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This article introduces the relevant knowledge of "how to achieve ADF inspection in python". In the operation of actual cases, many people will encounter such a dilemma, so let the editor lead you to learn how to deal with these situations. I hope you can read it carefully and be able to achieve something!

ADF test

In the use of many time series models, such as ARMA, ARIMA, time series will be required to be stationary, so generally in the study of a period of time series, the first step needs to be stationarity test, in addition to the naked eye detection method, another more commonly used strict statistical test method is the ADF test, also known as the unit root test.

The full name of ADF test is Augmented Dickey-Fuller test. As the name implies, ADF is an extended form of Dickey-Fuller test. The DF test can only be used in the first-order case, and the ADF test can be used when the sequence has high-order lag correlation, so ADF is an extension of the DF test.

Unit root (unit root)

When doing the ADF test, that is, the unit root test, we need to understand a concept first, that is, the object to be tested-the unit root.

When in an autoregressive process: y _ {t} = by_ {t color 1} + a +\ epsilon _ {t}, if the lag coefficient b is 1, it is called the unit root. When the unit root exists, the relationship between the independent variable and the dependent variable is deceptive, because any error of the residual sequence will not attenuate with the increase of the sample size (that is, the number of periods), that is, the influence of the residual in the model is permanent. This kind of return is also called pseudo-return. If the unit root exists, the process is a random walk.

The principle of ADF Test

ADF test is to determine whether there is a unit root in a sequence: if the sequence is stable, there is no unit root; otherwise, there will be a unit root.

Therefore, the H0 hypothesis of the ADF test is that there is a unit root. If the significance test statistics obtained are less than three confidence levels (10%, 5%, 1%), then reject the original hypothesis with a grasp of the due (90%, 95, 99%).

Python implementation of ADF Test

ADF verification can be done through the statsmodels module in python, which provides many statistical models.

The method of use is as follows:

Import adfuller function

From statsmodels.tsa.stattools import adfuller

The parameter meanings of the adfuller function are:

1. X: one-dimensional data sequence.

2. Maxlag: maximum number of lags.

3. Regression: inclusion term in regression (c: only constant term, default; ct: constant term and trend term; ctt: constant term, linear quadratic term; nc: no constant term and trend term)

4. Autolag: automatically select the number of lags (AIC: Chichi information criterion, default; BIC: Bayesian information criterion; t-stat: based on maxlag, start from maxlag and delete a lag until the last lag length is significantly less than 5% based on t-statistic; None: use the lag specified by maxlag)

5. Store:True False, default.

6. The complete regression result of regresults:True will be returned. False, default.

The meaning of the return value is:

1. Adf:Test statistic,T test, hypothesis test value.

2. Pvalue: the result of hypothesis test.

3. Usedlag: the degree of lag used.

4. Nobs: the number of observations used for ADF regression and calculating critical values.

5. Icbest: returns the maximum information criterion value if autolag is not None.

6. Resstore: merge the results into a single dummy.

Def adfuller (x, maxlag=None, regression= "c", autolag='AIC'

Store=False, regresults=False):

"

Augmented Dickey-Fuller unit root test

The Augmented Dickey-Fuller test can be used to test for a unit root in a

Univariate process in the presence of serial correlation.

Parameters

-

X: array_like, 1d

Data series

Maxlag: int

Maximum lag which is included in test, default 12 * (nobs/100) ^ {1DB 4}

Regression: {'cendry, thecontrol, ctbrush, cttony, and cc'}

Constant and trend order to include in regression

*'c': constant only (default)

* 'ct': constant and trend

* 'ctt': constant, and linear and quadratic trend

* 'nc': no constant, no trend

Autolag: {'AIC',' BIC', 'tmurf statuses, None}

* if None, then maxlag lags are used

* if 'AIC' (default) or' BIC', then the number of lags is chosen

To minimize the corresponding information criterion

* 'tMustat 'based choice of maxlag. Starts with maxlag and drops a

Lag until the t-statistic on the last lag length is significant

Using a 5%-sized test

Store: bool

If True, then a result instance is returned additionally to

The adf statistic. Default is False

Regresults: bool, optional

If True, the full regression results are returned. Default is False

Returns

-

Adf: float

Test statistic

Pvalue: float

MacKinnon's approximate p-value based on MacKinnon (1994, 2010)

Usedlag: int

Number of lags used

Nobs: int

Number of observations used for the ADF regression and calculation of

The critical values

Critical values: dict

Critical values for the test statistic at the 1%, 5%, and 10%

Levels. Based on MacKinnon (2010)

Icbest: float

The maximized information criterion if autolag is not None.

Resstore: ResultStore, optional

A dummy class with results attached as attributes

"

Now let's do the ADF test with the closing data of a RB1309 and take a look at the results:

Result = adfuller (rb_price)

Print (result)

(- 0.45153867687808574, 0.9011315454402649, 1,198, {'5% floor:-2.876250632135043,'1% floor:-3.463815171313286316,'10% floor:-2.574611347821651}, 1172.4579344852016)

We can see that the value of t-statistic-0.451 is greater than the significance level of 10%, so the original hypothesis cannot be rejected. In addition, the value of p-value is also very large.

Put the data into a first-order difference lag and see what the result is:

Rb_price = np.diff (rb_price)

Result = adfuller (rb_price)

Print (result)

(- 15.436034211511204, 2.90628134201655e-28, 0198, {'5% stories:-2.876250632135043,'1% stories:-3.4638151713286316,'10% stories:-2.574611347821651}, 1165.1556545612445)

It is seen that the value of-15 of t-statistic is less than 5%, so the original hypothesis is rejected. In addition, the value of p-value is also very small, so the data after the first-order difference is stable.

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