Autocorrelation / Autocovariance (Time Series)

Synopsis

This operators evaluates a function (autocorrelation, partial autocorrelation, autocovariance) on the selected time series attributes.

Description

The parameter function defines which method is applied on the time series data. For each selected time series, the function is evaluated and provided at the evaluated function outputport.

The autocorrelation function calculates the similarity (correlation) of the values of a time series with its own lagged values, normed on the autocorrelation of the time series to itself. The series is lagged step by step and the correlation between the original and the shifted series is calculated. This is done up to a max lag value.

The partial autocorrelation function also calculates the correlation of a time series with its own lagged values, but regressed by the values of the time series at all shorter lags. It can be used to identify the extend of the lag in an autoregressive model (e.g. to determine the parameter p of an ARIMA model).

The autocovariance calculates the covariance of a time series with itself. In contrast to the autocorrelation function it is not normed.

This operator works only on numerical time series.

Input

  • example set (IOObject)

    The ExampleSet which contains the time series data as attributes.

Output

  • evaluated function (IOObject)

    ExampleSet containing the values of the evaluated function for each lag up to the maximum lag.

  • original (IOObject)

    The ExampleSet that was given as input is passed through without changes.

Parameters

  • attribute_filter_type

    This parameter allows you to select the filter for the time series attributes selection filter; the method you want to select the attributes which holds the time series values. Only numeric attributes can be selected as time series attributes. The different filter types are:

    • all: This option selects all attributes of the ExampleSet to be time series attributes. This is the default option.
    • single: This option allows the selection of a single time series attribute. The required attribute is selected by the attribute parameter.
    • subset: This option allows the selection of multiple time series attributes through a list (see parameter attributes). If the meta data of the ExampleSet is known all attributes are present in the list and the required ones can easily be selected.
    • regular_expression: This option allows you to specify a regular expression for the time series attribute selection. The regular expression filter is configured by the parameters regular expression, use except expression and except expression.
    • value_type: This option allows selection of all the attributes of a particular type to be time series attributes. It should be noted that types are hierarchical. For example real and integer types both belong to the numeric type. The value type filter is configured by the parameters value type, use value type exception, except value type.
    • block_type: This option allows the selection of all the attributes of a particular block type to be time series attributes. It should be noted that block types may be hierarchical. For example value_series_start and value_series_end block types both belong to the value_series block type. The block type filter is configured by the parameters block type, use block type exception, except block type.
    • no_missing_values: This option selects all attributes of the ExampleSet as time series attributes which do not contain a missing value in any example. Attributes that have even a single missing value are not selected.
    • numeric_value_filter: All numeric attributes whose examples all match a given numeric condition are selected as time series attributes. The condition is specified by the numeric condition parameter.
    Range:
  • attribute

    The required attribute can be selected from this option. The attribute name can be selected from the drop down box of the parameter if the meta data is known.

    Range:
  • attributes

    The required attributes can be selected from this option. This opens a new window with two lists. All attributes are present in the left list. They can be shifted to the right list, which is the list of selected time series attributes.

    Range:
  • regular_expression

    Attributes whose names match this expression will be selected. The expression can be specified through the edit and preview regular expression menu. This menu gives a good idea of regular expressions and it also allows you to try different expressions and preview the results simultaneously.

    Range:
  • use_except_expression

    If enabled, an exception to the first regular expression can be specified. This exception is specified by the except regular expression parameter.

    Range:
  • except_regular_expression

    This option allows you to specify a regular expression. Attributes matching this expression will be filtered out even if they match the first expression (expression that was specified in regular expression parameter).

    Range:
  • value_type

    This option allows to select a type of attribute. One of the following types can be chosen: numeric, integer, real.

    Range:
  • use_value_type_exception

    If enabled, an exception to the selected type can be specified. This exception is specified by the except value type parameter.

    Range:
  • except_value_type

    The attributes matching this type will be removed from the final output even if they matched the before selected type, specified by the value type parameter. One of the following types can be selected here: numeric, integer, real.

    Range:
  • block_type

    This option allows to select a block type of attribute. One of the following types can be chosen: value_series, value_series_start, value_series_end.

    Range:
  • use_block_type_exception

    If enabled, an exception to the selected block type can be specified. This exception is specified by the except block type parameter.

    Range:
  • except_block_type

    The attributes matching this block type will be removed from the final output even if they matched the before selected type by the block type parameter. One of the following block types can be selected here: value_series, value_series_start, value_series_end.

    Range:
  • numeric_condition

    The numeric condition used by the numeric condition filter type. A numeric attribute is selected if all examples match the specified condition for this attribute. For example the numeric condition '> 6' will keep all numeric attributes having a value of greater than 6 in every example. A combination of conditions is possible: '> 6 && < 11' or '<= 5 || < 0'. But && and || cannot be used together in one numeric condition. Conditions like '(> 0 && < 2) || (>10 && < 12)' are not allowed because they use both && and ||.

    Range:
  • invert_selection

    If this parameter is set to true the selection is reversed. In that case all attributes not matching the specified condition are selected as time series attributes. Special attributes are not selected independent of the invert selection parameter as along as the include special attributes parameter is not set to true. If so the condition is also applied to the special attributes and the selection is reversed if this parameter is checked.

    Range:
  • include_special_attributes

    Special attributes are attributes with special roles. These are: id, label, prediction, cluster, weight and batch. Also custom roles can be assigned to attributes. By default special attributes are not selected as time series attributes irrespective of the filter conditions. If this parameter is set to true, special attributes are also tested against conditions specified and those attributes are selected that match the conditions.

    Range:
  • function

    This parameter defines the function used to evaluate the selected time series attributes.

    • autocorrelation function: Autocorrelation function
    • partial autocorrelation function: Partial Autocorrelation function
    • autocovariance: Autocovariance
    Range:
  • maximum_lag

    This parameter specifies the maximum length by which the time series is shifted. The maximum possible value is the length of the original time series.

    Range:

Tutorial Processes

Autocorrelation on Monthly Milk Production

This process generates the autocorrelation values of the monthly milk production data set. As it can be seen there are strong correlations for the yearly seasonality and multiples of twelve.