech recognition, 

video processing, etc. LSTM has a wide range of applications 

in finance, including determining market sentiment, asset 

management, predicting non-performing loans and fraud, and 

financial forecasting. LSTM can be used for forecasting 

financial temporal data such as stock prices and exchange 

rates. Based on historical data, the model can predict future 

trends and help investors make better investment decisions. 

 



 

266 

 
Figure 1. LSTM cell structure 

Compared to the traditional RNN, the LSTM model adds a 

cell state. Let's take the cell structure at the middle moment t 

of LSTM as an example. In figure 1, the 𝑋 denotes the input 
state, the ℎ denotes the hidden layer, and 𝐶 then denotes the 
cell update. In the model, the cell state at time 𝑡 − 1 will be 
affected by the hidden layer state at time 𝑡 − 1 and the input 
𝑋 at time 𝑡, and the resulting output from the cell and hidden 
states. 

There are three main unit structures within the LSTM: the 

oblivion gate, the update gate, and the output gate. It is called 

oblivion gate because 𝐻𝑡−1 and 𝑋𝑡 , after the state input, the 
output activated by the σ function as 𝑓𝑡 . If the output value is 
0, the 𝐶𝑡−1 , corresponding information is erased, which is 
equivalent to complete forgetting. If the output value is (0, 1), 

it is equivalent to partial retention, and only when the output 

value is 1, the corresponding information is completely 

retained. Therefore, this structure is called the forgetting gate 

structure. The output value 𝑖𝑡  activated by the σ function is 

multiplied by the output value 𝐶�̃�   normalized by the𝑡𝑎𝑛ℎ 
function, the output information is added with the information 

obtained from the previous forgetting gate, and this process 

can be regarded as an update process of the 𝐶 This process 
can be regarded as an update process of the Therefore it is 

called an update gate. 𝐶𝑡  is normalized by the 𝑡𝑎𝑛ℎ function 
and multiplied with the output value 𝑂𝑡  to acquire the output 
value of the next stage. 

2.3. ARIMA-LSTM Model 

For data in the form of time series, we assume that it 

consists of a linear part and a nonlinear part, which can be 

formulated as the following expression: 

𝑋𝑡 = 𝐿𝑡 + 𝑁𝑡 + 𝜉𝑡                 

Where 𝐿𝑡  is the linear part, 𝑁𝑡  is the nonlinear part, and 
𝜉𝑡   represents the error term. The ARIMA model performs 
well in successfully modeling nonlinear relational surfaces in 

time series data, whereas, the LSTM model is capable of 

modeling nonlinear components. To achieve the best 

prediction results, we constructed a hybrid model that 

combines the benefits of the ARIMA and LSTM models. This 

hybrid model can be operated within the framework 

illustrated in Figure 2. 

 
Figure 2. ARIMA-LSTM hybrid model 

The hybrid model can be generally categorized into four 

phases: (1) Data preprocessing. Time series data are generally 

non-stationary time series, needs to observe its scatter plot or 

directly conduct the ADF unit root test to observe whether its 

time series is smooth. If it is not smooth, it needs to be 

processed by logarithm or difference to transform it into a 

smooth time series. (2) Linear forecasting of ARIMA model. 

The ARIMA statistical model is used to extract the linear part 



 

267 

of the CPI 𝐿𝑡  and return the residual term 𝑁𝑡 , which is used 
as the input term in the next step. (3) The residual term 𝑁𝑡  
generated by the ARIMA model, that is, the nonlinear part, is 

fed into the LSTM network for the learning process, and the 

predicted value of the nonlinear part is generated. (4) The 

predicted values of the linear part of the ARIMA model and 

the predicted values of the nonlinear part of the LSTM 

network are added together to derive the ultimate forecasting 

outcomes, and the outcomes are evaluated. 

2.4. Evaluation Indicators 

In this work, four comprehensive evaluation indexes are 

chosen to evaluate the precision of the forecast of the 

ARIMA-LSTM model, which are Mean Absolute Error 

(MAE), Mean Square Error (MSE), Root Mean Square Error 

(RMSE) and Mean Absolute Percentage Error (MAPE). Its 

specific formula is as follows: 

(1) Mean Absolute Error. 

𝑀𝐴𝐸 =
1

𝑛
∑ |𝑦𝑖 − 𝑦�̂�|

𝑛
𝑖=1   ∈ [0, +∞]           

(2) Mean Square Error. 

𝑀𝑆𝐸 =
1

𝑛
∑ (𝑦𝑖 − 𝑦�̂�)

2𝑛
𝑖=1   ∈ [0, +∞]          

(3) Root mean square error. 

𝑅𝑀𝑆𝐸 = √
1

𝑛
∑ (𝑦𝑖 − 𝑦�̂�)

2𝑛
𝑖=1   ∈ [0, +∞]         

(4) Mean Absolute Percentage Error. 

𝑀𝐴𝑃𝐸 =
100%

𝑛
∑ |

𝑦𝑖−𝑦�̂�

𝑦𝑖
|𝑛𝑖=1 ∈ [0, +∞]         

Where 𝑦𝑖   denotes the 𝑖 th true value, and 𝑦�̂�  denotes the 
𝑖 th predicted value. The smaller the value of MAE, MSE, 
RMSE, MAPE, suggesting that the greater the model's 

precision, the more effective the fit. 

3. Empirical Analysis 

3.1. Data Sources and Pre-processing 

This paper uses monthly data of China CPI from January 

2016 to April 2023, with a total of 88 sample values. The 

source of data is the official website of the National Bureau 

of Statistics. Figure 3 shows China's CPI data over the past 88 

months. 

 
Figure 3. cpi data of China 

In order to analyze and forecast the CPI using the ARIMA 

model, the stability of the time series must be ensured first. 

However, the selected CPI data may be affected by 

unexpected events, resulting in data instability. Therefore, 

before ARIMA analysis and forecasting of CPI, unit root test 

is needed to guarantee the data's continuity. Unit root denotes 

the unit root process, if there is a unit root process in the time 

series it indicates that the series is not smooth, and there could 

be a spurious regression phenomenon within the context of 

regression analysis. Common unit root test methods include 

the augmented Dickey-Fuller (ADF) test, Phillips-Perro (PP) 

test, Ng-Perron (NP) test, etc. In this study, the ADF test is 

chosen. When using Stata software to carry out ADF test on 

the original CPI data, it is found that the T-statistic shows 

significance at a 1% level of significance, which means that 

the original CPI series is smooth, and can continue to carry 

out the subsequent empirical analysis. 

3.2. ARIMA Model Fitted with A Linear 
Component 

From the above, it is evident that the original sequence is 

smooth and does not need to be differenced, so the value of d 

in the ARIMA model is 0. The next step is to determine the 

value of p and q by observing the ACF diagram and PACF 

diagram of the sample data. As shown in Figure 3. 

 



 

268 

  

Figure 4. Sample autocorrelation and partial autocorrelation plots 

The four models ARIMA (1, 0, 1), ARIMA (1, 0, 2), 

ARIMA (2, 0, 1) and ARIMA (2, 0, 2) are evaluated. The 

residual series of the four models were subjected to Q-tests 

respectively, and the tests were all passed, indicating that the 

residual series of the four models were white noise and the 

models were all fully identified. Compare the fit of four 

models using the Akaike Information Criterion (AIC), the 

Bayesian Information Criterion (BIC), and Khundrin's Law of 

Iterated Logarithm Criterion (LILC) as evaluation metrics. 

The more reduced the values of AIC, BIC, and LILC, the 

more favorable the model fit and the higher the accuracy of 

the predicted values. By comparing the four models, it was 

determined that ARIMA (1, 0, 2) was used for sample fitting. 

Using stata econometrics software, the parameter values of 

the model can be calculated as shown in Table 1, with the 

coefficients of AR (1) being significant at the 1% level and 

MA (2) being significant at the 5% level. Therefore, the 

research of this paper can establish the forecasting model of 

China's CPI index as ARIMA (1, 0, 2), where the coefficients 

of the model are displayed in Table 1. 

 

Table 1. ARIMA (1, 0, 2) model correlation coefficients 

variable Coefficient Std. Error t-Statistic Prob. 

AR (1) 0.7635 .0718773 10.62 0.0000 

MA (1) -0.6549    

MA (2) -0.3451 0.1726 -2.00 0.046 

 

As shown in figure 4, the model is very close to the actual 

values in terms of fitted values, which fully reflects the trend 

of CPI index, thus suggesting that the model exhibits a 

positive performance in fitting effect. The residual series 

passes the Q-test and is a white noise series. ARIMA method 

is an effective tool, but not for nonlinear fluctuations. The 

blue line represents the residuals between the predicted values 

of the ARIMA model and the actual values and uses it as test 

data for the LSTM model. 

 
Figure 5. ARIMA (1, 0, 2) model fitted values, true values, and 

residual series 

3.3. LSTM Model Fitting the Nonlinear 
Component 

In order to find the nonlinear relationship of CPI, the 

LSTM model was developed. In the ARIMA-LSTM hybrid 

model, the LSTM network is fed exclusively with the 

residuals obtained from the ARIMA model. We predicted the 

CPI value of the day from the CPI data of the previous seven 

months, for example, we predicted the CPI value of August 

based on the data of January, February, March, April, May, 

June, and July. The learning rate is configured at 0.009, and 

the iteration count is set to 250. 

The loss function is determined by employing the smooth 

L1 loss function for computation. The smoothed loss function 

L1, also known as the absolute value loss function, serves as 

a frequently utilized function in addressing regression issues. 

It measures the error of the model by calculating the absolute 

difference between the forecasted outcome and the target 

value. 

The expression for the smoothing loss function L1 is: 

𝑳(𝒚, �̂�) = |𝒚 − �̂�|                 

Where 𝑦 denotes the desired outcome and �̂� signifies the 
model's estimated outcome. 

L1 smoothing loss function Compared to other common 

loss functions (e.g. mean square error), L1 loss has better 

robustness to outliers and outliers. Since the L1 loss uses 

absolute differences, outliers have less influence on the L1 

loss, making the model better adaptable to noise and outliers; 

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the L1 loss has a linear gradient at the origin, which means 

that the response of the L1 loss to parameter tuning remains 

consistent over different prediction error ranges. This 

property helps the optimization algorithm to converge better 

and reduces the risk of overfitting; moreover, the relationship 

between the form of the L1 loss and the absolute value is 

intuitively easy to understand. It directly measures the 

absolute difference between the objective value and the pre-

mean, which is more in line with the interpretation of errors 

in some practical problems. 

As depicted in figure 5, the function loss rate of the LSTM 

network for the residual sequence is relatively low, and the 

fitted values also highly overlap with the actual values, this 

suggests that the model possesses a high fitting accuracy. 

  
Figure 6. Residual series loss function and fitted values vs. true values 

As shown in Table 2, taken together, the LSTM model 

performs well in fitting the residual series, especially in terms 

of MAE and RMSE, showing a small prediction error. 

 

Table 2. Comprehensive evaluation metrics for residual sequence 
fitting in LSTM networks 

Comprehensive evaluation index Value 

MAE 0.1257 

MSE 0.3780 

RMSE 0.1944 

MAPE 0.8414 

4. Analysis of Results 

In addition, when using the ARIMA-LSTM model, the 

residual sequence fitting values obtained from the LSTM 

model are added to the linear parts obtained from the ARIMA 

model and the final prediction result can be obtained. It can 

be observed through figure 6 that the fitted values of the 

ARIMA-LSTM model are nearly identical to the actual values 

and completely reflect the trend of the CPI index, which 

further confirms the good fitting effect of the model. 

 
Figure 7. ARIMA-LSTM model predicted and true values 

As illustrated in Table 3, comparing the single ARIMA 

model with the ARIMA-LSTM model forecasting outcomes, 

by observing the values of the three evaluation indexes, MAE, 

MSE and MAPE, it can be found that the comprehensive 

evaluation values of the ARIMA-LSTM model are each less 

than those of the standalone ARIMA model, and it can be 

deduced that the ARIMA-LSTM model is superior to the 

single ARIMA model in CPI prediction. single ARIMA model 

with better model prediction accuracy. It is further observed 

that China's CPI index fluctuates more from 2018 to 2020, 

especially due to the impact of public health emergencies. In 

conclusion, when compared to the individual ARIMA models, 

the hybrid model separates the time series into the linear part 

of the ARIMA model and the nonlinear part of the LSTM 

model, which has higher forecasting accuracy. 

 

Table 3. ARIMA model and ARIMA-LSTM combined evaluation 
metrics 

 ARIMA ARIMA-LSTM 

MAE 0.3738 0.1536 

MSE 0.2320 0.0696 

MAPE 0.0037 0.0015 

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