# FracDiff: Fast Fractional Differencing In FCVAR: Estimation and Inference for the Fractionally Cointegrated VAR

 FracDiff R Documentation

## Fast Fractional Differencing

### Description

`FracDiff` is a fractional differencing procedure based on the fast fractional difference algorithm of Jensen & Nielsen (2014).

### Usage

```FracDiff(x, d)
```

### Arguments

 `x` A matrix of variables to be included in the system. `d` The order of fractional differencing.

### Value

A vector or matrix `dx` equal to (1-L)^d x of the same dimensions as x.

### Note

This function differs from the `diffseries` function in the `fracdiff` package, in that the `diffseries` function demeans the series first. In particular, the difference between the out put of the function calls `FCVAR::FracDiff(x - mean(x), d = 0.5)` and `fracdiff::diffseries(x, d = 0.5)` is numerically small.

### References

Jensen, A. N. and M. Ø. Nielsen (2014). "A fast fractional difference algorithm," Journal of Time Series Analysis 35, 428-436.

`FCVARoptions` to set default estimation options. `FCVARestn` calls `GetParams`, which calls `TransformData` to estimate the FCVAR model. `TransformData` in turn calls `FracDiff` and `Lbk` to perform the transformation.

Other FCVAR auxiliary functions: `FCVARforecast()`, `FCVARlikeGrid()`, `FCVARsimBS()`, `FCVARsim()`, `plot.FCVAR_grid()`

### Examples

```set.seed(42)
WN <- matrix(stats::rnorm(200), nrow = 100, ncol = 2)
MVWNtest_stats <- MVWNtest(x = WN, maxlag = 10, printResults = 1)
x <- FracDiff(x = WN, d = - 0.5)
MVWNtest_stats <- MVWNtest(x = x, maxlag = 10, printResults = 1)
WN_x_d <- FracDiff(x, d = 0.5)
MVWNtest_stats <- MVWNtest(x = WN_x_d, maxlag = 10, printResults = 1)
```

FCVAR documentation built on May 5, 2022, 9:06 a.m.