# Directional Accuracy Test

### Description

Implements the Directional Accuracy Test of Pesaran and Timmerman and Excess Profitability Test of Anatolyev and Gerko.

### Usage

1 |

### Arguments

`forecast` |
A numeric vector of the forecasted values. |

`actual` |
A numeric vector of the actual (realized) values. |

`test` |
Choice of Pesaran and Timmermann (‘PT’) or Anatolyev and Gerko (‘AG’) tests. |

`conf.level` |
The confidence level at which the Null Hypothesis is evaluated. |

### Details

See the references for details on the tests. The Null is effectively that of independence, and distributed as N(0,1).

### Value

A list with the following items:

`Test` |
The type of test performed. |

`Stat` |
The test statistic. |

`p-value` |
The p-value of the test statistic. |

`H0` |
The Null Hypothesis. |

`Decision` |
Whether to reject or not the Null given the conf.level. |

`DirAcc` |
The directional accuracy of the forecast. |

### Author(s)

Alexios Ghalanos

### References

Anatolyev, S. and Gerko, A. 2005, A trading approach to testing for
predictability, *Journal of Business and Economic Statistics*, **23(4)**,
455–461.

Pesaran, M.H. and Timmermann, A. 1992, A simple nonparametric test of predictive
performance, *Journal of Business and Economic Statistics*,
**10(4)**, 461–465.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## Not run:
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(6,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "nig")
fit = ugarchfit(spec, data = dji30ret[, 1, drop = FALSE], out.sample = 1000)
pred = ugarchforecast(fit, n.ahead = 1, n.roll = 999)
# Get Realized (Oberved) Data
obsx = tail(dji30ret[,1], 1000)
forc = as.numeric(as.data.frame(pred,rollframe="all",align=FALSE,which="series"))
print(DACTest(forc, obsx, test = "PT", conf.level = 0.95))
print(DACTest(forc, obsx, test = "AG", conf.level = 0.95))
## End(Not run)
``` |