Do time series, stochastic processes, and so on count as statistics?

There are similarities in mathematical foundations and some methods.

First, the nature is different.

1. Time series: It is a series of numbers that arrange the values of the same statistical indicator in the order of the time in which they occur.

2. Stochastic process: It is the whole of a family of random variables that depend on parameters, and the parameters are usually time.

Second, the role is different.

1. Time series: it can reflect the development and change process of social and economic phenomena, and describe the development status and results of phenomena; It is possible to study the development trend and speed of socio-economic phenomena; It is possible to explore the law of development and change of phenomena and carry out research on certain social and economic phenomena; Time series can be used for comparative analysis between different regions or countries, which is also one of the important methods of statistical analysis.

2. Stochastic process: The theory of stochastic process was born in the early part of this century, and was gradually developed in response to the needs of physics, biology, and management science. At present, it has a wide range of applications in automatic control, public utilities, management science, etc.

If a random time series has zero mean homoscedasticity and there is no series correlation, the series is said to be a white noise or white noise process, i.e., a purely random process.

Stationary time series, if the series values do not have any correlation with each other, it means that the series is a series without memory, and the past behavior has no effect on future development, this kind of series is called a pure random series, and from the perspective of statistical analysis, such a series is a series without any analytical value.

Purely random time series definition:

A sequence that satisfies the following two properties is a purely random sequence: any t belongs to t, there is ext any t and s belongs to t, and there is (t, s) when t s is equal to ping; When t≠s is equal to 0.

Properties: Pure randomness and homogeneity of variance.

The internal time series analysis method is different from the stochastic process theory, the former is to establish a mathematical model of the measured data, and then further analyze the statistical characteristics of the stochastic data. The latter is based on the prior probability knowledge obtained from the measured data.

It is determined by the time to which the pat cherry tree data belongs and the value of the statistical index in time.

1..A time series (or dynamic series) is a series of numbers that arrange the values of the same statistical indicator in chronological order. The main purpose of time series analysis is to make a future based on existing historical data**.

Most of the economic data is given in the form of time series. Depending on the time of observation, the time in a time series can be a year, a quarter, a month, or any other form of time.

2.A time series is a set of random variables ordered over time, usually the result of observations of a potential process at a given sampling rate over a period of time at equal intervals between the hungry acres. Time series data essentially reflects the changing trend of one or some random variables over time, and the core of the time series method is to mine this pattern from the data and use it to estimate future data.

Random sequences, like continuous random signals, can be described by probability distribution functions and probability densities and numerical features.

Probability distribution function.

For the random variable xn

The one-dimensional probability distribution function is represented by the following formula.

Fundamentals of Geophysical Information Processing.

The antithesis is denoted as a two-dimensional probability distribution function.

Fundamentals of Geophysical Information Processing.

Probability density. If the random variable xn

Take a continuous value, then the one-dimensional probability density function is .

Fundamentals of Geophysical Information Processing.

The two-dimensional probability density function is.

Fundamentals of Geophysical Information Processing.

Probability density or probability distribution functions provide a complete description of a random sequence, but it is often not possible to obtain it in practice. To this end, it is necessary to introduce the numerical features of the random sequence cavity to describe them, and these numerical features are relatively easy to measure and calculate in practice. In general, these numerical characteristics are sufficient to meet the requirements.

Commonly used numerical features are mathematical expectations, variance, and correlation functions.