Displays time series statistics useful for ARIMA model selection (G. Tunnicliffe Wilson & S.J. Welham).

### Options

`PRINT` = string token |
Controls printed output (`description` ); default `desc` |
---|---|

`GRAPHICS` = string token |
What type of graphics to use (`lineprinter` , `highresolution` ); default `high` |

`WINDOWS` = scalar or variate |
Windows to be used for the plots: a scalar `N` indicates that plots are to be produced on separate pages in window `N` (as currently defined), whereas a variate specifies four separate windows to be redefined (within the procedure) for plotting four graphs on one page; default 1 |

`PENS` = variate |
The three pens to be used (after being defined appropriately) for drawing the plots; default `!(1,2,3)` |

### Parameters

`SERIES` = variates |
Variates holding the time series for which the statistics are to be produced |
---|---|

`LENGTH` = scalars or variates |
Specifies the units to be used from each series: a scalar `N` indicates that the first `N` units of the series are to be used, a variate of length 2 gives the index of the first and last units of the subseries to be used; by default the whole series is used |

### Description

`BJIDENTIFY`

displays time series statistics useful for ARIMA model selection. For a time series, specified (in a variate) using the `SERIES`

parameter, four graphs are produced. These are of the series itself, its sample autocorrelation function and partial autocorrelation function, and its sample spectrum (or periodogram). The `LENGTH`

parameter can specify that only part of the series is to be used: setting `LENGTH`

to a scalar `N`

indicates that the first `N`

values are to be used; alternatively, a variate of length 2 can be specified holding the positions of the first and last units of the subseries. The maximum lag of the autocorrelations and the frequency grid for the periodogram are determined automatically by the procedure.

Printed output can be suppressed by setting the option `PRINT=*`

; by default, `PRINT=description`

, which gives a description of the series.

Graphical output is controlled by the options `GRAPHICS`

, `WINDOWS`

and `PENS`

. Option `GRAPHICS`

controls whether plots are produced for line-printer output or on the current high-resolution graphics device; by default high-resolution plots are given. Option `WINDOWS`

controls the way in which the high-resolution plots are arranged. If `WINDOWS`

is set to a scalar `N`

, all the graphs are produced in window `N`

on separate pages; the `FRAME`

directive can then be used to set the attributes of window `N`

before calling the procedure. Alternatively, `WINDOWS`

can be set to a variate of length four; the attributes of the four windows specified are then redefined within the procedure so that four graphs are produced on the same page. By default `WINDOWS=1`

. The `PENS`

option controls which pens are to be used for the plots; the attributes of these pens are modified within the procedure. By default pens 1-3 are used, but these can be changed by setting option `PENS`

to a variate of length 3 containing the numbers of the three different pens required.

Options: `PRINT`

, `GRAPHICS`

, `WINDOWS`

, `PENS`

.

Parameters: `SERIES`

, `LENGTH`

.

### Method

The autocorrelation and partial autocorrelation functions are calculated using the `CORRELATE`

directive. The maximum lag is chosen to be half the length of the series, but adjusted for very short or very long series. The number of periodogram ordinates is chosen to be approximately four times the length of the series. Before calculation of the periodogram, using the `FOURIER`

directive, the series is mean corrected and missing values are replaced by zero.

### Action with `RESTRICT`

Input structures must not be restricted. Restriction of the input `SERIES`

to a contiguous set of units can be achieved using the `LENGTH`

parameter.

### See also

Procedures: `BJESTIMATE`

, `BJFORECAST`

.

Commands for: Time series.

### Example

CAPTION 'BJIDENTIFY example',!t(\ 'Data from Andrews & Herzberg (1985), Data, A Collection',\ 'of Problems from Many Fields for the Student and Research',\ 'Worker, Springer-Verlag, pp. 369-370.'); STYLE=meta,plain VARIATE [VALUES=8.075,7.819,7.366,8.113,7.380,7.134,7.222,7.768,\ 7.386,6.965,6.478,8.105,8.060,7.684,7.580,7.093,\ 6.129,6.026,6.679,7.414,7.112,7.762,7.645,8.639,\ 7.667,8.080,6.678,6.739,5.569,5.049,5.642,6.808,\ 6.636,8.241,7.968,8.044,7.791,7.024,6.102,6.053,\ 5.941,5.386,5.811,6.716,6.923,6.939,6.705,6.914] Profit CALCULATE QdProfit = DIFFERENCE(Profit;4) PRINT Profit,QdProfit; DECIMALS=3 " Use BJIDENTIFY on complete series Profit and its 4th differences QdProfit." VARIATE [VALUES=1...4] Windows BJIDENTIFY [WINDOWS=Windows] Profit,QdProfit " Now look only at units 10-40 of the series Profit." BJIDENTIFY [WINDOWS=Windows] Profit; LENGTH=!(10,40)