Package 'highfrequency'

Description

The highfrequency package provides numerous tools for analyzing high-frequency financial data, including functionality to:

• Clean, handle, and manage high frequency trades and quotes data.

• Calculate liquidity measures

• Calculate (multivariate) realized measures of the distribution of high-frequency returns

• Estimate models for realized measures of volatility and the corresponding forecasts

• Detect jumps in prices

• Analyze market microstructure noise in asset prices

• Estimate spot volatility and drift as well as analyze intraday periodicity of spot volatility

Author(s)

Kris Boudt, Jonathan Cornelissen, Onno Kleen, Scott Payseur, Emil Sjoerup Maintainer: Kris Boudt <[email protected]>

Contributors: Giang Nguyen

Thanks: We would like to thank Brian Peterson, Chris Blakely, Dirk Eddelbuettel, Maarten Schermer, and Eric Zivot

See Also

Useful links:

• https://github.com/jonathancornelissen/highfrequency

• Report bugs at https://github.com/jonathancornelissen/highfrequency/issues

Description

Function to aggregate high frequency data by last tick aggregation to an arbitrary periodicity based on wall clocks. Alternatively the aggregation can be done by number of ticks. In case we DON'T do tick-based aggregation, this function accepts arbitrary number of symbols over a arbitrary number of days. Although the function has the word Price in the name, the function is general and works on arbitrary time series, either xts or data.table objects the latter requires a DT column containing POSIXct time stamps.

Usage

aggregatePrice(
  pData,
  alignBy = "minutes",
  alignPeriod = 1,
  marketOpen = "09:30:00",
  marketClose = "16:00:00",
  fill = FALSE,
  tz = NULL
)

Arguments

Details

The time stamps of the new time series are the closing times and/or days of the intervals. The element of the returned series with e.g. time stamp 09:35:00 contains the last observation up to that point, including the value at 09:35:00 itself.

In case alignBy = "ticks", the sampling is done such the sampling starts on the first tick, and the last tick is always included. For example, if 14 observations are made on one day, and these are 1, 2, 3, ... 14. Then, with alignBy = "ticks" and alignPeriod = 3, the output will be 1, 4, 7, 10, 13, 14.

Value

A data.table or xts object containing the aggregated time series.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

Examples

# Aggregate price data to the 30-second frequency
aggregatePrice(sampleTData, alignBy = "secs", alignPeriod = 30)

# Aggregate price data to 30-minute frequency including zero return price changes
aggregatePrice(sampleTData, alignBy = "minutes", alignPeriod = 30, fill = TRUE)

Description

Aggregate tick-by-tick quote data and return a data.table or xts object containing the aggregated quote data. See sampleQData for an example of the argument qData. This function accepts arbitrary number of symbols over an arbitrary number of days.

Usage

aggregateQuotes(
  qData,
  alignBy = "minutes",
  alignPeriod = 5,
  marketOpen = "09:30:00",
  marketClose = "16:00:00",
  tz = NULL
)

Arguments

Details

The output "BID" and "OFR" columns are constructed using previous tick aggregation.

The variables "BIDSIZ" and "OFRSIZ" are aggregated by taking the sum of the respective inputs over each interval.

The timestamps of the new time series are the closing times of the intervals.

Please note: Returned objects always contain the first observation (i.e. opening quotes,...).

Value

A data.table or an xts object containing the aggregated quote data.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

Examples

# Aggregate quote data to the 30 second frequency
qDataAggregated <- aggregateQuotes(sampleQData, alignBy = "seconds", alignPeriod = 30)
qDataAggregated # Show the aggregated data

Description

Aggregate tick-by-tick trade data and return a time series as a data.table or xts object where first observation is always the opening price and subsequent observations are the closing prices over the interval. This function accepts arbitrary number of symbols over an arbitrary number of days.

Usage

aggregateTrades(
  tData,
  alignBy = "minutes",
  alignPeriod = 5,
  marketOpen = "09:30:00",
  marketClose = "16:00:00",
  tz = NULL
)

Arguments

Details

The time stamps of the new time series are the closing times and/or days of the intervals.

The output "PRICE" column is constructed using previous tick aggregation.

The variable "SIZE" is aggregated by taking the sum over each interval.

The variable "VWPRICE" is the aggregated price weighted by volume.

The time stamps of the new time series are the closing times of the intervals.

In case of previous tick aggregation or alignBy = "seconds"/"minutes"/"hours", the element of the returned series with e.g. time stamp 09:35:00 contains the last observation up to that point, including the value at 09:35:00 itself.

Value

A data.table or xts object containing the aggregated time series.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

Examples

# Aggregate trade data to 5 minute frequency
tDataAggregated <- aggregateTrades(sampleTData, alignBy = "minutes", alignPeriod = 5)
tDataAggregated

Description

Aggregate a time series as xts or data.table object. It can handle irregularly spaced time series and returns a regularly spaced one. Use univariate time series as input for this function and check out aggregateTrades and aggregateQuotes to aggregate Trade or Quote data objects.

Usage

aggregateTS(
  ts,
  FUN = "previoustick",
  alignBy = "minutes",
  alignPeriod = 1,
  weights = NULL,
  dropna = FALSE,
  tz = NULL,
  ...
)

Arguments

Details

The time stamps of the new time series are the closing times and/or days of the intervals. For example, for a weekly aggregation the new time stamp is the last day in that particular week (namely Sunday).

In case of previous tick aggregation, for alignBy is either "seconds" "minutes", or "hours", the element of the returned series with e.g. timestamp 09:35:00 contains the last observation up to that point, including the value at 09:35:00 itself.

Please note: In case an interval is empty, by default an NA is returned.. In case e.g. previous tick aggregation it makes sense to fill these NAs by the function na.locf (last observation carried forward) from the zoo package.

In case alignBy = "ticks", the sampling is done such the sampling starts on the first tick and the last tick is always included. For example, if 14 observations are made on one day, and these are 1, 2, 3, ... 14. Then, with alignBy = "ticks" and alignPeriod = 3, the output will be 1, 4, 7, 10, 13, 14.

Value

An xts object containing the aggregated time series.

Author(s)

Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.

Examples

# Load sample price data
## Not run: 
library(xts)
ts <- as.xts(sampleTData[, list(DT, PRICE, SIZE)])

# Previous tick aggregation to the 5-minute sampling frequency:
tsagg5min <- aggregateTS(ts, alignBy = "minutes", alignPeriod = 5)
head(tsagg5min)
# Previous tick aggregation to the 30-second sampling frequency:
tsagg30sec <- aggregateTS(ts, alignBy = "seconds", alignPeriod = 30)
tail(tsagg30sec)
tsagg3ticks <- aggregateTS(ts, alignBy = "ticks", alignPeriod = 3)

## End(Not run)

Description

This test examines the presence of jumps in highfrequency price series. It is based on the theory of Ait-Sahalia and Jacod (2009). It consists in comparing the multi-power variation of equi-spaced returns computed at a fast time scale ($h$), $r_{t,i}$ ($i=1, \ldots,N$) and those computed at the slower time scale ($kh$), $y_{t,i}$($i=1, \ldots ,\mbox{N/k}$).

They found that the limit (for $N$ $\to$ $\infty$ ) of the realized power variation is invariant for different sampling scales and that their ratio is $1$ in case of jumps and $\mbox{k}^{p/2}-1$ if no jumps. Therefore the AJ test detects the presence of jump using the ratio of realized power variation sampled from two scales. The null hypothesis is no jumps.

The function returns three outcomes: 1.z-test value 2.critical value under confidence level of $95\%$ and 3. $p$-value.

Assume there is $N$ equispaced returns in period $t$. Let $r_{t,i}$ be a return (with $i=1, \ldots,N$) in period $t$.

And there is $N/k$ equispaced returns in period $t$. Let $y_{t,i}$ be a return (with $i=1, \ldots ,\mbox{N/k}$) in period $t$.

Then the AJjumpTest is given by:

$\mbox{AJjumpTest}_{t,N}= \frac{S_t(p,k,h)-k^{p/2-1}}{\sqrt{V_{t,N}}}$

in which,

$\mbox{S}_t(p,k,h)= \frac{PV_{t,M}(p,kh)}{PV_{t,M}(p,h)}$

$\mbox{PV}_{t,N}(p,kh)= \sum_{i=1}^{N/k}{|y_{t,i}|^p}$

$\mbox{PV}_{t,N}(p,h)= \sum_{i=1}^{N}{|r_{t,i}|^p}$

$\mbox{V}_{t,N}= \frac{N(p,k) A_{t,N(2p)}}{N A_{t,N(p)}}$

$\mbox{N}(p,k)= \left(\frac{1}{\mu_p^2}\right)(k^{p-2}(1+k))\mu_{2p} + k^{p-2}(k-1) \mu_p^2 - 2k^{p/2-1}\mu_{k,p}$

$\mbox{A}_{t,n(2p)}= \frac{(1/N)^{(1-p/2)}}{\mu_p} \sum_{i=1}^{N}{|r_{t,i}|^p} \ \ \mbox{for} \ \ |r_j|< \alpha(1/N)^w$

$\mu_{k,p}= E(|U|^p |U+\sqrt{k-1}V|^p)$

$U, V$: independent standard normal random variables; $h=1/N$; $p, k, \alpha, w$: parameters.

Usage

AJjumpTest(
  pData,
  p = 4,
  k = 2,
  alignBy = NULL,
  alignPeriod = NULL,
  alphaMultiplier = 4,
  alpha = 0.975,
  ...
)

Arguments

Details

The theoretical framework underlying jump test is that the logarithmic price process $X_t$ belongs to the class of Brownian semimartingales, which can be written as:

$\mbox{X}_{t}= \int_{0}^{t} a_udu + \int_{0}^{t}\sigma_{u}dW_{u} + Z_t$

where $a$ is the drift term, $\sigma$ denotes the spot volatility process, $W$ is a standard Brownian motion and $Z$ is a jump process defined by:

$\mbox{Z}_{t}= \sum_{j=1}^{N_t}k_j$

where $k_j$ are nonzero random variables. The counting process can be either finite or infinite for finite or infinite activity jumps.

Using the convergence properties of power variation and its dependence on the time scale on which it is measured, Ait-Sahalia and Jacod (2009) define a new variable which converges to 1 in the presence of jumps in the underlying return series, or to another deterministic and known number in the absence of jumps (Theodosiou and Zikes, 2009).

Value

a list or xts in depending on whether input prices span more than one day.

Author(s)

Giang Nguyen, Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.

References

Ait-Sahalia, Y. and Jacod, J. (2009). Testing for jumps in a discretely observed process. The Annals of Statistics, 37(1), 184-222.

Theodosiou, M., & Zikes, F. (2009). A comprehensive comparison of alternative tests for jumps in asset prices. Unpublished manuscript, Graduate School of Business, Imperial College London.

Examples

jt <- AJjumpTest(sampleTData[, list(DT, PRICE)], p = 2, k = 3, 
                 alignBy = "seconds", alignPeriod = 5, makeReturns = TRUE)

Description

Filters raw quote data and return only data that stems from the exchange with the highest value for the sum of "BIDSIZ" and "OFRSIZ", i.e. the highest quote volume.

Usage

autoSelectExchangeQuotes(qData, printExchange = TRUE)

Arguments

Value

data.table or xts object depending on input.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

Examples

autoSelectExchangeQuotes(sampleQDataRaw)

Description

Filters raw trade data and return only data that stems from the exchange with the highest value for the variable "SIZE", i.e. the highest trade volume.

Usage

autoSelectExchangeTrades(tData, printExchange = TRUE)

Arguments

Value

data.table or xts object depending on input.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

Examples

autoSelectExchangeTrades(sampleTDataRaw)

Description

This test examines the presence of jumps in highfrequency price series. It is based on theory of Barndorff-Nielsen and Shephard (2006). The null hypothesis is that there are no jumps.

Usage

BNSjumpTest(
  rData,
  IVestimator = "BV",
  IQestimator = "TP",
  type = "linear",
  logTransform = FALSE,
  max = FALSE,
  alignBy = NULL,
  alignPeriod = NULL,
  makeReturns = FALSE,
  alpha = 0.975
)

Arguments

Details

Assume there is $N$ equispaced returns in period $t$. Assume the Realized variance (RV), IVestimator and IQestimator are based on $N$ equi-spaced returns.

Let $r_{t,i}$ be a return (with $i = 1, \ldots, N$) in period $t$.

Then the BNSjumpTest is given by

$\mbox{BNSjumpTest}= \frac{\code{RV} - \code{IVestimator}}{\sqrt{(\theta-2)\frac{1}{N} {\code{IQestimator}}}}.$

The options for IVestimator and IQestimator are listed above. $\theta$ depends on the chosen IVestimator (Huang and Tauchen, 2005).

The theoretical framework underlying the jump test is that the logarithmic price process $X_t$ belongs to the class of Brownian semimartingales, which can be written as:

$\mbox{X}_{t}= \int_{0}^{t} a_u \ du + \int_{0}^{t}\sigma_{u} \ dW_{u} + Z_t$

where $a$ is the drift term, $\sigma$ denotes the spot volatility process, $W$ is a standard Brownian motion and $Z$ is a jump process defined by:

$\mbox{Z}_{t}= \sum_{j=1}^{N_t}k_j$

where $k_j$ are nonzero random variables. The counting process can be either finite or infinite for finite or infinite activity jumps.

Since the realized volatility converges to the sum of integrated variance and jump variation, while the robust IVestimator converges to the integrated variance, it follows that the difference between RV and the IVestimator captures the jump part only, and this observation underlines the BNS test for jumps (Theodosiou and Zikes, 2009).

Value

a list or xts (depending on whether input prices span more than one day) with the following values:

• $z$-test value.

• critical value (with confidence level of 95%).

• $p$-value of the test.

Author(s)

Giang Nguyen, Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.

References

Barndorff-Nielsen, O. E., and Shephard, N. (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics, 4, 1-30.

Corsi, F., Pirino, D., and Reno, R. (2010). Threshold bipower variation and the impact of jumps on volatility forecasting. Journal of Econometrics, 159, 276-288.

Huang, X., and Tauchen, G. (2005). The relative contribution of jumps to total price variance. Journal of Financial Econometrics, 3, 456-499.

Theodosiou, M., and Zikes, F. (2009). A comprehensive comparison of alternative tests for jumps in asset prices. Unpublished manuscript, Graduate School of Business, Imperial College London.

Examples

bns <- BNSjumpTest(sampleTData[, list(DT, PRICE)], IVestimator= "rMinRVar",
                   IQestimator = "rMedRQuar", type= "linear", makeReturns = TRUE)
bns

Description

Time series aggregation based on 'business time' statistics. Instead of equidistant sampling based on time during a trading day, business time sampling creates measures and samples equidistantly using these instead. For example when sampling based on volume, business time aggregation will result in a time series that has an equal amount of volume between each observation (if possible).

Usage

businessTimeAggregation(
  pData,
  measure = "volume",
  obs = 390,
  bandwidth = 0.075,
  tz = NULL,
  ...
)

Arguments

Value

A list containing "pData" which is the aggregated data and a list containing the intensity process, split up day by day.

Author(s)

Emil Sjoerup.

References

Dong, Y., and Tse, Y. K. (2017). Business time sampling scheme with applications to testing semi-martingale hypothesis and estimating integrated volatility. Econometrics, 5, 51.

Oomen, R. C. A. (2006). Properties of realized variance under alternative sampling schemes. Journal of Business & Economic Statistics, 24, 219-237

Examples

pData <- sampleTData[,list(DT, PRICE, SIZE)]
# Aggregate based on the trade intensity measure. Getting 390 observations.
agged <- businessTimeAggregation(pData, measure = "intensity", obs = 390, bandwidth = 0.075)
# Plot the trade intensity measure
plot.ts(agged$intensityProcess$`2018-01-02`)
rCov(agged$pData[, list(DT, PRICE)], makeReturns = TRUE)
rCov(pData[,list(DT, PRICE)], makeReturns = TRUE, alignBy = "minutes", alignPeriod = 1)

# Aggregate based on the volume measure. Getting 78 observations.
agged <- businessTimeAggregation(pData, measure = "volume", obs = 78)
rCov(agged$pData[,list(DT, PRICE)], makeReturns = TRUE)
rCov(pData[,list(DT, PRICE)], makeReturns = TRUE, alignBy = "minutes", alignPeriod = 5)

Description

Calculates the test-statistic for the drift burst hypothesis

Let the efficient log-price be defined as:

$dX_{t} = \mu_{t}dt + \sigma_{t}dW_{t} + dJ_{t},$

where $\mu_{t}$, $\sigma_{t}$, and $J_{t}$ are the spot drift, the spot volatility, and a jump process respectively. However, due to microstructure noise, the observed log-price is

$Y_{t} = X_{t} + \varepsilon_{t}$

In order robustify the results to the presence of market microstructure noise, the pre-averaged returns are used:

$\Delta_{i}^{n}\overline{Y} = \sum_{j=1}^{k_{n}-1}g_{j}^{n}\Delta_{i+j}^{n}Y,$

where $g(\cdot)$ is a weighting function, $min(x, 1-x)$, and $k_{n}$ is the pre-averaging horizon.

The test statistic for the Drift Burst Hypothesis can then be calculated as

$\bar{T}_{t}^{n} = \sqrt{\frac{h_{n}}{K_{2}}}\frac{\hat{\bar{\mu}}_{t}^{n}}{\sqrt{\hat{\bar{\sigma}}_{t}^{n}}},$

where

$\hat{\bar{\mu}}_{t}^{n} = \frac{1}{h_{n}}\sum_{i=1}^{n-k_{n}+2}K\left(\frac{t_{i-1}-t}{h_{n}}\right)\Delta_{i-1}^{n}\overline{Y},$

and

$\hat{\bar{\sigma}}_{t}^{n} = \frac{1}{h_{n}'}\bigg[\sum_{i=1}^{n-k_{n}+2}\left(K\left(\frac{t_{i-1}-t}{h'_{n}}\right)\Delta_{i-1}^{n}\overline{Y}\right)^{2} \\ + 2\sum_{L=1}^{L_{n}}\omega\left(\frac{L}{L_{n}}\right)\sum_{i=1}^{n-k_{n}-L+2}K\left(\frac{t_{i-1}-t}{h_{n}'}\right)K\left(\frac{t_{i+L-1}-t}{h_{n}'}\right)\Delta_{i-1}^{n}\overline{Y}\Delta_{i-1+L}^{n}\overline{Y}\bigg],$

where $\omega(\cdot)$ is a smooth kernel function, in this case the Parzen kernel. $L_{n}$ is the lag length for adjusting for auto-correlation and $K(\cdot)$ is a kernel weighting function, which in this case is the left-sided exponential kernel.

Usage

driftBursts(
  pData,
  testTimes = seq(34260, 57600, 60),
  preAverage = 5,
  ACLag = -1L,
  meanBandwidth = 300L,
  varianceBandwidth = 900L,
  parallelize = FALSE,
  nCores = NA,
  warnings = TRUE
)

Arguments

Details

If the testTimes vector contains instructions to test before the first trade, or more than 15 minutes after the last trade, these entries will be deleted, as not doing so may cause crashes. The test statistic is unstable before max(meanBandwidth , varianceBandwidth) seconds has passed. The lags from the Newey-West algorithm is increased by 2 * (preAveage-1) due to the pre-averaging we know at least this many lags should be corrected for. The maximum of 20 lags is also increased by this factor for the same reason.

Value

An object of class DBH and list containing the series of the drift burst hypothesis test-statistic as well as the estimated spot drift and variance series. The list also contains some information such as the variance and mean bandwidths along with the pre-averaging setting and the amount of observations. Additionally, the list will contain information on whether testing happened for all testTimes entries. Objects of class DBH has the methods print.DBH, plot.DBH, and getCriticalValues.DBH which prints, plots, and retrieves critical values for the test described in appendix B of Christensen, Oomen, and Reno (2020).

Author(s)

Emil Sjoerup

References

Christensen, K., Oomen, R., and Reno, R. (2020) The drift burst hypothesis. Journal of Econometrics. Forthcoming.

Examples

# Usage with data.table object
dat <- sampleTData[as.Date(DT) == "2018-01-02"]
# Testing every 60 seconds after 09:45:00
DBH1 <- driftBursts(dat, testTimes = seq(35100, 57600, 60), preAverage = 2, ACLag = -1L,
                    meanBandwidth = 300L, varianceBandwidth = 900L)
print(DBH1)

plot(DBH1, pData = dat)
# Usage with xts object (1 column)
library("xts")
dat <- xts(sampleTData[as.Date(DT) == "2018-01-03"]$PRICE, 
           order.by = sampleTData[as.Date(DT) == "2018-01-03"]$DT)
# Testing every 60 seconds after 09:45:00
DBH2 <- driftBursts(dat, testTimes = seq(35100, 57600, 60), preAverage = 2, ACLag = -1L,
                    meanBandwidth = 300L, varianceBandwidth = 900L)
plot(DBH2, pData = dat)

## Not run:  
# This block takes some time
dat <- xts(sampleTDataEurope$PRICE, 
           order.by = sampleTDataEurope$DT)
# Testing every 60 seconds after 09:00:00
system.time({DBH4 <- driftBursts(dat, testTimes = seq(32400 + 900, 63000, 60), preAverage = 2, 
             ACLag = -1L, meanBandwidth = 300L, varianceBandwidth = 900L)})

system.time({DBH4 <- driftBursts(dat, testTimes = seq(32400 + 900, 63000, 60), preAverage = 2, 
                                 ACLag = -1L, meanBandwidth = 300L, varianceBandwidth = 900L,
                                 parallelize = TRUE, nCores = 8)})
plot(DBH4, pData = dat)

# The print method for DBH objects takes an argument alpha that determines the confidence level
# of the test performed
print(DBH4, alpha = 0.99)
# Additionally, criticalValue can be passed directly
print(DBH4, criticalValue = 3)
max(abs(DBH4$tStat)) > getCriticalValues(DBH4, 0.99)$quantile

## End(Not run)

Description

Filter raw trade data such and return only data between market close and market open. By default, marketOpen = "09:30:00" and marketClose = "16:00:00" (see Brownlees and Gallo (2006) for more information on good choices for these arguments).

Usage

exchangeHoursOnly(
  data,
  marketOpen = "09:30:00",
  marketClose = "16:00:00",
  tz = NULL
)

Arguments

Value

xts or data.table object depending on input.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

References

Brownlees, C. T. and Gallo, G. M. (2006). Financial econometric analysis at ultra-high frequency: Data handling concerns. Computational Statistics & Data Analysis, 51, pages 2232-2245.

Examples

exchangeHoursOnly(sampleTDataRaw)

Description

Convenience function to gather data from one xts or data.table with at least "DT", and d columns containing price data to a "DT", "SYMBOL", and "PRICE" column. This function the opposite of spreadPrices.

Usage

gatherPrices(data)

Arguments

Value

a data.table with columns DT, SYMBOL, and PRICE

Author(s)

Emil Sjoerup

See Also

spreadPrices

Examples

## Not run: 
library(data.table)
data1 <- copy(sampleTData)[,  `:=`(PRICE = PRICE * runif(.N, min = 0.99, max = 1.01),
                                               DT = DT + runif(.N, 0.01, 0.02))]
data2 <- copy(sampleTData)[, SYMBOL := 'XYZ']
dat1 <- rbind(data1[, list(DT, SYMBOL, PRICE)], data2[, list(DT, SYMBOL, PRICE)])
setkeyv(dat1, c("DT", "SYMBOL"))
dat1
dat <- spreadPrices(dat1) # Easy to use for realized measures
dat
dat <- gatherPrices(dat)
dat
all.equal(dat1, dat) # We have changed to RM format and back.

## End(Not run)

Description

Function to retrieve high frequency data from Alpha Vantage - wrapper around quantmod's getSymbols.av function

Usage

getAlphaVantageData(
  symbols = NULL,
  interval = "5min",
  outputType = "xts",
  apiKey = NULL,
  doSleep = TRUE
)

Arguments

Details

The doSleep argument is set to true as default because Alpha Vantage has a limit of five calls per minute. The function does not try to extract when the last API call was made which means that if you made successive calls to get 3 symbols in rapid succession, the function may not retrieve all the data.

Value

An object of type xts or data.table in case the length of symbols is 1. If the length of symbols > 1 the xts and data.table objects will be put into a list.

Author(s)

Emil Sjoerup (wrapper only) Paul Teetor (for quantmod's getSymbols.av)

See Also

The getSymbols.av function in the quantmod package

Examples

## Not run: 
# Get data for SPY at an interval of 1 minute in the standard xts format.
data <- getAlphaVantageData(symbols = "SPY", apiKey = "yourKey", interval = "1min")

# Get data for 3M and Goldman Sachs  at a 5 minute interval in the data.table format. 
# The data.tables will be put in a list.
data <- getAlphaVantageData(symbols = c("MMM", "GS"), interval = "5min", 
                  outputType = "DT", apiKey = 'yourKey')

# Get data for JPM and Citicorp at a 15 minute interval in the xts format. 
# The xts objects will be put in a list.
data <- getAlphaVantageData(symbols = c("JPM", "C"), interval = "15min", 
                  outputType = "xts", apiKey = "yourKey")

## End(Not run)

Description

Method for DBH objects to calculate the critical value for the presence of a burst of drift. The critical value is that of the test described in appendix B in Christensen Oomen Reno

Usage

getCriticalValues(x, alpha = 0.95)

Arguments

Author(s)

Emil Sjoerup

References

Christensen, K., Oomen, R., and Reno, R. (2020) The drift burst hypothesis. Journal of Econometrics. Forthcoming.

Description

Function returns an xts or data.table object containing 23 liquidity measures. Please see details below.

Note that this assumes a regular time grid.

Usage

getLiquidityMeasures(tqData, win = 300)

Arguments

Details

NOTE: xts or data.table should only contain one day of observations Some markets have publish information about whether it was a buyer or a seller who initiated the trade. This information can be passed in a column DIRECTION this column must only have 1 or -1 as values.

The respective liquidity measures are defined as follows:

• effectiveSpread

  $\mbox{effective spread}_t = 2*D_t*(\mbox{PRICE}_{t} - \frac{(\mbox{BID}_{t}+\mbox{OFR}_{t})}{2}),$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)). Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered quote timestamp).

• realizedSpread: realized spread

  $\mbox{realized spread}_t = 2*D_t*(\mbox{PRICE}_{t} - \frac{(\mbox{BID}_{t+300}+\mbox{OFR}_{t+300})}{2}),$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)). Note that the time indication of $\mbox{BID}$ and $\mbox{OFR}$ refers to the registered time of the quote in seconds.

• valueTrade: trade value

  $\mbox{trade value}_t = \mbox{SIZE}_{t}*\mbox{PRICE}_{t}.$

• signedValueTrade: signed trade value

  $\mbox{signed trade value}_t = D_t * (\mbox{SIZE}_{t}*\mbox{PRICE}_{t}),$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)).

• depthImbalanceDifference: depth imbalance (as a difference)

  $\mbox{depth imbalance (as difference)}_t = \frac{D_t *(\mbox{OFRSIZ}_{t}-\mbox{BIDSIZ}_{t})}{(\mbox{OFRSIZ}_{t}+\mbox{BIDSIZ}_{t})},$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)). Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered quote timestamp).

• depthImbalanceRatio: depth imbalance (as ratio)

  $\mbox{depth imbalance (as ratio)}_t = (\frac{\mbox{OFRSIZ}_{t}}{\mbox{BIDSIZ}_{t}})^{D_t},$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)). Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered quote timestamp).

• proportionalEffectiveSpread: proportional effective spread

  $\mbox{proportional effective spread}_t = \frac{\mbox{effective spread}_t}{(\mbox{OFR}_{t}+\mbox{BID}_{t})/2}$

  (Venkataraman, 2001).

  Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered quote timestamp).

• proportionalRealizedSpread: proportional realized spread

  $\mbox{proportional realized spread}_t = \frac{\mbox{realized spread}_t}{(\mbox{OFR}_{t}+\mbox{BID}_{t})/2}$

  (Venkataraman, 2001).

  Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered

• priceImpact: price impact

  $\mbox{price impact}_t = \frac{\mbox{effective spread}_t - \mbox{realized spread}_t}{2}$

  (see Boehmer (2005), Bessembinder (2003)).

• proportionalPriceImpact: proportional price impact

  $\mbox{proportional price impact}_t = \frac{\frac{(\mbox{effective spread}_t - \mbox{realized spread}_t)}{2}}{\frac{\mbox{OFR}_{t}+\mbox{BID}_{t}}{2}}$

  (Venkataraman, 2001). Note that the input of this function consists of the matched trades and quotes, so this is where the time indication refers to (and thus not to the registered quote timestamp).

• halfTradedSpread: half traded spread

  $\mbox{half traded spread}_t = D_t*(\mbox{PRICE}_{t} - \frac{(\mbox{BID}_{t}+\mbox{OFR}_{t})}{2}),$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)). Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered quote timestamp).

• proportionalHalfTradedSpread: proportional half traded spread

  $\mbox{proportional half traded spread}_t = \frac{\mbox{half traded spread}_t}{\frac{\mbox{OFR}_{t}+\mbox{BID}_{t}}{2}}.$

  Note that the input of this function consists of the matched trades and quotes, so this is were the time indication refers to (and thus not to the registered quote timestamp).

• squaredLogReturn: squared log return on trade prices

  $\mbox{squared log return on Trade prices}_t = (\log(\mbox{PRICE}_{t})-\log(\mbox{PRICE}_{t-1}))^2.$

• absLogReturn: absolute log return on trade prices

  $\mbox{absolute log return on Trade prices}_t = |\log(\mbox{PRICE}_{t})-\log(\mbox{PRICE}_{t-1})|.$

• quotedSpread: quoted spread

  $\mbox{quoted spread}_t = \mbox{OFR}_{t}-\mbox{BID}_{t}$

  Note that the input of this function consists of the matched trades and quotes, so this is where the time indication refers to (and thus not to the registered quote timestamp).

• proportionalQuotedSpread: proportional quoted spread

  $\mbox{proportional quoted spread}_t = \frac{\mbox{quoted spread}_t}{\frac{\mbox{OFR}_{t}+\mbox{BID}_{t}}{2}}$

  (Venkataraman, 2001). Note that the input of this function consists of the matched trades and quotes, so this is where the time indication refers to (and thus not to the registered quote timestamp).

• logQuotedSpread: log quoted spread

  $\mbox{log quoted spread}_t = \log(\frac{\mbox{OFR}_{t}}{\mbox{BID}_{t}})$

  (Hasbrouck and Seppi, 2001). Note that the input of this function consists of the matched trades and quotes, so this is where the time indication refers to (and thus not to the registered quote timestamp).

• logQuotedSize: log quoted size

  $\mbox{log quoted size}_t = \log(\mbox{OFRSIZ}_{t})+\log(\mbox{BIDSIZ}_{t})$

  (Hasbrouck and Seppi, 2001). Note that the input of this function consists of the matched trades and quotes, so this is where the time indication refers to (and thus not to the registered quote timestamp).

• quotedSlope: quoted slope

  $\mbox{quoted slope}_t = \frac{\mbox{quoted spread}_t}{\mbox{log quoted size}_t}$

  (Hasbrouck and Seppi, 2001).

• logQSlope: log quoted slope

  $\mbox{log quoted slope}_t = \frac{\mbox{log quoted spread}_t}{\mbox{log quoted size}_t}.$

• midQuoteSquaredReturn: midquote squared return

  $\mbox{midquote squared return}_t = (\log(\mbox{midquote}_{t})-\log(\mbox{midquote}_{t-1}))^2,$

  where $\mbox{midquote}_{t} = \frac{\mbox{BID}_{t} + \mbox{OFR}_{t}}{2}$.

• midQuoteAbsReturn: midquote absolute return

  $\mbox{midquote absolute return}_t = |\log(\mbox{midquote}_{t})-\log(\mbox{midquote}_{t-1})|,$

  where $\mbox{midquote}_{t} = \frac{\mbox{BID}_{t} + \mbox{OFR}_{t}}{2}$.

• signedTradeSize: signed trade size

  $\mbox{signed trade size}_t = D_t * \mbox{SIZE}_{t},$

  where $D_t$ is 1 (-1) if $trade_t$ was buy (sell).

Value

A modified (enlarged) xts or data.table with the new measures.

References

Bessembinder, H. (2003). Issues in assessing trade execution costs. Journal of Financial Markets, 223-257.

Boehmer, E. (2005). Dimensions of execution quality: Recent evidence for US equity markets. Journal of Financial Economics, 78, 553-582.

Hasbrouck, J. and Seppi, D. J. (2001). Common factors in prices, order flows and liquidity. Journal of Financial Economics, 59, 383-411.

Venkataraman, K. (2001). Automated versus floor trading: An analysis of execution costs on the Paris and New York exchanges. The Journal of Finance, 56, 1445-1485.

Examples

tqData <- matchTradesQuotes(sampleTData[as.Date(DT) == "2018-01-02"], 
                            sampleQData[as.Date(DT) == "2018-01-02"])
res <- getLiquidityMeasures(tqData)
res

Description

Function returns a vector with the inferred trade direction which is determined using the Lee and Ready algorithm (Lee and Ready, 1991).

Usage

getTradeDirection(tqData)

Arguments

Details

NOTE: By convention the first observation is always marked as a buy.

Value

A vector which has values 1 or (-1) if the inferred trade direction is buy or sell respectively.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup. Special thanks to Dirk Eddelbuettel.

References

Lee, C. M. C. and Ready, M. J. (1991). Inferring trade direction from intraday data. Journal of Finance, 46, 733-746.

Examples

# Generate matched trades and quote data set
tqData <- matchTradesQuotes(sampleTData[as.Date(DT) == "2018-01-02"], 
                            sampleQData[as.Date(DT) == "2018-01-02"])
directions <- getTradeDirection(tqData)
head(directions)

Description

Function returns the estimates for the heterogeneous autoregressive model (HAR) for realized volatility discussed in Andersen et al. (2007) and Corsi (2009). This model is mainly used to forecast the next day's volatility based on the high-frequency returns of the past.

Usage

HARmodel(
  data,
  periods = c(1, 5, 22),
  periodsJ = c(1, 5, 22),
  periodsQ = c(1),
  leverage = NULL,
  RVest = c("rCov", "rBPCov", "rQuar"),
  type = "HAR",
  inputType = "RM",
  jumpTest = "ABDJumptest",
  alpha = 0.05,
  h = 1,
  transform = NULL,
  externalRegressor = NULL,
  periodsExternal = c(1),
  ...
)

Arguments

Details

The basic specification in Corsi (2009) is as follows. Let $RV_{t}$ be the realized variances at day $t$ and $RV_{t-k:t}$ the average realized variance in between $t-k$ and $t$, $k \geq 0$.

The dynamics of the model are given by

$RV_{t+1} = \beta_0 + \beta_1 \ RV_{t} + \beta_2 \ RV_{t-4:t} + \beta_3 \ RV_{t-21:t} + \varepsilon_{t+1}$

which is estimated by ordinary least squares under the assumption that at time $t$, the conditional mean of $\varepsilon_{t+1}$ is equal to zero.

For other specifications, please refer to the cited papers.

The standard errors reporting in the print and summary methods are Newey-West standard errors calculated with the sandwich package.

Value

The function outputs an object of class HARmodel and lm (so HARmodel is a subclass of lm). Objects of class HARmodel has the following methods plot.HARmodel, predict.HARmodel, print.HARmodel, and summary.HARmodel.

Author(s)

Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.

References

Andersen, T. G., Bollerslev, T., and Diebold, F. (2007). Roughing it up: Including jump components in the measurement, modelling and forecasting of return volatility. The Review of Economics and Statistics, 89, 701-720.

Corsi, F. (2009). A simple approximate long memory model of realized volatility. Journal of Financial Econometrics, 7, 174-196.

Corsi, F. and Reno R. (2012). Discrete-time volatility forecasting with persistent leverage effect and the link with continuous-time volatility modeling. Journal of Business & Economic Statistics, 30, 368-380.

Bollerslev, T., Patton, A., and Quaedvlieg, R. (2016). Exploiting the errors: A simple approach for improved volatility forecasting, Journal of Econometrics, 192, 1-18.

Examples

# Example 1: HAR
# Forecasting daily Realized volatility for the S&P 500 using the basic HARmodel: HAR
library(xts)
RVSPY <- as.xts(SPYRM$RV5, order.by = SPYRM$DT)

x <- HARmodel(data = RVSPY , periods = c(1,5,22), RVest = c("rCov"),
              type = "HAR", h = 1, transform = NULL, inputType = "RM")
class(x)
x
summary(x)
plot(x)
predict(x)


# Example 2: HARQ
# Get the highfrequency returns
dat <- as.xts(sampleOneMinuteData[, makeReturns(STOCK), by = list(DATE = as.Date(DT))])
x <- HARmodel(dat, periods = c(1,5,10), periodsJ = c(1,5,10),
            periodsQ = c(1), RVest = c("rCov", "rQuar"),
              type="HARQ", inputType = "returns")
# Estimate the HAR model of type HARQ
class(x)
x
# plot(x)
# predict(x)

# Example 3: HARQJ with already computed realized measures
dat <- SPYRM[, list(DT, RV5, BPV5, RQ5)]
x <- HARmodel(as.xts(dat), periods = c(1,5,22), periodsJ = c(1),
              periodsQ = c(1), type = "HARQJ")
# Estimate the HAR model of type HARQJ
class(x)
x
# plot(x)
predict(x)

# Example 4: CHAR with already computed realized measures
dat <- SPYRM[, list(DT, RV5, BPV5)]

x <- HARmodel(as.xts(dat), periods = c(1, 5, 22), type = "CHAR")
# Estimate the HAR model of type CHAR
class(x)
x
# plot(x)
predict(x)

# Example 5: CHARQ with already computed realized measures
dat <- SPYRM[, list(DT, RV5, BPV5, RQ5)]

x <- HARmodel(as.xts(dat), periods = c(1,5,22), periodsQ = c(1), type = "CHARQ")
# Estimate the HAR model of type CHARQ
class(x)
x
# plot(x)
predict(x)

# Example 6: HARCJ with pre-computed test-statistics
## BNSJumptest manually calculated.
testStats <- sqrt(390) * (SPYRM$RV1 - SPYRM$BPV1)/sqrt((pi^2/4+pi-3 - 2) * SPYRM$medRQ1)
model <- HARmodel(cbind(as.xts(SPYRM[, list(DT, RV5, BPV5)]), testStats), type = "HARCJ")

Description

This function calculates the High frEquency bAsed VolatilitY (HEAVY) model proposed in Shephard and Sheppard (2010).

Usage

HEAVYmodel(data, startingValues = NULL)

Arguments

Details

Let $r_{t}$ and $RM_{t}$ be series of demeaned returns and realized measures of daily stock price variation. The HEAVY model is a two-component model. We assume $r_{t} = h_{t}^{1/2} Z_{t}$ where $Z_t$ is an i.i.d. zero-mean and unit-variance innovation term. The dynamics of the HEAVY model are given by

$h_{t} = \omega + \alpha RM_{t-1} + \beta h_{t-1}$

and

$\mu_{t} = \omega_{R} + \alpha_{R} RM_{t-1} + \beta_{R} \mu_{t-1}.$

The two equations are estimated separately as mentioned in Shephard and Sheppard (2010). We report robust standard errors based on the matrix-product of inverted Hessians and the outer product of gradients.

Note that we always demean the returns in the data input as we don't include a constant in the mean equation.

Value

The function outputs an object of class HEAVYmodel, a list containing

• coefficients = estimated coefficients.

• se = robust standard errors based on inverted Hessian matrix.

• residuals = the residuals in the return equation.

• llh = the two-component log-likelihood values.

• varCondVariances = conditional variances in the variance equation.

• RMCondVariances = conditional variances in the RM equation.

• data = the input data.

The class HEAVYmodel has the following methods: plot.HEAVYmodel, predict.HEAVYmodel, print.HEAVYmodel, and summary.HEAVYmodel.

Author(s)

Onno Kleen and Emil Sjorup.

References

Shephard, N. and Sheppard, K. (2010). Realising the future: Forecasting with high frequency based volatility (HEAVY) models. Journal of Applied Econometrics 25, 197–231.

See Also

predict.HEAVYmodel

Examples

# Calculate returns in percentages
logReturns <- 100 * makeReturns(SPYRM$CLOSE)[-1]

# Combine both returns and realized measures into one xts
# Due to return calculation, the first observation is missing
dataSPY <- xts::xts(cbind(logReturns, SPYRM$BPV5[-1] * 10000), order.by = SPYRM$DT[-1])

# Fit the HEAVY model
fittedHEAVY <- HEAVYmodel(dataSPY)

# Examine the estimated coefficients and robust standard errors
fittedHEAVY

# Calculate iterative multi-step-ahead forecasts
predict(fittedHEAVY, stepsAhead = 12)

Description

This documentation page functions as a point of reference to quickly look up the estimators of the integrated covariance provided in the highfrequency package.

The implemented estimators are:

Realized covariance rCov

Realized bipower covariance rBPCov

Hayashi-Yoshida realized covariance rHYCov

Realized kernel covariance rKernelCov

Realized outlyingness-weighted covariance rOWCov

Realized threshold covariance rThresholdCov

Realized two-scale covariance rTSCov

Robust realized two-scale covariance rRTSCov

Subsampled realized covariance rAVGCov

Realized semi-covariance rSemiCov

Modulated Realized covariance rMRCov

Realized Cholesky covariance rCholCov

Beta-adjusted realized covariance rBACov

See Also

IVar for a list of implemented estimators of the integrated variance.

Description

This function can be used to test for jumps in intraday price paths.

The tests are of the form $L(t) = (R(t) - mu(t))/sigma(t)$.

See spotVol and spotDrift for Estimators for $\sigma(t)$ and $\mu(t)$, respectively.

Usage

intradayJumpTest(
  pData,
  volEstimator = "RM",
  driftEstimator = "none",
  alpha = 0.95,
  alignBy = "minutes",
  alignPeriod = 5,
  marketOpen = "09:30:00",
  marketClose = "16:00:00",
  tz = NULL,
  n = NULL,
  ...
)

Arguments

Author(s)

Emil Sjoerup

References

Christensen, K., Oomen, R. C. A., Podolskij, M. (2014): Fact or Friction: Jumps at ultra high frequency. Journal of Financial Economics, 144, 576-599

Examples

## Not run: 
# We can easily make a Lee-Mykland jump test.
LMtest <- intradayJumpTest(pData = sampleTData[, list(DT, PRICE)], 
                           volEstimator = "RM", driftEstimator = "none",
                           RM = "rBPCov", lookBackPeriod = 20,
                           alignBy = "minutes", alignPeriod = 5, marketOpen = "09:30:00", 
                           marketClose = "16:00:00")
plot(LMtest)

# We can just as easily use the pre-averaged version from the "Fact or Friction" paper
FoFtest <- intradayJumpTest(pData = sampleTData[, list(DT, PRICE)], 
                            volEstimator = "PARM", driftEstimator = "none",
                            RM = "rBPCov", lookBackPeriod = 20, theta = 1.2,
                            marketOpen = "09:30:00", marketClose = "16:00:00")
plot(FoFtest)


## End(Not run)

Description

This documentation page functions as a point of reference to quickly look up the estimators of the integrated variance provided in the highfrequency package.

The implemented estimators are: Realized Variance rRVar

Median realized variance rMedRVar

Minimum realized variance rMinRVar

Realized quadpower variance rQPVar

Realized multipower variance rMPVar

Realized semivariance rSVar

Note that almost all estimators in the list in ICov also work yield estimates of the integrated variance on the diagonals.

See Also

ICov for a list of implemented estimators of the integrated covariance.

Description

This function supplies information about standard error and confidence band of integrated variance (IV) estimators under Brownian semimartingales model such as: bipower variation, rMinRV, rMedRV. Depending on users' choices of estimator (integrated variance (IVestimator), integrated quarticity (IQestimator)) and confidence level, the function returns the result.(Barndorff (2002)) Function returns three outcomes: 1.value of IV estimator 2.standard error of IV estimator and 3.confidence band of IV estimator.

Assume there is $N$ equispaced returns in period $t$.

Then the IVinference is given by:

$\mbox{standard error}= \frac{1}{\sqrt{N}} *sd$

$\mbox{confidence band}= \hat{IV} \pm cv*se$

in which,

$\mbox{sd}= \sqrt{\theta \times \hat{IQ}}$

$cv:$ critical value.

$se:$ standard error.

$\theta:$ depending on IQestimator, $\theta$ can take different value (Andersen et al. (2012)).

$\hat{IQ}$ integrated quarticity estimator.

Usage

IVinference(
  rData,
  IVestimator = "RV",
  IQestimator = "rQuar",
  confidence = 0.95,
  alignBy = NULL,
  alignPeriod = NULL,
  makeReturns = FALSE,
  ...
)

Arguments

Details

The theoretical framework is the logarithmic price process $X_t$ belongs to the class of Brownian semimartingales, which can be written as:

$\mbox{X}_{t}= \int_{0}^{t} a_udu + \int_{0}^{t}\sigma_{u}dW_{u}$

where $a$ is the drift term, $\sigma$ denotes the spot vivInferenceolatility process, $W$ is a standard Brownian motion (assume that there are no jumps).

Value

list

Author(s)

Giang Nguyen, Jonathan Cornelissen and Kris Boudt

References

Andersen, T. G., Dobrev, D., and Schaumburg, E. (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169, 75-93.

Barndorff-Nielsen, O. E. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64, 253-280.

Examples

## Not run: 
library("xts") # This function only accepts xts data currently
ivInf <- IVinference(as.xts(sampleTData[, list(DT, PRICE)]), IVestimator= "rMinRV",
                     IQestimator = "rMedRQ", confidence = 0.95, makeReturns = TRUE)
ivInf

## End(Not run)

Description

This test examines the jump in highfrequency data. It is based on theory of Jiang and Oomen (JO). They found that the difference of simple return and logarithmic return can capture one half of integrated variance if there is no jump in the underlying sample path. The null hypothesis is no jumps.

Function returns three outcomes: 1.z-test value 2.critical value under confidence level of $95\%$ and 3.p-value.

Assume there is $N$ equispaced returns in period $t$.

Let $r_{t,i}$ be a logarithmic return (with $i=1, \ldots,N$) in period $t$.

Let $R_{t,i}$ be a simple return (with $i=1, \ldots,N$) in period $t$.

Then the JOjumpTest is given by:

$\mbox{JOjumpTest}_{t,N}= \frac{N BV_{t}}{\sqrt{\Omega_{SwV}} \left(1-\frac{RV_{t}}{SwV_{t}} \right)}$

in which, $BV$: bipower variance; $RV$: realized variance (defined by Andersen et al. (2012));

$\mbox{SwV}_{t}=2 \sum_{i=1}^{N}(R_{t,i}-r_{t,i})$

$\Omega_{SwV}= \frac{\mu_6}{9} \frac{{N^3}{\mu_{6/p}^{-p}}}{N-p-1} \sum_{i=0}^{N-p}\prod_{k=1}^{p}|r_{t,i+k}|^{6/p}$

$\mu_{p}= \mbox{E}[|\mbox{U}|^{p}] = 2^{p/2} \frac{\Gamma(1/2(p+1))}{\Gamma(1/2)}$

$U$: independent standard normal random variables

p: parameter (power).

Usage

JOjumpTest(
  pData,
  power = 4,
  alignBy = NULL,
  alignPeriod = NULL,
  alpha = 0.975,
  ...
)

Arguments

Details

The theoretical framework underlying jump test is that the logarithmic price process $X_t$ belongs to the class of Brownian semimartingales, which can be written as:

$\mbox{X}_{t}= \int_{0}^{t} a_udu + \int_{0}^{t}\sigma_{u}dW_{u} + Z_t$

where $a$ is the drift term, $\sigma$ denotes the spot volatility process, $W$ is a standard Brownian motion and $Z$ is a jump process defined by:

$\mbox{Z}_{t}= \sum_{j=1}^{N_t}k_j$

where $k_j$ are nonzero random variables. The counting process can be either finite or infinite for finite or infinite activity jumps.

The the Jiang and Ooment test is that in the absence of jumps, the accumulated difference between the simple returns and log returns captures half of the integrated variance. (Theodosiou and Zikes, 2009). If this difference is too great, the null hypothesis of no jumps is rejected.

Value

list

Author(s)

Giang Nguyen, Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup

References

Andersen, T. G., Dobrev, D., and Schaumburg, E. (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169, 75- 93.

Jiang, J. G., and Oomen, R. C. A (2008). Testing for jumps when asset prices are observed with noise- a "swap variance" approach. Journal of Econometrics, 144, 352-370.

Theodosiou, M., Zikes, F. (2009). A comprehensive comparison of alternative tests for jumps in asset prices. Unpublished manuscript, Graduate School of Business, Imperial College London.

Examples

joDT <- JOjumpTest(sampleTData[, list(DT, PRICE)])

Description

Function to choose the tuning parameter, kn in ReMeDI estimation. The optimal parameter kn is the smallest value that where the criterion:

$SqErr(k_{n})^{n}_{t} = \left(\hat{R}^{n,k_{n}}_{t,0} - \hat{R}^{n,k_{n}}_{t,1} - \hat{R}^{n,k_{n}}_{t,2} + \hat{R}^{n,k_{n}}_{t,3} - \hat{R}^{n, k_{n}}_{t,l}\right)^{2}$

is perceived to be zero. The tuning parameter tol can be set to choose the tolerance of the perception of 'close to zero', a higher tolerance will lead to a higher optimal value.

Usage

knChooseReMeDI(
  pData,
  knMax = 10,
  tol = 0.05,
  size = 3,
  lower = 2,
  upper = 5,
  plot = FALSE
)

Arguments

Details

This is the algorithm B.2 in the appendix of the Li and Linton (2019) working paper.

Value

integer containing the optimal kn

Note

We Thank Merrick Li for contributing his Matlab code for this estimator.

Author(s)

Emil Sjoerup.

References

Li, M. and Linton, O. (2019). A ReMeDI for microstructure noise. Cambridge Working Papers in Economics 1908.

Examples

optimalKn <- knChooseReMeDI(sampleTData[as.Date(DT) == "2018-01-02",],
                            knMax = 10, tol = 0.05, size = 3,
                            lower = 2, upper = 5, plot = TRUE)
optimalKn
## Not run: 
# We can also have a much larger search-space
optimalKn <- knChooseReMeDI(sampleTDataEurope,
                            knMax = 50, tol = 0.05,
                            size = 3, lower = 2, upper = 5, plot = TRUE)
optimalKn

## End(Not run)

Description

Function that estimates whether one series leads (or lags) another.

Let $X_{t}$ and $Y_{t}$ be two observed price over the time interval $[0,1]$.

For every integer $k \in \cal{Z}$, we form the shifted time series

$Y_{\left(k+i\right)/n}, \quad i = 1, 2, \dots$

$H=\left(\underline{H},\overline{H}\right]$ is an interval for $\vartheta\in\Theta$, define the shift interval $H_{\vartheta}=H+\vartheta=\left(\underline{H}+\vartheta,\overline{H}+\vartheta\right]$ then let

$X\left(H\right)_{t}=\int_{0}^{t}1_{H}\left(s\right)\textrm{d}X_{s}$

Which will be abbreviated:

$X\left(H\right)=X\left(H\right)_{T+\delta}=\int_{0}^{T+\delta}1_{H}\left(s\right)\textrm{d}X_{s}$

Then the shifted HY contrast function is:

$\tilde{\vartheta}\rightarrow U^{n}\left(\tilde{\vartheta}\right)= \\ 1_{\tilde{\vartheta}\geq0}\sum_{I\in{\cal{I}},J\in{\cal{J}},\overline{I}\leq T}X\left(I\right)Y\left(J\right)1_{\left\{ I\cap J_{-\tilde{\vartheta}}\neq\emptyset\right\}} \\ +1_{\tilde{\vartheta}<0}\sum_{I\in{\cal{I}},J\in{\cal{J}},\overline{J}\leq T}X\left(I\right)Y\left(Y\right)1_{\left\{ J\cap I_{\tilde{\vartheta}}\neq\emptyset\right\} }$

This contrast function is then calculated for all the lags passed in the argument lags

Usage

leadLag(
  price1 = NULL,
  price2 = NULL,
  lags = NULL,
  resolution = "seconds",
  normalize = TRUE,
  parallelize = FALSE,
  nCores = NA
)

Arguments

Details

The lead-lag-ratio (LLR) can be used to see if one asset leads the other. If LLR < 1, then price1 MAY be leading price2 and vice versa if LLR > 1.

Value

A list with class leadLag which contains contrasts, lead-lag-ratio, and lags, denoting the estimated values for each lag calculated, the lead-lag-ratio, and the tested lags respectively.

References

Hoffmann, M., Rosenbaum, M., and Yoshida, N. (2013). Estimation of the lead-lag parameter from non-synchronous data. Bernoulli, 19, 1-37.

Examples

## Not run: 
# Toy example to show the usage
# Spread prices
spread <- spreadPrices(sampleMultiTradeData[SYMBOL %in% c("ETF", "AAA")])
# Use lead-lag estimator
llEmpirical <- leadLag(spread[!is.na(AAA), list(DT, PRICE = AAA)], 
                       spread[!is.na(ETF), list(DT, PRICE = ETF)], seq(-15,15))
plot(llEmpirical)

## End(Not run)

Description

Returns a vector of the available kernels.

Usage

listAvailableKernels()

Details

The available kernels are:

• Rectangular: $K(x) = 1$.

• Bartlett: $K(x) = 1 - x$.

• Second-order: $K(x) = 1 - 2x - x^2$.

• Epanechnikov: $K(x) = 1 - x^2$.

• Cubic: $K(x) = 1 - 3 x^2 + 2 x^3$.

• Fifth: $K(x) = 1 - 10 x^3 + 15 x^4 - 6 x^5$.

• Sixth: $K(x) = 1 - 15 x^4 + 24 x^5 - 10 x^6$

• Seventh: $K(x) = 1 - 21 x^5 + 35 x^6 - 15 x^7$.

• Eighth: $K(x) = 1 - 28 x^6 + 48 x^7 - 21 x^8$.

• Parzen: $K(x) = 1- 6 x^2 + 6 x^3$ if $k \leq 0.5$ and $K(x) = 2 (1-x)^3$ if $k > 0.5$.

• TukeyHanning: $K(x) = 1 + \sin(\pi/2 - \pi \cdot x))/2$.

• ModifiedTukeyHanning: $K(x) = (1 - \sin(\pi/2 - \pi \ (1 - x)^2 ) / 2$.

Value

a character vector.

Author(s)

Scott Payseur.

References

Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., and Shephard, N. (2008). Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica, 76, 1481-1536.

Examples

listAvailableKernels

Description

Utility function listing the available estimators for the CholCov estimation

Usage

listCholCovEstimators()

Value

This function returns a character vector containing the available estimators.

Description

This function makes OHLC-V bars at arbitrary intervals. If the SIZE column is not present in the input, no volume column is created.

Usage

makeOHLCV(pData, alignBy = "minutes", alignPeriod = 5, tz = NULL)

Arguments