IRIS Toolbox Reference Manual

## cumsumk

Cumulative sum with a k-period leap

#### Syntax

    Y = cumsumk(X,K,Rho,Range)
    Y = cumsumk(X,K,Rho)
    Y = cumsumk(X,K)
    Y = cumsumk(X)

#### Input arguments

- `X` [ tseries ] - Input data.

- `K` [ numeric ] - Number of periods that will be leapt the cumulative sum will be taken; if not specified, `K` is chosen to match the frequency of the input data (e.g. `K = -4` for quarterly data), or `K = -1` for indeterminate frequency.

- `Rho` [ numeric ] - Autoregressive coefficient; if not specified, `Rho = 1`.

- `Range` [ numeric ] - Range on which the cumulative sum will be computed and the output series returned.

#### Output arguments

- `Y` [ tseries ] - Output data constructed as described below.

#### Options

- `'log='` [ `true` | `false` ] - Logarithmise the input data before, and de-logarithmise the output data back after, running `x12`.

#### Description

If `K < 0`, the first `K` observations in the output series `Y` are copied from `X`, and the new observations are given recursively by

    Y{t} = Rho*Y{t-K} + X{t}.

If `K > 0`, the last `K` observations in the output series `Y` are copied from `X`, and the new observations are given recursively by

    Y{t} = Rho*Y{t+K} + X{t},

going backwards in time.

If `K == 0`, the input data are returned.

#### Example

Construct random data with seasonal pattern, and run X12 to seasonally adjust these series.

    x = tseries(qq(1990,1):qq(2020,4),@randn);
    x1 = cumsumk(x,-4,1);
    x2 = cumsumk(x,-4,0.7);
    x1sa = x12(x1);
    x2sa = x12(x2);

The new series `x1` will be a unit-root process while `x2` will be stationary. Note that the command on the second line could be replaced with `x1 = cumsumk(x)`.

IRIS Toolbox. Copyright © 2007—2013 Jaromir Benes.