# A Review of ARIMA vs. Machine Learning Approaches for Time Series Forecasting in Data Driven Networks

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## Abstract

**:**

## 1. Introduction

#### 1.1. Data Driven Networks

#### 1.2. Scientific Contributions

#### 1.3. Rationale and Structure

## 2. Background: Data and Autoregressive Models

#### 2.1. Time Series Data: Forecasting

- Mean Squared Error (MSE)

- Mean Absolute Percentage Error (MAPE)

- =Mean Absolute Error (MAE)

- Coefficient of determination (${R}^{2}$)

- Mean Absolute Deviation (MAD)

- Nash–Sutcliffe model efficiency coefficient (NSE)

- Kolmogorov-Smirnov test (K-S distance)

- Normalized Mean Absolute Error (NMAE)

#### 2.2. Time Series Data: Characteristics

- Trend: This characteristic is associated with the presence of an upward, downward, or stable course of the series, with respect to the time dimension.
- Seasonality: This characteristic indicates the existence of periodic patterns in the behavior of the time series, which repeat with a fixed frequency.
- Stationarity: Stationary is a time series whose statistical properties (average, variance, dispersion of values, etc.) are stable over time. A stationary time series with no trend implies that its fluctuations around its mean have a constant width. Furthermore, the autocorrelation of static time series remains constant over time. Based on these assumptions, a time series of this form can be thought of as a combination of signal and noise [11].

#### 2.3. Time Series Data Sources

#### 2.4. AutoRegressive Integrated Moving Average (ARIMA) Models

- AR: Autoregression. A regression model that uses the dependence relationship between an observation and a number of lagged observations (model parameter p).
- I: Integration. Calculating the differences between observations at different time points (model parameter d), aiming to make the time series stationary.
- MA: Moving Average. This approach considers the dependence that may exist between observations and the error terms created when a moving average model is used on observations that have a time lag (model parameter q).

#### 2.4.1. ARIMA Parameter Determination

#### 2.4.2. ARIMA Variants

#### 2.4.3. Advantages and Disadvantages

## 3. Machine Learning Models

#### 3.1. Support Vector Machines (SVM)

**Table 2.**Summary of ARIMA and SVM Comparison Studies in Time Series Forecasting. In the works of Singh et al. and Zhang et al. the ARIMA parameters were optimized for each observation site.

Article | Algorithms | Metrics | Dataset |
---|---|---|---|

Makala et al. [20] | ARIMA$(2,1,2)\times {(2,1,2)}_{12}$ | RMSE | gold price |

SVM | MAPE | ||

Singh et al. [21] | SVM | MAE | COVID-19 confirmed cases |

MSE | |||

RMSE | |||

Atique et al. [22] | ARIMA$(0,1,2)\times {(1,0,1)}_{30}$ | MAPE | solar energy generation |

SVM | |||

ANN | |||

Tiwari et al. [23] | ARIMA${(0,1,12)}_{day}$ | MSE | ambient noise levels |

ARIMA${(0,1,10)}_{night}$ | RMSE | ||

SVM | MAPE | ||

${R}^{2}$ | |||

Zhang et al. [24] | ARIMA | ${R}^{2}$ | drought forecasting |

WNN | MSE | ||

SVM | NSE | ||

K-S distance | |||

Al Amin et al. [25] | ARIMA$(2,1,1)$ | MAPE | short time load forecasting |

SVM (for non-linear | MSE | ||

load pattern) | |||

Liu et al. [26] | ARIMA | various | urban water consumption |

BP | |||

SVM |

#### 3.1.1. Financial Data

#### 3.1.2. Healthcare Data

#### 3.1.3. Energy and Noise Prediction

#### 3.1.4. Weather

#### 3.1.5. Utilities

#### 3.2. Decision Trees and Random Forests

**Table 3.**Summary of ARIMA and Decision Tree-based models’ Comparison Studies in Time Series Forecasting.

Article | Algorithms | Metrics | Dataset |
---|---|---|---|

Alim et al. [33] | ARIMA$(0,1,1)\times {(0,1,1)}_{12}$ | MAE | infectious disease prediction |

XGBoost | RMSE | ||

MAPE | |||

Lv et al. [34] | ARIMA$(3,1,0)\times {(1,1,0)}_{12}$ | MAE | infectious disease prediction |

XGBoost | MPE | ||

MAPE | |||

RMSE | |||

MASE | |||

Fang et al. [35] | ARIMA$(0,1,1)\times {(0,1,1)}_{7}$ | MAE | COVID-19 confirmed cases |

XGBoost | RMSE | ||

MAPE | |||

Noorunnahar et al. [36] | ARIMA$(0,1,1)$ | MAE | annual rice production |

XGBoost | MPE | ||

RMSE | |||

MAPE | |||

Zhang et al. [37] | ARIMA | RMSE | retail sales volume |

LSTM | MAE | ||

Prophet | |||

GBDT | |||

XGBoost | |||

Priyadarshini et al. [38] | ARIMA$(2,1,1)$ | MSE | short time load forecasting |

SARIMA | RMSE | ||

LSTM | MAE | ||

LightGBM | |||

Prophet | |||

VAR | |||

Makridakis et al. [39] | various | various | retail unit sales (M5) |

multiple categories (M4) |

#### 3.2.1. Healthcare Data

#### 3.2.2. Utilities

#### 3.2.3. Forecasting Competitions

#### 3.3. Deep Learning Models

#### 3.3.1. Artificial Neural Networks (ANN)

#### 3.3.2. Recurrent Neural Networks (RNN)

#### 3.3.3. Long-Short Term Memory Networks (LSTM)

- The forget gate outputs a number between 0 and 1, where 1 indicates full retention of the content, while 0 indicates full discarding of it.
- The memory gate chooses which of the new data will be stored in each cell.
- The output gate decides the output of the cell. The value of the output is based on the current state of the cell, along with the filtered new data.

Article | Algorithms | Metrics | Dataset |
---|---|---|---|

Namini et al. [8] | LSTM | RMSE | stock indices |

BiLSTM | |||

Paliari et al. [32] | ARIMA$(5,1,0)$ | MAE | daily stock price |

LSTM | (R)MSE | ||

XGBoost | |||

Nguyen et al. [44] | ARIMA$(6,1,5)$ | RMSE | bitcoin price |

FFNN | MAPE | ||

CNN | |||

LSTM | |||

SVR | |||

Yamak et al. [6] | ARIMA$(1,1,0)$ | RMSE | bitcoin price |

LSTM | MAPE | ||

GRU | |||

Hua et al. [45] | ARIMA$(1,1,0)$ | precision rate | bitcoin price |

LSTM | time efficiency | ||

Latif et al. [46] | ARIMA$(3,1,3)$ | RMSE | short-term bitcoin price |

LSTM | MAPE | ||

MAE | |||

MAD | |||

Rhanoui et al. [47] | ARIMA$(0,1,0)$ | (R)MSE | financial budget |

LSTM | MAE | ||

Menculini et al. [48] | Prophet | MAE | wholesale food prices |

LSTM | MAPE | ||

CNN | RMSE | ||

Ning et al. [49] | ARIMA$(0,1,1)$ | RMSE | oil production |

LSTM | MAE | ||

Prophet | |||

Kirbas et al. [50] | ARIMA$(2,2,5)$ | MSE | COVID-19 cases |

LSTM | MAPE | ||

NARNN | PSNR | ||

SMAPE | |||

R-value | |||

ArunKumar et al. [51] | ARIMA | MSE | COVID-19 trends |

SARIMA | RMSE | ||

RNN-GRU | |||

RNN-LSTM | |||

De Saa et al. [52] | custom CNN/LSTM | MSE | temperature forecast |

Verma et al. [53] | ARIMA$(5,0,6)$ | RMSE | air quality index |

Prophet | MAPE | ||

LSTM | MAE | ||

Liu et al. [54] | ARIMA$(2,0,3)\times {(2,1,3)}_{24}$ | MSE | short-term wind speed |

LSTM | MAE | ||

GRU | ${R}^{2}$ | ||

Spyrou et al. [17] | ARIMA$(1,1,0)$ | RMSE | CO_{2} levels forecast |

LSTM | MAE | ||

Zhou et al. [55] | ARIMA$(1,1,2)$ | RMSE | web traffic |

LSTM | MAE | ||

Azari et al. [56] | ARIMA$(6,1,0)$ | RMSE | cellular traffic |

LSTM |

#### Financial Data

#### Utilities

#### Healthcare Data

#### Weather and Environmental Parameter Studies

#### Network Traffic

## 4. Hybrid Models

#### 4.1. Financial Data

#### 4.2. Weather

#### 4.3. Healthcare Data

#### 4.4. Utilities

#### 4.5. Network Traffic

## 5. Discussion and Practical Evaluation

Article | Algorithms | Metrics | Dataset |
---|---|---|---|

Zhang et al. [4] | ARIMA/ANN | MSE | variety |

MAD | |||

Nguyen et al. [44] | ARIMA/FFNN | RMSE | bitcoin price |

ARIMA/CNN | MAPE | ||

ARIMA/LSTM | |||

ARIMA/SVR | |||

Biswas et al. [57] | ARIMA/RF | NMAE | wind power |

ARIMA/BCART | |||

Prajapati et al. [58] | ARIMA/NARNN | RMSE | COVID-19 cases |

Nie et al. [5] | ARIMA/SVM | MAPE | short-term load forecasting |

RMSE | |||

Ma et al. [59] | NN/ARIMA | MSE | network-wide |

MSVR/ARIMA | MAPE | traffic |

- ARIMA over SVM Models

- ARIMA over Deep Learning Models

- Hybrid Models over ARIMA

- Final Remarks

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An example of a linearly separable problem of two classes in the two dimensional space. The support vectors are defined by the three samples on the lines that define the margin of optimal separation between the two classes.

**Figure 2.**A graph of the support vector machine model architecture. The support vectors that define the regressive process are created by the feature space and the output space consists of the forecasted time series, which represent the objective variable.

**Figure 3.**Basic architecture of an artificial neural network. By increasing the number of hidden layers (depth of the network), we also increase the capacity of the model.

**Figure 5.**Building block of a Long-short term memory network. The variables c and h represent the current state and the hidden state of the LSTM cell, while the input is represented by the x variable. The sigmoid gates inside the block constitute the forget, input and output gate respectively. The current state is updated with respect to the input, according to the sum of the current state and a combination of the input and the hidden state of the block.

**Figure 6.**Flowchart of hybrid Arima and Machine Learning model for time series forecasting. This particular workflow is not the only one used in the scientific literature. Different combinations of the ARIMA and ML models have been proposed ([5,44]), based on the nature of the forecasting problem and the modeling approach.

**Figure 7.**Flowchart of hybrid Arima and Machine Learning for time series forecasting, based on the fluctuation interval.

**Table 1.**Nonseasonal ARIMA models for time series forecasting. Random-walk and random-trend, autoregressive and exponential smoothing models constitute specific cases of the general ARIMA models. The additional presence of a constant in the models, accounts for any underlying trend or mean in the data, in order to improve their predictions and overall performance in the forecasting tasks.

Forecasting Equation | ARIMA(p,d,q) |
---|---|

first-order autoregressive model | ARIMA(1,0,0) |

random walk | ARIMA(0,1,0) |

differenced first-order autoregressive model | ARIMA(1,1,0) |

simple exponential smoothing | ARIMA(0,1,1) |

simple exponential smoothing with growth | ARIMA(0,1,1) |

linear exponential smoothing | ARIMA(0,2,1) |

linear exponential smoothing | ARIMA(0,2,2) |

damped-trend linear exponential smoothing | ARIMA(1,1,2) |

**Table 6.**Advantages and disadvantages of ARIMA over Artificial Intelligence models, regarding time series forecasting tasks.

Criterion | ARIMA | Artificial Intelligence |
---|---|---|

Model | Explainable | Regarded as a “black box” |

Flexible specification | Need training | |

Reliable performance | Need optimization | |

Designed to model dependencies | Better at modelling | |

that can be linearizable | non-linear time dependencies | |

through a single transformation | ||

Parameter specification | Standard training procedure | |

depending on user-experience | ||

Dataset | Suitable for small datasets | Need large datasets to train |

Missing values not important | Difficult modelling | |

when values are missing | ||

Multiple seasonality | Complex modelling | |

not handled natively | ||

Designed for univariate series | Handle multivariate datasets | |

Sensitive to outliers | Depend on model complexity | |

Assume data integrated | Data agnostic | |

of a finite order | ||

Handles independent forecasting tasks | Joint forecast of multiple time series | |

Complexity | Low time complexity | Training and validation needed |

in general (depending on the model) | ||

Small computational requirements | Hardware and computational | |

[61] | demands higher (depending on model) |

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**MDPI and ACS Style**

Kontopoulou, V.I.; Panagopoulos, A.D.; Kakkos, I.; Matsopoulos, G.K.
A Review of ARIMA vs. Machine Learning Approaches for Time Series Forecasting in Data Driven Networks. *Future Internet* **2023**, *15*, 255.
https://doi.org/10.3390/fi15080255

**AMA Style**

Kontopoulou VI, Panagopoulos AD, Kakkos I, Matsopoulos GK.
A Review of ARIMA vs. Machine Learning Approaches for Time Series Forecasting in Data Driven Networks. *Future Internet*. 2023; 15(8):255.
https://doi.org/10.3390/fi15080255

**Chicago/Turabian Style**

Kontopoulou, Vaia I., Athanasios D. Panagopoulos, Ioannis Kakkos, and George K. Matsopoulos.
2023. "A Review of ARIMA vs. Machine Learning Approaches for Time Series Forecasting in Data Driven Networks" *Future Internet* 15, no. 8: 255.
https://doi.org/10.3390/fi15080255