Package 'IndexConstruction'

Title: Index Construction for Time Series Data
Description: Derivation of indexes for benchmarking purposes. A methodology with flexible number of constituents is implemented. Also functions for market capitalization and volume weighted indexes with fixed number of constituents are available. The main function of the package, indexComp(), provides the derived index, suitable for analysis purposes. The functions indexUpdate(), indexMemberSelection() and indexMembersUpdate() are components of indexComp() and enable one to construct and continuously update an index, e.g. for display on a website. The methodology behind the functions provided gets introduced in Trimborn and Haerdle (2018) <doi:10.1016/j.jempfin.2018.08.004>.
Authors: Simon Trimborn <[email protected]>
Maintainer: Simon Trimborn <[email protected]>
License: GPL (>= 3)
Version: 0.1-3
Built: 2024-11-15 04:51:36 UTC
Source: https://github.com/cran/IndexConstruction

Help Index

Index derivation for price and liquidity indices

Description

indexComp derives an Index from the given price and market capitalization or liquidity data. The number of constituents can be fixed or being chosen flexible based on the methodology from Trimborn and Haerdle (2018). This is the main function of the package. The derived index is meant for analysis purposes. For a continuous updating and display of an index on a website, please refer to the remaining functions.

Usage

indexComp(market, price, vol = NULL, weighting = "market", weighting.all = "market", 
ic = "AIC", eval.seq = c("sequential", "all.together"), 
optimum = c("local", "global"), start.const = 1, steps = 1, fixed.value = NULL, 
base.value = 1000, derivation.period = 1, derivation.period.ic = 3, days.line)

Arguments

market

An xts object with the market capitalization data. The default is NULL, an entry is necessary if weighting is set to "market".

price

An xts object with the price data. An entry is always required.

vol

An xts object with the trading volume (liquidity) data. The default is NULL, an entry is necessary if weighting is set to "volume".

weighting

The weighting scheme to be applied. "market" refers to weighting by market capitalization, "volume" refers to weighting by trading volume.

weighting.all

The weighting scheme to be applied to the full market index. "market" refers to weighting by market capitalization, "volume" refers to weighting by trading volume.
ic

Information Criterion to be used for the evaluation of the appropriate index to be used. Possible entries are "AIC", "GCV", "GFCV", "SH", "Cp" and "FPE".

eval.seq

Indicates how the evaluation of the candidate indices by the ic shall be performed. "all.together" evaluates all indices against each other, "sequential" evaluates always two consecutive indices against each other.

optimum

Define how to choose the optimal index. Either a "local" optimum is chosen, thus the derivation stops the first time the results become worse under the chosen ic, or a "global" optimum is chosen, thus all indices are derived and the best fitting one under the ic is chosen.

start.const

The number of constituents to start constructing the indices with. The default is 1.

steps

The step width for the number of constituents to construct the next index from. The default is 1.

fixed.value

In case no ic for the number of constituents for the index shall be applied, give the number of constituents the index shall contain. In that case, "ic", "eval.seq", "optimum", "start.const" and "steps" are inactive parameters. The default is NULL.

base.value

The starting value for the index. The default is 1000.

derivation.period

The number of month after which the weights of the index are reallocated. The default is 1.

derivation.period.ic

The number of month after which the composition of the index is derived again, thus the number of constituents is reevaluated. The default is 3.

days.line

The days of the month to perform the recalculation on. Can be calculated from switchDates.

Details

For more details, please see the methodology section of the paper Trimborn and Haerdle (2018).

Value

An object of the class IndexConstruction with the components

results

A list containing the results of the model fitting

  • index The optimal index

  • totalIndex The index of all constituents

  • totalIndexRebased The index of all constituents rebased at the index each time after altering the number of index constituents which is useful for comparisons with the market

  • assets A list containing the assets considered for index construction in each period

  • weights A list containing the weights assigned to the selected index constituents in each period

  • weightsRelative A list containing the relative weights assigned to the selected index constituents in each period

inputs

A list containing the inputs for model fitting

  • marketCap The provided dataset of the market capitalization of each asset for index construction

  • price The provided dataset of the price series of each asset for index construction

  • tradingVolume The provided dataset of the trading volume of each asset for index construction

  • daysDerivation The provided vector of dates on which to rederive the index weights and number of index constituents

weighting

The selected weighting scheme
weighting.all

The selected weighting.all scheme
ic

The selected ic
eval.seq

The selected eval.seq scheme
optimum

The selected optimization scheme
start.const

The selected number of starting constituents for the index
steps

The selected step size for the selection of the constituents for the index
derivation.period

The selected period for rederivation of the weights of the index constituents
derivation.period.ic

The selected period for rederivation of the number of index constituents

References

Trimborn, S. and Haerdle, W.K. (2018). CRIX an Index for cryptocurrencies, Journal of Empirical Finance 49, pp. 107-122. https://doi.org/10.1016/j.jempfin.2018.08.004

Examples

data(CryptoData)

price = price["2014-03-31::2015-01-31"]
market = market["2014-03-31::2015-01-31"]
vol = vol["2014-03-31::2015-01-31"]
days.line = switchDates(price, specificDate = "1")

indexComp(market = market, price = price, vol = vol, weighting = "market", 
weighting.all = "market", ic = "AIC", eval.seq = "sequential", optimum = "local", 
start.const = 5, steps = 5, days.line = days.line)

Number of Index Members Derivation

Description

indexMemberSelection derives the number of index members for the coming period based on an Information Criterion, e.g. AIC. The methodology is according to Trimborn and Haerdle (2018). The method derives the new weights according to the specifications of the weight reevaluation. The function expects the data period provided to be twice the number of months specified in derivation.period.ic. In case of a mismatch, a warning is given. This function is meant for continuous updating and display of an index on a website. For the derivation of an index for analysis purposes, please refer to the function "indexComp".

Usage

indexMemberSelection(market, price, vol, weighting = "market", 
weighting.all = "market", ic = "AIC", eval.seq = c("sequential", "all.together"), 
optimum = c("local", "global"), start.const = 1, steps = 1, fixed.value = NULL, 
derivation.period = 1, derivation.period.ic = 3, base.value = 1000, days.line)

Arguments

market

An xts object with the market capitalization data. The default is NULL, an entry is necessary if weighting is set to "market".

price

An xts object with the price data. An entry is always required.

vol

An xts object with the trading volume (liquidity) data. The default is NULL, an entry is necessary if weighting is set to "volume".

weighting

The weighting scheme to be applied. "market" refers to weighting by market capitalization, "volume" refers to weighting by trading volume.

weighting.all

The weighting scheme to be applied to the full market index. "market" refers to weighting by market capitalization, "volume" refers to weighting by trading volume.
ic

Information Criterion to be used for the evaluation of the appropriate index to be used. Possible entries are "AIC", "GCV", "GFCV", "SH", "Cp" and "FPE".

eval.seq

Indicates how the evaluation of the candidate indices by the ic shall be performed. "all.together" evaluates all indices against each other, "sequential" evaluates always two consecutive indices against each other.

optimum

Define how to choose the optimal index. Either a "local" optimum is chosen, thus the derivation stops the first time the results become worse under the chosen ic, or a "global" optimum is chosen, thus all indices are derived and the best fitting one under the ic is chosen.

start.const

The number of constituents to start constructing the indices with. The default is 1.

steps

The step width for the number of constituents to construct the next index from. The default is 1.

fixed.value

In case no ic for the number of constituents for the index shall be applied, give the number of constituents the index shall contain. In that case, "ic", "eval.seq", "optimum", "start.const" and "steps" are inactive parameters. The default is NULL.

base.value

The starting value for the index. The default is 1000.

derivation.period

The number of month after which the weights of the index are reallocated. The default is 1.

derivation.period.ic

The number of month after which the composition of the index is derived again, thus the number of constituents is reevaluated. The default is 3.

days.line

The days of the month to perform the recalculation on. Can be calculated from SwitchDates.

Details

indexMemberSelection derives the number of index members for the coming period based on an Information Criterion, e.g. AIC. The methodology is according to Trimborn and Haerdle (2018). The method derives the new weights according to the specifications of the weight reevaluation. The function expects the data period provided to be twice the number of months specified in derivation.period.ic. In case of a mismatch, a warning is given. The data from the first period are used to derived the likelihood, the second period is used for out-of-sample derivation of the number of constituents. Hence for a 3 month reevaluation period, 6 month of data are required by this function. For more details, please see the methodology section of the paper Trimborn and Haerdle (2018).

Value

Returns the number of index members for application in the next period.

References

Trimborn, S. and Haerdle, W.K. (2018). CRIX an Index for cryptocurrencies, Journal of Empirical Finance 49, pp. 107-122. https://doi.org/10.1016/j.jempfin.2018.08.004

Examples

data(CryptoData)

price = price["2016-07-31::2017-01-31"]
market = market["2016-07-31::2017-01-31"]
vol = vol["2016-07-31::2017-01-31"]
days.line = switchDates(price, specificDate = "1")

indexMemberSelection(market = market, price = price, vol = vol, 
weighting = "market", weighting.all = "market", ic = "AIC", eval.seq = "sequential", 
optimum = "local", start.const = 5, steps = 5, days.line = days.line)

Reevaluation of Index constituents weights

Description

indexMembersUpdate derives the new weights for the coming period. The methodology is according to Trimborn and Haerdle (2018). The method derives the new weights over the data period provided. The data input defines the length of the period, hence it can be different from full month. This function is meant for continuous updating and display of an index on a website. For the derivation of an index for analysis purposes, please refer to the function "indexComp".

Usage

indexMembersUpdate(market, price, vol, weighting, index.const, last.value)

Arguments

market

An xts object with the market capitalization data. The default is NULL, an entry is necessary if weighting is set to "market".

price

An xts object with the price data. An entry is always required.

vol

An xts object with the trading volume (liquidity) data. The default is NULL, an entry is necessary if weighting is set to "volume".

weighting

The weighting scheme to be applied. "market" refers to weighting by market capitalization, "volume" refers to weighting by trading volume.

index.const

Number of Index constituents. The number can be derived from indexComp, indexMemberSelection or be chosen by alternative means.
last.value

The last index value before rederivation.

Details

indexMembersUpdate derives the new weights for the coming period. The methodology is according to Trimborn and Haerdle (2018). The method derives the new weights over the data period provided. The data input defines the length of the period, hence it can be different from full month. For more details, please see the methodology section of the paper Trimborn and Haerdle (2018).

Value

A list, entry 1 is the ordered names of index members, entry 2 the respective consideration of the index constituents, entry 3 the weights of the index members which gives multiplied with entry 2 the actual weight and entry 4 the new divisor of the index.

References

Trimborn, S. and Haerdle, W.K. (2018). CRIX an Index for cryptocurrencies, Journal of Empirical Finance 49, pp. 107-122. https://doi.org/10.1016/j.jempfin.2018.08.004

Examples

data(CryptoData)

price = price["2017-01-01::2017-01-31"]
market = market["2017-01-01::2017-01-31"]
vol = vol["2017-01-01::2017-01-31"]
indexMembersUpdate(market = market, price = price, vol = vol, 
weighting = "market", index.const = 5, last.value = 1000)

Updating an existing index with new index values

Description

indexUpdate derives the next values of an Index from the given price, weights and its divisor. This function is meant for continuous updating and display of an index on a website. For the derivation of an index for analysis purposes, please refer to the function "indexComp".

Usage

indexUpdate(price, index.weights, divisor)

Arguments

price

An xts object with the price data. An entry is always required.

index.weights

A vector with the absolute weights expressed as number of shares of each asset. The weights are provided by indexComp. They can be also easily derived from the market capitalization by dividing with the respective price.

divisor

The divisor required for the index derivation. The divisor is provided by indexComp. For details on its derivation, see Trimborn and Haerdle (2018).

Details

For more details, please see the methodology section of the paper Trimborn and Haerdle (2018).

Value

The next value(s) of the Index.

References

Trimborn, S. and Haerdle, W.K. (2018). CRIX an Index for cryptocurrencies, Journal of Empirical Finance 49, pp. 107-122. https://doi.org/10.1016/j.jempfin.2018.08.004

Examples

data(CryptoData)

const.names = c("btc", "eth", "xrp", "ltc", "xmr")
index.weights = c(16136712, 88440036, 36856524148, 49589181, 13859864)
divisor = 17185084

indexUpdate(price["2017-02-01", const.names], index.weights = index.weights, divisor = divisor)

Market capitalization data for Cryptocurrencies.

Description

The dataset contains market capitalization information for cryptocurrencies.

Usage

data(CryptoData)

Format

A dataset with a xts matrix. Load the R library xts for proper visualization of the dataset.

Source

The dataset was provided by CoinGecko. Up-to-date data are accessible via https://www.coingecko.com/api.

Pricing data for Cryptocurrencies.

Description

The dataset contains pricing information for cryptocurrencies.

Usage

data(CryptoData)

Format

A dataset with a xts matrix. Load the R library xts for proper visualization of the dataset.

Source

The dataset was provided by CoinGecko. Up-to-date data are accessible via https://www.coingecko.com/api.

Retrieving the relative weights of the assets in the index

Description

relativeWeights retrieves the relative weights of the assets in the index from the absolute weights expressed in shares of the assets. The latter is a direct output of indexComp.

Usage

relativeWeights(price, index.weights)

Arguments

price

An xts object with the price data. An entry is always required.

index.weights

A vector with the absolute weights expressed as number of shares of each asset. The weights are provided by indexComp. They can be also easily derived from the market capitalization by dividing with the respective price.

Value

The relative weights of the assets in the Index.

References

Trimborn, S. and Haerdle, W.K. (2018). CRIX an Index for cryptocurrencies, Journal of Empirical Finance 49, pp. 107-122. https://doi.org/10.1016/j.jempfin.2018.08.004

Examples

data(CryptoData)

const.names = c("btc", "eth", "xrp", "ltc", "xmr")
index.weights = c(16136712, 88440036, 36856524148, 49589181, 13859864)

relativeWeights(price = price["2017-02-01", const.names], index.weights = index.weights)

Deriving the dates on which the index constituents are going to be reevaluated

Description

switchDates derives the dates on which the index constituents are going to be reevaluated.

Usage

switchDates(price, specificDate = NULL, WeekDay = NULL, Appearance = 1)

Arguments

price

An xts object with the price data. An entry is always required.

specificDate

A specific date of each month on which the index members get reevaluated. A common date would be the 1st of each month or the 15th of each month. specificDate is dominating WeekDay.

WeekDay

Only active when specificDate is NULL. A specific weekday of each month on which the index members get reevaluated. The input has to be a character describing the weekday in English. By default the first weekday with this appearancce is returned. The argument Appearance defines if it is the 1st, 2nd or another appearance of this weekday. E.g. the 3rd Friday of each month can be returned.

Appearance

Defines if the 1st, 2nd or another appearance of a weekday gets returned. E.g. the 3rd Friday of each month can be returned. Only active when specificDate is NULL. The argument works in combination with WeekDay.

Value

A vector of class date with the respective dates on which the index members become reevaluated. This is a necessary input to IndexComp.

References

Trimborn, S. and Haerdle, W.K. (2018). CRIX an Index for cryptocurrencies, Journal of Empirical Finance 49, pp. 107-122. https://doi.org/10.1016/j.jempfin.2018.08.004

Examples

data(CryptoData)

switchDates(price, specificDate = "1")

Volume data for Cryptocurrencies.

Description

The dataset contains trading volume information for cryptocurrencies.

Usage

data(CryptoData)

Format

A dataset with a xts matrix. Load the R library xts for proper visualization of the dataset.

Source

The dataset was provided by CoinGecko. Up-to-date data are accessible via https://www.coingecko.com/api.