# calc_theo_sercor: Calculate theoretical serial correlation at a given lag from... In PaulMTeggin/practechniques: Functions for the Practical Actuarial Techniques online book

 calc_theo_sercor R Documentation

## Calculate theoretical serial correlation at a given lag from overlapped data

### Description

Serial correlation arises from overlapped data because some of the information is 'shared' between successive overlapping observations. The amount of serial correlation is a function of the lag between observations and the extent of the overlap. For example the serial correlation between Jan-Dec and Feb-Jan observations is higher than between Jan-Dec and Sep-Aug-next-year observations.

### Usage

``````calc_theo_sercor(noverlap, lag)
``````

### Arguments

 `noverlap` The extent of the overlap, e.g. 12 means annual overlaps from monthly data. 1 means no overlap. `lag` The lag in time between two overlapped observations. The serial correlation at lags equal to or higher than `noverlap` is zero.

### Details

The formula follows from writing each overlapping observation as the sum of `noverlap` independent observations and counting the extent to which these two sets overlap. Where the lag is higher than the overlap no information is shared and the theoretical serial correlation becomes zero.

### Value

The theoretical serial correlation.

Other Overlapping data functions: `build_theo_sercor_mtx()`
``````calc_theo_sercor(12, 0:12)