Data analysis of time series (I): main components

A time series is a group arranged in the order of time , And a sequence of data points containing some information , The development trend of data is usually included in time series data ( Up 、 Down 、 keep ) And the changing law of data ( Seasonality ) Other characteristics . These characteristics often have certain regularity and predictability , Specifically, time series data has the following characteristics ：

1. Trend ： A variable changes over time or an independent variable , It presents a relatively slow and long-term continuous rise 、 falling 、 Keep the same trend , But the range of change may not be equal .
2. Seasonality ： Due to external influences, such as the law of peaks and valleys with the alternation of natural seasons .
3. Randomness ： Individual moments show random changes , The whole is in a statistical law .

In some application scenarios, it is necessary to predict time series data , For example, in retail , E-commerce and other industries need the sales amount for a period of time in the future , passenger flow , Forecast the order quantity , Accurate prediction results can provide decision-making reference for the leadership of enterprises , And help to improve the human efficiency of the enterprise , Bring more profits to the enterprise .

One , trend (Trend)

Time series data often contain certain data development trends , For example, the data in the figure below has a very obvious trend :

  Two , Seasonality (Seasonal)

Seasonality in time series data refers to the regularity of periodic changes contained in the data , These cyclical changes are often related to the year , month , quarter , Week and other seasonal time points are closely related . Usually, seasonal factors can be divided into 1. Additive seasonality ,2. Multiplicative seasonality .

2.1 Additive seasonality (Additive)

The so-called additive seasonality means that the amplitude of periodic change of time series data will not change with the development of time , In other words, the magnitude of data changes is not affected by time ( The amplitude remains unchanged ) As shown in the figure below ：

As you can see from the above figure , The data shows a seasonal change law , But the magnitude of this change has not changed with the development of time , That is, time has no effect on seasonal changes .

 2.2 Multiplicative seasonality (Multiplicative)

The so-called multiplicative seasonality means that the amplitude of periodic change of time series data will change with the development of time , In other words, the magnitude and time of data change show a linear relationship, as shown in the figure below ：

  As you can see from the above figure , The data shows a seasonal change law , And the amplitude of this seasonal change changes with the development of time ( Such as getting bigger or smaller ).

3、 ... and , residual (Residual)

Residual refers to the remaining part after the trend and seasonal characteristics are deleted from the time series data , We generally believe that the mean value of the residuals of time series data with seasonal characteristics is 0 The positive distribution of , Residuals are generally considered as white noise signals , We can get the residual by gradually deleting the trend and seasonal characteristics in the time series data ：

  As shown in the above figure, when the trend is deleted from the original data , The remaining ingredient is ： Seasonality + residual , Next we will start from the seasonal + The residual is obtained by deleting seasonal components from the components of the residual .

So let's go through python Third party Library of statsmodes Of seasonal_decompose To decompose time series data ：

from statsmodels.tsa.seasonal import seasonal_decompose

df=pd.read_csv("airline_Passengers.csv")
df.set_index('Period',inplace=True)
df.index = pd.to_datetime(df.index)
data = df["#Passengers"]
seasonal_decomp = seasonal_decompose(data, model="additive")
seasonal_decomp.plot();

summary

The main components of time series data include : trend 、 Seasonality 、 residual . Seasonality is divided into additive seasonality and multiplicative seasonality . have access to statsmodes Bag seasonal_decompose Method to decompose time series .

Reference material

statsmodels.tsa.seasonal.seasonal_decompose — statsmodels