# Time Series Analysis Based on Informer Algorithms: A Survey

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## Abstract

**:**

## 1. Introduction

- In this paper, the principle of the Informer algorithm model, related structure, and attention algorithm are restated in detail, and the advantages and shortcomings of the informer algorithm model are analyzed.
- In this paper, we kindly discuss in detail the innovations and improvements in the model structure of several other advanced algorithmic models (including TCCT, Autoformer, FEDformer, Pyraformer, and Triformer)
- We study an overview of the attentional algorithm structure and innovations for each model, and we also provide a critical analysis of the models and attention mechanisms that were studied and summarize the advantages and disadvantages of each model.
- In this paper, we compare and analyze each algorithm model with the informer algorithm model, showing the feasibility of the attention mechanism and related models such as the informer algorithm model and making predictions and outlooks on future research directions.

## 2. Background of Informer Algorithm Model and Architecture

#### 2.1. Basic Forecasting Problem Definition

#### 2.2. Informer Architecture

**Lemma 1.**

#### 2.3. Encoder

#### 2.4. Decoder

#### 2.5. Informer Algorithm Model Values

## 3. Relevant Model Development

#### 3.1. TCCT Algorithmic Model

#### 3.1.1. Dilated Causal Convolutions

#### 3.1.2. TCCT Architecture and Passthrough Mechanism

#### 3.1.3. Transformer with TCCT Architectures

#### 3.1.4. TCCT Algorithm Model Value

#### 3.2. Autoformer

#### 3.2.1. Deep Decomposition Architecture

#### 3.2.2. Encoder

#### 3.2.3. Decoder

#### 3.2.4. Autoformer Algorithm Model Architecture Value

#### 3.3. FEDformer

#### 3.3.1. Application of Neural Networks in Frequency Domain Operations

#### 3.3.2. FEDformer Algorithm Model Architecture

#### 3.3.3. Learning Principles for Models in the Frequency and Time Domains

#### 3.3.4. FEDformer Algorithm Model Values

#### 3.4. Pyraformer

#### 3.4.1. Pyraformer Algorithm Model Architecture

#### 3.4.2. Coarser Scale Construction Module (CSCM)

#### 3.5. Triformer

#### 3.5.1. Variable Agnostic and Variable-Specific Modeling

#### 3.5.2. Triangular Stacking Attention

#### 3.5.3. Lightweight Modeling for Generating Variable-Specific Parameters

## 4. Innovation of Attention Algorithms

#### 4.1. Innovation of Attention in the TCCT Algorithm Model

#### 4.1.1. CSPAttention

#### 4.1.2. CSPAttention Model Applications

#### 4.2. Autoformer

#### 4.2.1. Auto-Correlation Algorithm

#### 4.2.2. Time Delay Aggregation

#### 4.2.3. Autocorrelation Algorithm Note Innovation Points

#### 4.3. FEDformer

#### 4.3.1. Discrete Fourier Transform

#### 4.3.2. Frequency Enhanced Block of Fourier Transform

#### 4.3.3. Fourier Transform Frequency Enhancement Attention

#### 4.3.4. Discrete Wavelet Transform

#### 4.3.5. Frequency Enhancement Block of Wavelet Transform

#### 4.4. Pyraformer

#### 4.4.1. Traditional Attention Model and Patch Attention Structure

**Lemma 2.**

**Proposition 1.**

**Proposition 2.**

#### 4.4.2. Forecasting Module

#### 4.5. Triformer

#### 4.5.1. Linear Patch Attention

#### 4.5.2. Triangular Stacking

## 5. Experimental Evaluation and Discussion

#### 5.1. Experimental Analysis of TCCT-Related Model Data

#### 5.2. Experimental Analysis of Other Algorithmic Model Data

#### 5.3. Comparison of Algorithm Model Complexity

#### 5.4. Algorithm Model Effectiveness Analysis and Discussion

## 6. Conclusions and Prospects

#### 6.1. Conclusions

#### 6.2. Time Series Forecasting Development Prospect Analysis

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Network of a stack of three CSPAttention blocks. Dilated causal convolution and a pass-through mechanism are used. Final output has the same dimensions as the input.

**Figure 6.**A single Informer encoder stacks three self-attention blocks that work in concert with all TCCT model architectures.

**Figure 12.**(

**a**) Traditional matrix naive learning method; (

**b**) variable-specific projection matrix light-weight learning method.

**Figure 14.**Comparison of classical self-attention block and CSPAttention block. (

**a**) a classic multi-head self-attention architecture. (

**b**) a CSPAttention block.

**Figure 20.**Wavelet frequency-enhanced block decomposition stage, wavelet frequency-enhanced cross-notice decomposition stage, and wavelet block reconstruction stage.

**Figure 24.**Comparison of MSE results between TCCT algorithm model and informer algorithm model for univariate as well as multivariate long series time series forecasting with different prediction length models. (

**a**) Univariate long sequence time series forecasting results on ETTh1. (

**b**) Univariate long sequence time series forecasting results on ETTm1. (

**c**) Multivariate long sequence time series forecasting results on ETTh1. (

**d**) Multivariate long sequence time series forecasting results on ETTm1.

**Figure 25.**Prediction performance (MSE) of each algorithm model on ETTh1 as well as the ETTM1 data set.

**Table 1.**Univariate long series time series prediction results of the TCCT correlation model for ETTh1 and ETTm1.

Metric | Length | Informer | Informer+ | TCCT_I | TCCT_II | TCCT_III | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||

ETTh1 | 48 | 0.1821 | 0.3611 | 0.1552 | 0.3220 | 0.1761 | 0.3453 | 0.1589 | 0.3261 | 0.1245 | 0.2910 |

96 | 0.2173 | 0.3952 | 0.1811 | 0.3635 | 0.2027 | 0.3805 | 0.1979 | 0.3738 | 0.1862 | 0.3569 | |

192 | 0.2618 | 0.4309 | 0.2402 | 0.4183 | 0.2416 | 0.4165 | 0.2121 | 0.3895 | 0.1995 | 0.3730 | |

384 | 0.2719 | 0.4513 | 0.2611 | 0.4499 | 0.2652 | 0.4367 | 0.2240 | 0.3935 | 0.2154 | 0.3813 | |

ETTm1 | 48 | 0.1121 | 0.2819 | 0.0603 | 0.1805 | 0.1022 | 0.2712 | 0.0751 | 0.2378 | 0.0612 | 0.1849 |

96 | 0.1557 | 0.3381 | 0.1265 | 0.2951 | 0.1454 | 0.3108 | 0.1362 | 0.3080 | 0.1245 | 0.2899 | |

192 | 0.2636 | 0.4324 | 0.2257 | 0.3961 | 0.2495 | 0.4151 | 0.2560 | 0.4122 | 0.2186 | 0.3923 | |

384 | 0.3762 | 0.5590 | 0.3543 | 0.5189 | 0.3811 | 0.5396 | 0.3659 | 0.5430 | 0.3502 | 0.5216 |

**Table 2.**Multivariate long series time series prediction results of the TCCT correlation model for ETTh1 and ETTm1.

Metric | Length | Informer | Informer+ | TCCT_I | TCCT_II | TCCT_III | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||

ETTh1 | 48 | 1.1309 | 0.8549 | 0.9483 | 0.7157 | 0.9737 | 0.7839 | 0.9694 | 0.7724 | 0.8877 | 0.7537 |

96 | 1.2433 | 0.9132 | 1.0575 | 0.8184 | 1.0761 | 0.8477 | 1.0578 | 0.8142 | 1.0199 | 0.8069 | |

192 | 1.3011 | 0.9324 | 1.1477 | 0.8566 | 1.2101 | 0.8745 | 1.1785 | 0.8715 | 1.1104 | 0.8458 | |

384 | 1.3313 | 0.9340 | 1.2665 | 0.8810 | 1.2284 | 0.8825 | 1.1913 | 0.8520 | 1.1527 | 0.8356 | |

ETTm1 | 48 | 0.5282 | 0.5170 | 0.4890 | 0.4887 | 0.5172 | 0.4941 | 0.5036 | 0.4732 | 0.4464 | 0.4354 |

96 | 0.6596 | 0.5915 | 0.5867 | 0.5646 | 0.6101 | 0.5649 | 0.5811 | 0.5440 | 0.5772 | 0.5424 | |

192 | 0.7687 | 0.6699 | 0.6683 | 0.5992 | 0.6854 | 0.6153 | 0.6510 | 0.5947 | 0.6375 | 0.5823 | |

384 | 0.7996 | 0.6754 | 0.7650 | 0.6463 | 0.7812 | 0.6744 | 0.7460 | 0.6222 | 0.7415 | 0.6250 |

Metric | Length | Informer | Autoformer | FEDformer | Pyraformer | ||||
---|---|---|---|---|---|---|---|---|---|

MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||

ETTh1 | 96 | 0.941 | 0.769 | 0.435 | 0.446 | 0.376 | 0.415 | 0.664 | 0.612 |

192 | 1.007 | 0.786 | 0.456 | 0.457 | 0.423 | 0.446 | 0.790 | 0.681 | |

336 | 1.038 | 0.784 | 0.486 | 0.487 | 0.444 | 0.462 | 0.891 | 0.738 | |

720 | 1.144 | 0.857 | 0.515 | 0.517 | 0.469 | 0.492 | 0.963 | 0.782 | |

ETTm1 | 96 | 0.355 | 0.462 | 0.205 | 0.293 | 0.180 | 0.271 | 0.435 | 0.507 |

192 | 0.725 | 0.586 | 0.278 | 0.336 | 0.252 | 0.318 | 0.730 | 0.673 | |

336 | 1.270 | 0.871 | 0.343 | 0.379 | 0.324 | 0.364 | 1.201 | 0.845 | |

720 | 3.001 | 1.267 | 0.414 | 0.419 | 0.410 | 0.420 | 3.625 | 1.451 |

Methods | Informer | LogTrans | Reformer | LSTMa | DeepAR | ARIMA | Prophet | |
---|---|---|---|---|---|---|---|---|

Metric | MSE MAE | MSE MAE | MSE MAE | MSE MAE | MSE MAE | MSE MAE | MSE MAE | |

ETTh1 | 24 | 0.098 0.247 | 0.103 0.259 | 0.222 0.389 | 0.114 0.272 | 0.107 0.280 | 0.108 0.284 | 0.115 0.275 |

48 | 0.158 0.319 | 0.167 0.328 | 0.284 0.445 | 0.193 0.358 | 0.162 0.327 | 0.175 0.424 | 0.168 0.330 | |

168 | 0.183 0.346 | 0.207 0.375 | 1.522 1.191 | 0.236 0.392 | 0.239 0.422 | 0.396 0.504 | 1.224 0.763 | |

336 | 0.222 0.387 | 0.230 0.398 | 1.860 1.124 | 0.590 0.698 | 0.445 0.552 | 0.468 0.593 | 1.549 1.820 | |

720 | 0.269 0.435 | 0.273 0.463 | 2.112 1.436 | 0.683 0.768 | 0.658 0.707 | 0.659 0.766 | 2.735 3.253 | |

ETTh2 | 24 | 0.093 0.240 | 0.102 0.255 | 0.263 0.437 | 0.155 0.307 | 0.098 0.263 | 3.554 0.445 | 0.199 0.381 |

48 | 0.155 0.314 | 0.169 0.348 | 0.458 0.545 | 0.190 0.348 | 0.163 0.341 | 3.190 0.474 | 0.304 0.462 | |

168 | 0.232 0.389 | 0.246 0.422 | 1.029 0.879 | 0.385 0.514 | 0.255 0.414 | 2.800 0.595 | 2.145 1.068 | |

336 | 0.263 0.417 | 0.267 0.437 | 1.668 1.228 | 0.558 0.606 | 0.604 0.607 | 2.753 0.738 | 2.096 2.543 | |

720 | 0.277 0.431 | 0.303 0.493 | 2.030 1.721 | 0.640 0.681 | 0.429 0.580 | 2.878 1.044 | 3.355 4.664 | |

ETTm1 | 24 | 0.030 0.137 | 0.065 0.202 | 0.095 0.228 | 0.121 0.233 | 0.091 0.243 | 0.090 0.206 | 0.120 0.290 |

48 | 0069 0203 | 0.078 0.220 | 0.249 0390 | 0.305 0411 | 0.219 0362 | 0179 0.306 | 0.133 0.305 | |

96 | 0.194 0.372 | 0.199 0.386 | 0.920 0.767 | 0.287 0.420 | 0.364 0.496 | 0.272 0.399 | 0.194 0.396 | |

288 | 0.401 0.554 | 0.411 0.572 | 1.108 1.245 | 0.524 0.584 | 0.948 0.795 | 0.462 0.558 | 0.452 0.574 | |

672 | 0.512 0.644 | 0.598 0.702 | 1.793 1.528 | 1.064 0.873 | 2.437 1.352 | 0.639 0.697 | 2.747 1.174 |

**Table 5.**Comparison of the complexity of popular time series algorithm models with different attention modules.

Methods | Training | Testing | |
---|---|---|---|

Time | Memory | Steps | |

Informer | $\mathrm{O}(L/\mathrm{log}L)$ | $\mathrm{O}(L/\mathrm{log}L)$ | 1 |

TCCT | $\mathrm{O}(L/\mathrm{log}L)$ | $\mathrm{O}(L/\mathrm{log}L)$ | 1 |

Autoformer | $\mathrm{O}(L/\mathrm{log}L)$ | $\mathrm{O}(L/\mathrm{log}L)$ | 1 |

FEDformer | $\mathrm{O}(L)$ | $\mathrm{O}(L)$ | 1 |

Pyraformer | $\mathrm{O}(L)$ | $\mathrm{O}(L)$ | 1 |

Triformer | $\mathrm{O}(L)$ | $\mathrm{O}(L)$ | 1 |

**Table 6.**Inference speed of different models on the platform. PyTorch(PT), and TensorFlow (TF) on Intel CPU, Nvidia GPU.

Methods | Intel CPU | Nvidia GPU | |
---|---|---|---|

PyTorch | LSTM | 103.6 | 80.6 |

Informer | 73.8 | 68.2 | |

TCCT | 65.4 | 61.5 | |

Autoformer | 62.1 | 59.8 | |

FEDformer | 44.9 | 41.2 | |

Pyraformer | 46.2 | 42.7 | |

Triformer | 51.4 | 50.3 | |

TensorFlow | LSTM | 301.4 | 304.7 |

Informer | 221.8 | 225.3 | |

TCCT | 196.3 | 181.2 | |

Autoformer | 191.7 | 197.5 | |

FEDformer | 121.9 | 116.9 | |

Pyraformer | 119.3 | 106.5 | |

Triformer | 132.5 | 122.1 |

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**MDPI and ACS Style**

Zhu, Q.; Han, J.; Chai, K.; Zhao, C.
Time Series Analysis Based on Informer Algorithms: A Survey. *Symmetry* **2023**, *15*, 951.
https://doi.org/10.3390/sym15040951

**AMA Style**

Zhu Q, Han J, Chai K, Zhao C.
Time Series Analysis Based on Informer Algorithms: A Survey. *Symmetry*. 2023; 15(4):951.
https://doi.org/10.3390/sym15040951

**Chicago/Turabian Style**

Zhu, Qingbo, Jialin Han, Kai Chai, and Cunsheng Zhao.
2023. "Time Series Analysis Based on Informer Algorithms: A Survey" *Symmetry* 15, no. 4: 951.
https://doi.org/10.3390/sym15040951