# Time scale conversions for time series

### Description

Convert `tis`

series from one frequency to another using a
variety of algorithms.

### Usage

1 2 |

### Arguments

`x` |
a univariate or multivariate |

`tif` |
a number or a string indicating the desired ti frequency of the
return series. See |

`method` |
method by which the conversion is done: one of "discrete",
"constant", "linear", or "cubic". Note that this argument is
effectively ignored if |

`observed.` |
"observed" attribute of the input series: one of "beginning", "end",
"high", "low", "summed", "annualized", or "averaged". If this argument is not
supplied and observed( |

`basis.` |
"daily" or "business". If this argument is not supplied and
basis( |

`ignore` |
governs how missing (partial period) values at the beginning and/or end of the series are handled. For method == "discrete" or "constant" and ignore == T, input values that cover only part the first and/or last output time intervals will still result in output values for those intervals. This can be problematic, especially for observed == "summed", as it can lead to atypical values for the first and/or last periods of the output series. |

### Details

This function is a close imitation of the way FAME handles time scale conversions. See the chapter on "Time Scale Conversion" in the Users Guide to Fame if the explanation given here is not detailed enough.

Start with some definitions. Combining values of a higher frequency
input series to create a lower frequency output series is known as
`aggregation`

. Doing the opposite is known as `disaggregation`

.

If observed == "high" or "low", the "discrete" method is always used.

Disaggration for "discrete" series: (i) for observed == "beginning" ("end"), the first (last) output period that begins (ends) in a particular input period is assigned the value of that input period. All other output periods that begin (end) in that input period are NA. (ii) for observed == "high", "low", "summed" or "averaged", all output periods that end in a particular input period are assigned the same value. For "summed", that value is the input period value divided by the number of output periods that end in the input period, while for "high", "low" and "averaged" series, the output period values are the same as the corresponding input period values.

Aggregation for "discrete" series: (i) for observed == "beginning" ("end"), the output period is assigned the value of the first (last) input period that begins (ends) in the output period. (ii) for observed == "high" ("low"), the output period is assigned the value of the maximum (minimum) of all the input values for periods that end in the output period. (iii) for observed == "summed" ("averaged"), the output value is the sum (average) of all the input values for periods that end in the output period.

Methods "constant", "linear", and "cubic" all work by constructing a
continuous function F(t) and then reading off the appropriate
point-in-time values if observed == "beginning" or "end", or by
integrating F(t) over the output intervals when observed == "summed",
or by integrating F(t) over the output intervals and dividing by the
lengths of those intervals when observed == "averaged". The unit of
time itself is given by the `basis`

argument.

The form of F(t) is determined by the conversion method. For "constant" conversions, F(t) is a step function with jumps at the boundaries of the input periods. If the first and/or last input periods only partly cover an output period, F is linearly extended to cover the first and last output periods as well. The heights of the steps are set such that F(t) aggregates over the input periods to the original input series.

For "linear" ("cubic") conversions, F(t) is a linear (cubic) spline. The x-coordinates of the spline knots are the beginnings or ends of the input periods if observed == "beginning" or "end", else they are the centers of the input periods. The y-coordinates of the splines are chosen such that aggregating the resulting F(t) over the input periods yields the original input series.

For "constant" conversions, if `ignore`

== F, the first (last)
output period is the first (last) one for which complete input data is
available. For observed == "beginning", for example, this means that
data for the first input period that begins in the first output period
is available, while for observed == "summed", this means that the
first output period is completely contained within the available input
periods. If `ignore`

== T, data for only a single input period
is sufficient to create an output period value. For example, if
converting weekly data to monthly data, and the last observation is
June 14, the output series will end in June if `ignore`

== T, or
May if it is F.

Unlike the "constant" method, the domain of F(t) for "linear" and "cubic" conversions is NOT extended beyond the input periods, even if the ignore option is T. The first (last) output period is therefore the first (last) one that is completely covered by input periods.

Series with observed == "annualized" are handled the same as observed == "averaged".

### Value

a `tis`

time series covering approximately the same time span as
`x`

, but with the frequency specified by `tif`

.

### BUGS

Method "cubic" is not currently implemented for observed "summed", "annualized", and "averaged".

### References

Users Guide to Fame

### See Also

`aggregate`

, `tif`

, `ti`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
wSeries <- tis(1:105, start = ti(19950107, tif = "wsaturday"))
observed(wSeries) <- "ending" ## end of week values
mDiscrete <- convert(wSeries, "monthly", method = "discrete")
mConstant <- convert(wSeries, "monthly", method = "constant")
mLinear <- convert(wSeries, "monthly", method = "linear")
mCubic <- convert(wSeries, "monthly", method = "cubic")
## linear and cubic are identical because wSeries is a pure linear trend
cbind(mDiscrete, mConstant, mLinear, mCubic)
observed(wSeries) <- "averaged" ## weekly averages
mDiscrete <- convert(wSeries, "monthly", method = "discrete")
mConstant <- convert(wSeries, "monthly", method = "constant")
mLinear <- convert(wSeries, "monthly", method = "linear")
cbind(mDiscrete, mConstant, mLinear)
``` |