Lm09 Fisher inverse transform inversion mesh strategy

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Hello everyone , Heterogeneity in current period CTA（ Alternative communities ） The community continues to bring a series of grid strategies .

There were a lot of materials in the last issue （ grid ） The study of , Released LM08 Grid reversal strategy of grid series . In this issue, we continue to publish the grid strategy content of the previous research grid , In this issue, we have abandoned the grid logic of price , Instead, try to use the logic of periodic fluctuation index . What do you mean by that ？ As shown in the figure below ：

The content of this strategy comes from the heterogeneous community “ Quantitative research on heterogeneous communities ” One of the contents . As we can see from the picture above , The index algorithm is a kind of oscillation index similar to mean regression （ Later, try to use it for arbitrage and so on ）, And RSI and KD The logic of moving average and price difference is completely different .

One 、 Strategic logic

The strategy logic consists of three parts ：

1、 Take the derivative of the data to whiten the spectrum .

2、 Limit the amplitude swing of the derivative , Glass volatility from time composition

3、 Integrate the limited waveform , Smoothing filter , Act as an integrator . Then the integral recreates the data waveform , As a zero mean with smoothing index .

Did you listen a little confused ？ Today I will tell you something about academic , A official account in Sichuan Province is always full of strange things , Dislike that we have too much dry goods , Too little academic .

Spectral albinism （Spectral Whitening） It is a common method of seismic exploration data processing , It can broaden the spectrum of the signal and improve the signal resolution , It's a kind of “ Pure amplitude ” Filtering process .

The above sentence is ： Noise reduction 、 wave filtering

  So why do you do this ？ From the perspective of machine learning , The purpose of whitening is to remove the redundant information of input data . Suppose the training data is an image , Due to the strong correlation between adjacent pixels in the image , So the input is redundant for training ; The purpose of whitening is to reduce the redundancy of input .

  Input data set X, After whitening , The new data X' It satisfies two properties ：

(1) The correlation between features is low ;
(2) All features have the same variance .

We all know PCA For dimensionality reduction . Actually PCA You can also find eigenvectors , And then the data X Map to the new feature space , Such a mapping process , In fact, it satisfies the first property of our albinism ： Remove correlation between features . Therefore, the implementation process of whitening algorithm , The first step is PCA, Find... In the new feature space X The new coordinates of , Then, the variance of the new coordinates is normalized .

The mathematical derivation is as follows ：

For example, for any matrix X, Find the covariance , The resulting covariance matrix cov(X) Not necessarily a unit matrix （ Diagonal matrix ）;（ Be careful ： Covariance matrix is a symmetric matrix , But not necessarily a diagonal matrix ）

Matrix whitening is to find a transformation matrix P, bring Y=PX The covariance matrix of cov(Y) It's a unit array （ Diagonal matrix ）. Because after whitening the matrix , Covariance is a diagonal matrix ( Unit matrix ), So it represents the matrix Y Each vector of ( Whether a vector is a column vector or a row vector depends on the covariance cov(X)=XXT still XTX To judge ) There is no correlation between them . Or say , The purpose of matrix whitening is to make the variance of the transformed matrix vector the same after transformation （ Because it's a unit matrix ） So how do I find this transformation matrix P Well ？

For matrices X, Its covariance matrix cov(X)=XXT

Not necessarily a diagonal matrix , But for the real symmetric covariance matrix, there can be the following eigenvalue decomposition ： See 【 Eigenvalue decomposition 】

cov(X)=QΛQT

Among them Λ

Is a diagonal matrix composed of eigenvalues ,Q Is the corresponding eigenvector , It's an orthogonal matrix . Now we have to find the linear transformation matrix P, bring Y=PX

The covariance matrix of can be a unit matrix , namely

cov(Y)=YYT=PX(PX)T=PXXTPT=Pcov(X)PT=E（ Unit matrix ）

Now make P=Λ−1/2QT（ The open root of a matrix is the open root of each element ）, So there are

cov(Y) =Pcov(x)PT

   =Λ−1/2QTQΛQT(Λ−1/2QT)T

=Λ−1/2QTQΛQTQΛ−1/2

=Λ−1/2ΛΛ−1/2=E

（ because Q It's an orthogonal matrix , namely QQT=E）

So when P=Λ−1/2QT when , You can make Y=PX The covariance matrix of is the unit matrix ( Diagonal matrix ).

therefore , After whitening , matrix Y Each vector of ( Column vector or row vector is determined according to the above ) There is no correlation between them .

In the third step , We're talking about integrating restricted waveforms … Then the integral recreates the data waveform ,ZCA Albinism is in PCA On the basis of albinism , Another operation for processing . The specific implementation is to put the above PCA The result of albinism , And then change to the coordinates under the original coordinate system ：

The code is as follows ：

In this strategy , We have stop loss protection for bulls , It is found that in this mean reversion oscillation algorithm test , You can't add stop loss to a certain extent , Otherwise, no one can do it .

The logic is as follows ：

Two 、 visualization

T_long

CJ_short

SR_long

Nr_short

In fact, the main usage is in the oscillation algorithm of Fisher inverse transform we have built , Look for reverse signal points similar to mean regression .

Specifically, the algorithm , I already shared it in the heterogeneous community last month , You can read the original text or my translated articles in detail .

3、 ... and 、 The performance of

5 Combinations of varieties

I eliminated   Soybean meal 、 Rubber and other varieties due to historical market reasons , for example ： The rubber fell 10 year , Natural bears are definitely better . Bulls in general . Choose the varieties that are always in the concussion type .

T

In fact, the most satisfactory thing is the performance and results of national debt , This piece has been rolled 2 In addition to the samples of treasury bonds in the second half of the year , It still conforms to the valid range of the parameter . Previously, we used the logic of trend or band to find the strategy of treasury bonds , There have been no research results . This time it was a compensation .

Due to the differences of various platforms , Back test performance to TBQ The version shall prevail

This strategy is only used for learning and communication , The investor is personally responsible for the profit and loss of the firm offer .