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Original source:Tuo End number according to the tribe public number

 

Unlike macroeconomic data, financial markets tend to use high-frequency data, such as stock return sequences. Intuitively speaking, the latter is a sequence with more “fluctuations” and random fluctuations than the former. In the case of unary or multivariate, it is the best choice to build Copula function model and GARCH model.

In the multivariate GARCH family, there are many kinds, so we need to deduce and understand more by ourselves and choose the optimal model. This paper uses R software to model the weekly return rate of three listed companies in the past decade.

First we can plot these three time series.

The multivariable Arma-Garch model is used here.

In this paper, we consider the multivariable GARCH process of the residuals of two model 1 ARMA models

2. Multivariate Model of Arma-GARCH Process Residual (based on Copula)

1 ARMA – GARCH model

> fit1 = garchFit (formula = ~arma (2,1) + garch (1,1), data = dat [,1], cond.dist = "STD")Copy the code

Visual fluctuation

Implicit correlation

> emwa_series_cor = function (I = 1, j = 2) {if (min (I, j) == 1) & (Max (I, j) == 2)) {if (Max (I, j) == 2); B = 5; AB = 2} +}Copy the code

2 BEKK (1,1) model:

BEKK11 (dat_arma)

Implicit correlation

 

Residual modeling of univariate GARCH model

The first step might be to consider a static (joint) distribution of residuals. The marginal univariate distribution is zero

And the combined density is zero

Visual density

  

See if the correlation stabilizes over time.

  

Spearman correlation

Kendall correlation

For correlation modeling, consider the DCC model

  

Make predictions about the data

> FCST = DCCforecast (dcc.fit, n.ahead = 200)Copy the code

 

 

Now that we have fully mastered the use of the multivariate GARCH model, we are free to use R for time series!

 

Most welcome insight

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