TimeSeriesAnalysis[TimeSeries]  object representing time series data

Calling Sequence


TimeSeries(data, opts)
TS[rows]
TS[rows, columns]


Parameters


data



list, Vector, or Matrix of numbers, or another TimeSeries object

opts



(optional) equations of the form , described below

TS



TimeSeries object, constructed using e.g. the first calling sequence

rows



range of the form start .. end, where start and end are either integers or strings

columns



integer, string, or range of integers or strings, or list of these





Options


•

headers = string or list of strings or a positive integer


Names for the data sets. If a single string is given and there is more than one data set, then the names for the data sets are obtained by appending the numbers , , and so on, to that string. A name or list of names can be given instead of a string or list of strings. If a positive integer is given, the data argument must be a list of lists or a Matrix; the integer is taken to be a row number. In this case, the contents of that row form the names of the data sets, and that row and all rows above it are discarded. If no headers are given and data is a TimeSeries object, the headers are copied from data. If no headers are given and data is not a TimeSeries object, the string "data set" is used.


This option may be specified as header (singular), rather than headers (plural)  there is no difference between the two.

•

dates = list or Vector of strings or numbers, or a single positive integer


This option specifies the time points corresponding to the data. If you specify strings, they will be parsed as described below, at the format option. If you specify a list or Vector of numbers, they will be interpreted as "seconds since the epoch"  that is, number of seconds elapsed since midnight, January 1st, 1970. If you specify a single positive integer (not as a list or Vector), it will be taken to mean that the th column of the data argument contains the date information. In this case, data must be a Matrix or a list of lists.


Maple cannot deal with dates before December 14, 1901, or dates after January 17, 2038.


The dates option cannot be combined with any of the frequency, startdate, and enddate options.

•

frequency = a positive integer or one of the keywords annual, yearly, quarterly, monthly, weekly, daily, and hourly (as name or string)


These three options give a few alternative methods of specifying the time points corresponding to the data. If using these options, you can use at most two of the three options. The options cannot be combined with the dates option.


If the frequency option is given as a positive integer, it represents a time interval of that number of seconds. The keywords represent the time intervals that they take their name from; annual and yearly mean exactly the same.


The startdate and enddate options are parsed as explained below, at the format option.


If the startdate and enddate options are given, then the interval between the two time points is divided into intervals (where is the number of rows in data) that are as close as possible to evenly sized, and every boundary between intervals as well as the start and end dates are taken as time points. If startdate and frequency options are given, then the time points start at the given start date and continue with the given frequency. If the enddate and frequency options are given, the time points end at the given end date and are counted backwards in time according to the frequency options.


If only the startdate or only the enddate option is given, then frequency is by default set to annual, except if a higher frequency is needed to make all dates fall within the range between December 14, 1901 and January 14, 2038. If only the frequency is given, then enddate is set to one year before the current date.


If frequency is specified as annual or yearly or quarterly or monthly, then the increments are not fixed numbers of seconds; they take leap years and the varying lengths of months into account.

•

format = string or the names deduce or default, or a list of any of these values


All dates specified are parsed by the command StringTools[ParseTime]. The format option determines the format string used for that command. This applies to dates specified with the dates, startdate, and enddate options.


If a single string is specified, then it is the format string used for parsing.


If the name default is given, Maple uses the value stored by the Finance package with , which is by default "%B %e, %Y", matching strings such as "January 1, 2000".


If the name deduce is given, Maple tries the same sequence of formats as the command Finance[ParseDate].


If a list is given, then first any occurrence of default and deduce are replaced by the format or sequence of formats that they represent, and then each format in the resulting list is tried in turn.

•

If dates are not specified through any options and data is a TimeSeries object, then the dates are copied from data. Otherwise, it is as if frequency was specified as annual and enddate was specified as one year before the current date, with the format "%Y"  that is, only the year is printed.

•

period = positive integer


If there is potentially a seasonal aspect to the time series, you can specify the length of the season with this parameter. It is expressed as the number of data points that constitute one period. For example, monthly data will often have annual seasonality; that would correspond to the option period = 12. For nonseasonal data, period = 1 is used.


If the period option is not specified, then its default value depends on the frequency option. It is given by the following table:

frequency

default for period

not specified

1

annual, yearly

1

quarterly

4

monthly

12

weekly

1

daily

7

hourly

24





Description


•

The TimeSeries command creates a time series object, for use with the TimeSeriesAnalysis package. A TimeSeries object contains one or more sets of data, measured at one set of time points.

•

In the computations of the TimeSeriesAnalysis package, time intervals are all treated as equal  that is, if you specify time points that are irregularly spaced, this information is used only for purposes such as supplying appropriate tickmarks on the axes for graphs.

•

The TimeSeries methods help page describes the commands that can be used to interrogate TimeSeries objects.



Indexing


•

If you construct a time series object TS, you can index it as TS[rows] or TS[rows, columns] to get a new time series object representing a subset of the data.

•

Selecting rows is done using a range of the form start .. end, where start indicates the first row to be selected and end indicates the last.

–

If start or end is a positive integer, it indicates the number of the row, counting the earliest row of data as and counting up for later rows ().

–

If start or end is a negative integer, it indicates the number of the row, counting the last row of data as and counting down for earlier rows ().

–

If start or end is a string, Maple interprets it as a date in the format selected for this time series. The range then includes all data points later than or equal to the given time (for start), or before or equal to the given time (for end).

•

Selecting columns can be done with a string, an integer, a range of strings or integers, or a list of strings, integers, or ranges.

–

A positive integer selects the given column number, counting from left to right.

–

A negative integer selects the given column number, counting as the rightmost column and counting down as you move left.

–

A string selects the column with the given header ("name"). The string has to be an exact match. If there are multiple columns with the same header (which is inadvisable), the first column with this header is selected.

–

A range selects all columns from the left hand side to the right hand side of the range, inclusive.

–

A list selects all columns included in the list.

•

To select some columns but not restrict the rows, you can use . Specifying for the rows selects all rows.



Compatibility


•

The TimeSeriesAnalysis[TimeSeries] command was introduced in Maple 18.



Examples


>


A simple time series object.
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 (1) 
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 (2) 
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 (3) 
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 (4) 
The same data, but now specifying the header and the times.
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 (5) 
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 (6) 
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 (7) 
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 (8) 
A time series with three data sets.
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 (9) 
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 (10) 
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 (11) 
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 (12) 
Let's show this time series as a plot.
>


We can select the data for region 1 and 3 only.
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 (13) 
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We select the rows corresponding to March and April of region two.
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 (14) 
Taking a quality measurement every minute, for one day.
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 (15) 
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 (16) 
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 (17) 
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 (18) 
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 (19) 
We can select the quality measurements starting at 6pm and exclude the last ten measurements.
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 (20) 
Hourly data is by default considered potentially seasonal with a period of one day.
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 (21) 
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 (22) 
If we want to override that because we expect it might be better modeled by assuming seasonality with a period of 12 hours, such as is approximately the case for tidal information, we can override this parameter.
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 (23) 
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 (24) 
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