Commonly used algorithms in timing analysis are all here

Time series analysis is to use the characteristics of an event in the past period to predict the characteristics of the event in the future period. This is a relatively complex predictive modeling problem that is different from the predictions of regression analysis models. The time series model depends on the order in which events occur. Values ​​of the same size will produce different results if the order is changed.

See all timing issues It is a regression problem, but there are certain differences in the regression methods (linear regression, tree model, deep learning, etc.).

Timing analysis includes static timing analysis (STA) and dynamic timing analysis.

The following are several common timing analysis algorithms

1 Deep learning timing analysis

RNN (Recurrent Neural Network)

Recurrent neural network refers to a structure that occurs repeatedly over time. It has a very wide range of applications in natural language processing (NLP), speech images and other fields. The biggest difference between RNN networks and other networks is that RNN can achieve a certain "memory function" and is the best choice for time series analysis. Just like human beings can better understand the world through their own past memories. RNN also implements a mechanism similar to that of the human brain, retaining a certain amount of memory for the processed information, unlike other types of neural networks that cannot retain memory for the processed information.

Advantages:

This method can memorize time and is suitable for solving problems with short intervals in the time series

Disadvantages:

Long-term step data is prone to gradient disappearance and gradient explosion problems

LSTM (Long Short-Term Memory Network)

LSTM (Long Short-Term Memory Network) Memory Network (Long Short-Term Memory) is a temporal recurrent neural network designed to solve the long-term dependency problem existing in conventional recurrent neural networks (RNN). All RNNs are composed of a series of repeated neural network modules

Strengths:

Suitable for processing and predicting important events with very long intervals and delays in time series.

Disadvantages:

Too many model parameters will lead to overfitting problems

2 Traditional time series analysis model

• Auto Regression (AR)
• Moving Average (MA)
• Autoregressive Moving Average (ARMA)
• Autoregressive Integrated Moving Average (ARIMA)
• Seasonal Autoregressive Integrated Moving Average (SARIMA)
• Seasonal Autoregressive Integrated Moving Average with exogenous regressor (Seasonal Autoregressive Integrated Moving-Average with Exogenous Regressors, SARIMAX)

Autoregressive Model AR

Autoregressive Model (AR model for short) is a time series analysis method. Used to describe the relationship between a time series variable and its past values. The AR model assumes a linear relationship between current observations and past observations, and uses past observations to predict future observations.

Strengths:

• Simplicity: The AR model is a linear model that is easy to understand and implement. It only uses past observations as independent variables, with no other complex factors to consider.
• Modeling capabilities: AR models can capture the autocorrelation structure of time series data, that is, the relationship between current observations and past observations. It provides predictions of future observations and reveals trends and patterns in the data.

shortcoming:

• Only applicable to stationary series: The AR model requires that the time series is stationary, that is, the mean, variance and autocorrelation do not change with time. If the series is non-stationary, you may need to perform differentiating operations or use other models to handle the non-stationarity.
• Sensitive to past observations: The prediction results of the AR model are affected by past observations, so the problem of error accumulation may occur when dealing with long-term predictions. A larger order may lead to model overfitting, while a smaller order may not capture the complex dynamics of the time series.
• Unable to handle seasonal data: The AR model cannot directly handle time series with obvious seasonality. For data with seasonal patterns, seasonal AR models (SAR) or ARIMA models can be used for modeling.

Moving Average Method (MA)

Moving Average Method (MA): This method is based on the average of the data and assumes that future values ​​are consistent with There is a certain stability between past values

Strengths:

Be able to capture the moving average relationship in time series data. The MA model utilizes a linear combination of white noise error terms from past time steps to predict current observations and therefore captures the moving average nature in the data.

Relatively simple and intuitive. The parameters of the MA model represent the weights of the white noise error terms at past time steps, and the model can be fitted by estimating these weights.

Disadvantages:

• can only capture the moving average relationship, but cannot capture the autoregressive relationship. The MA model ignores past time step observations and may not capture autocorrelation in the data.
• For some time series data, the MA model may require a higher order to fit the data well, resulting in increased model complexity.

Autoregressive Moving Average Model

Autoregressive Moving Average Model (ARMA model, Auto-Regression and Moving AverageModel) is an important method for studying time series. It is "mixed" based on the autoregressive model (AR model) and the moving average model (MA model). It has the characteristics of wide application range and small prediction error.

Autoregressive Integrated Moving Average (ARIMA)

The ARIMA model is the abbreviation of the autoregressive difference moving average model, and the full name is Autoregressive Integrated Moving Average Model. This model mainly consists of three parts, namely the autoregressive model (AR), the difference process (I) and the moving average model (MA)

The basic idea of ​​the ARIMA model is to use data Use its own historical information to predict the future. The tag value at a point in time is affected by both the tag value in the past period and accidental events in the past period. In other words, the ARIMA model assumes that the tag value fluctuates around the general trend of time. , where the trend is affected by historical labels, fluctuations are affected by accidental events within a period of time, and the general trend itself is not necessarily stable

ARIMA model is a The time series analysis method extracts the time series patterns hidden in the data by modeling the autocorrelation and difference of the data, and then predicts the future data

• AR part Used to process the autoregressive part of a time series, which takes into account the impact of observations from past periods on the current value.
• Part I is used to make the non-stationary time series stationary. Through first-order or second-order difference processing, the trend and seasonal factors in the time series are eliminated.
• The MA part is used to process the moving average part of the time series, which takes into account the impact of past prediction errors on the current value.

Combining these three parts, the ARIMA model can not only capture the trend changes of the data, but also handle data with temporary, sudden changes or large noise. Therefore, the ARIMA model performs well in many time series forecasting problems.

Strengths:

The construction of the model is very simple, only using endogenous variables without resorting to other exogenous variables. The so-called endogenous variables refer to variables that only depend on the data itself, unlike regression models that require the support of other variables

Disadvantages:

The requirement for time series data is stability , or become stable after differential processing

In essence, it can only capture linear relationships, but not non-linear relationships.

Seasonal Autoregressive Integrated Moving Average Model SARIMA

SARIMA is a commonly used time series analysis method, which is an extension of the ARIMA model on seasonal data. SARIMA models can be used to predict seasonal time series data, such as annual sales or weekly website visits. The following are the advantages and disadvantages of the SARIMA model:

Strengths:

• The SARIMA model can handle seasonal data well because it takes into account the time series data seasonal factors.
• The SARIMA model can make long-term forecasts on time series data because it can capture trends and cyclical changes in the data.
• The SARIMA model can be used for multi-variable time series data because it can consider the relationship between multiple variables at the same time.

Disadvantages:

• The SARIMA model requires a large amount of historical data to train, so it may not be suitable when the amount of data is small.
• The SARIMA model is sensitive to outliers, so outliers need to be processed.
• The SARIMA model has a high computational complexity and requires a lot of calculations and optimization.

Seasonal Autoregressive Integrated Moving Average Model SARIMAX with Exogenous Regressor

Seasonal Autoregressive Integrated Moving Average Model (SARIMAX) is a model in the difference A model based on the moving autoregressive model (ARIMA) plus exogenous regressors. It is suitable for time series data with obvious periodic and seasonal characteristics

3 Other time series models

This type of method is represented by lightgbm and xgboost. Generally, Time series problems are converted into supervised learning and predicted through feature engineering and machine learning methods; this model can solve the vast majority of complex time series prediction models. Supports complex data modeling, multi-variable collaborative regression, and nonlinear problems.

The importance of feature engineering is self-evident, and it plays a key role in the success of machine learning. However, feature engineering is not a simple task and requires complex manual processing and unique expertise. The level of feature engineering often determines the upper limit of machine learning, and the machine learning algorithm is just as close to this upper limit as possible. Once the feature engineering is completed, we can directly apply the tree model algorithms - lightgbm and xgboost. These two models are very common and efficient modeling methods. In addition, they also have the following characteristics:

• Fast calculation speed and high model accuracy;
• Missing values ​​are not required Processing is more convenient;
• supports category variables;
• supports feature crossover.

#The specific method to choose needs to be comprehensively considered based on the nature of the data, the characteristics of the problem, and your own experience and abilities.

You need to choose an appropriate time series forecasting method based on specific data characteristics, problem requirements and your own capabilities. Sometimes, combining multiple methods can improve the accuracy and stability of predictions. At the same time, in order to better select models and evaluate prediction results, it is also important to perform visual analysis of data and model diagnosis.

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