Description Usage Arguments Details Value Author(s) References See Also Examples

Performs Variance-Time Analysis for a Spike Train (or any univariate time series) assuming a Poisson Process with the same Rate as the Spike Train.

1 2 3 4 5 | ```
varianceTime(spikeTrain, CI = c(0.95, 0.99), windowSizes)
is.varianceTime(obj)
## S3 method for class 'varianceTime'
plot(x, style = c("default", "Ogata"),
unit = "s", xlab, ylab, main, sub, xlim, ylim, ...)
``` |

`spikeTrain` |
a |

`obj` |
a object to test against a |

`x` |
a |

`CI` |
a numeric vector with at most two elements. The coverage probability of the confidence intervals. |

`windowSizes` |
a numeric increasing vector of positive numbers. The window sizes used to split the spike train. |

`style` |
a character. The style of the plot, |

`unit` |
a character. The unit in which the spike times are expressed. |

`xlab` |
a character. The x label. |

`ylab` |
a character. The y label. |

`main` |
a character. The title. |

`sub` |
a character. The subtitle. |

`xlim` |
a numeric. See |

`ylim` |
a numeric. See |

`...` |
see |

See Fig. 5 of Ogata (1988) for details. The confidence intervals are obtained with a Normal approximation of the Poisson distribution.

`varianceTime`

returns a list of class `varianceTime`

with the following elements:

`s2` |
numeric vector of empirical variance. |

`sigma2` |
numeric vector of expected variance under the Poisson hypothesis. |

`ciUp` |
a numeric vector or a 2 rows matrix with the upper limits of the confidence interval(s). |

`ciLow` |
a numeric vector or a 2 rows matrix with the lower limits of the confidence interval(s). |

`windowSizes` |
numeric vector of window sizes actually used. |

`CI` |
a numeric vector, the coverage probabilities of the confidence intervals. |

`call` |
the matched call |

`plot.varianceTime`

is used for its side effect: a graph is
produced.

`is.varianceTime`

returns `TRUE`

if its argument is a
`varianceTime`

object and `FALSE`

otherwise.

Christophe Pouzat christophe.pouzat@gmail.com and Chong Gu chong@stat.purdue.edu for a correction on the sampling variance of the variance of a normal distribution.

Ogata, Yosihiko (1988) Statistical Models for Earthquake Occurrences and Residual
Analysis for Point Processes. *Journal of the American
Statistical Association* **83**: 9-27.

`acf.spikeTrain`

,
`renewalTestPlot`

1 2 3 4 5 | ```
## Replicate (almost) Fig. 5 of Ogata 1988
data(ShallowShocks)
vtShallow <- varianceTime(ShallowShocks$Date,,c(5,10,20,40,60,80,seq(100,500,by = 25))*10)
is.varianceTime(vtShallow)
plot(vtShallow, style="Ogata")
``` |

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