Package 'sovereign' reference manual

Title:	State-Dependent Empirical Analysis
Description:	A set of tools for state-dependent empirical analysis through both VAR- and local projection-based state-dependent forecasts, impulse response functions, historical decompositions, and forecast error variance decompositions.
Authors:	Tyler J. Pike [aut, cre]
Maintainer:	Tyler J. Pike <[email protected]>
License:	GPL-3
Version:	1.2.1
Built:	2024-11-26 04:23:36 UTC
Source:	https://github.com/tylerjpike/sovereign

Lenza-Primiceri Covid Shock Correction

Description

Implement the deterministic volatility correction method of Lenza, Michele and Giorgio Primiceri "How to Estimate a VAR after March 2020" (2020) [NBER Working Paper]. Correction factors are estimated via maximum likelihood.

Usage

covid_volatility_correction(var, theta_initial = c(5, 2, 1.5, 0.8))
covid_volatility_correction(var, theta_initial = c(5, 2, 1.5, 0.8))

Arguments

`var`	VAR object
`theta_initial`	double: four element vector with scaling parameters, theta in Lenza and Primiceri (2020)

Value

var object

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2018-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
 var =
   sovereign::VAR(
     data = Data,
     horizon = 10,
     freq = 'month',
     lag.ic = 'BIC',
     lag.max = 4)

# correct VAR for COVID shock
var = sovereign::covid_volatility_correction(var)

# impulse response functions
var.irf = sovereign::var_irf(var)

# forecast error variance decomposition
var.fevd = sovereign::var_fevd(var)

# historical shock decomposition
var.hd = sovereign::var_hd(var)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2018-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
 var =
   sovereign::VAR(
     data = Data,
     horizon = 10,
     freq = 'month',
     lag.ic = 'BIC',
     lag.max = 4)

# correct VAR for COVID shock
var = sovereign::covid_volatility_correction(var)

# impulse response functions
var.irf = sovereign::var_irf(var)

# forecast error variance decomposition
var.fevd = sovereign::var_fevd(var)

# historical shock decomposition
var.hd = sovereign::var_hd(var)

Estimate forecast error variance decomposition

Description

Estimate the forecast error variance decomposition for VARs with either short or 'IV-short' structural errors. See VAR and RVAR documentation for details regarding structural errors.

Usage

FEVD(model, horizon = 10, scale = TRUE)
FEVD(model, horizon = 10, scale = TRUE)

Arguments

`model`	VAR or RVAR class object
`horizon`	int: number of periods
`scale`	boolean: scale variable contribution as percent of total error

Value

long-form data.frame

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::IRF(var)

# forecast error variance decomposition
var.fevd = sovereign::FEVD(var)

# historical shock decomposition
var.hd = sovereign::HD(var)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::IRF(var)

# forecast error variance decomposition
var.fevd = sovereign::FEVD(var)

# historical shock decomposition
var.hd = sovereign::HD(var)

Estimate historical decomposition

Description

Estimate the historical decomposition for VARs with either 'short' or 'IV-short' structural errors. See VAR and RVAR documentation for details regarding structural errors.

Usage

HD(model)
HD(model)

Arguments

model

VAR or RVAR class object

Value

long-from data.frame

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::IRF(var)

# forecast error variance decomposition
var.fevd = sovereign::FEVD(var)

# historical shock decomposition
var.hd = sovereign::HD(var)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::IRF(var)

# forecast error variance decomposition
var.fevd = sovereign::FEVD(var)

# historical shock decomposition
var.hd = sovereign::HD(var)

Estimate impulse response functions

Description

See VAR, RVAR, LP, and RLP documentation for details regarding models and structural errors.

Usage

IRF(
  model,
  horizon = 10,
  CI = c(0.1, 0.9),
  bootstrap.type = "auto",
  bootstrap.num = 100,
  bootstrap.parallel = FALSE,
  bootstrap.cores = -1
)
IRF(
  model,
  horizon = 10,
  CI = c(0.1, 0.9),
  bootstrap.type = "auto",
  bootstrap.num = 100,
  bootstrap.parallel = FALSE,
  bootstrap.cores = -1
)

Arguments

`model`	VAR, RVAR, LP, or RLP class object
`horizon`	int: number of periods
`CI`	numeric vector: c(lower ci bound, upper ci bound)
`bootstrap.type`	string: bootstrapping technique to use ('auto', 'standard', or 'wild'); if auto then wild is used for IV or IV-short, else standard is used
`bootstrap.num`	int: number of bootstraps
`bootstrap.parallel`	boolean: create IRF draws in parallel
`bootstrap.cores`	int: number of cores to use in parallel processing; -1 detects and uses half the available cores

Value

data frame with columns target, shock, horizon, response.lower, response, response.upper; regime-based models return a list with a data frame per regime.

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4
    )

 # impulse response function
 var.irf = sovereign::IRF(var)

  # local projection forecasts
  lp =
    sovereign::LP(
      data = Data,
      horizon = c(1:10),
      lag.ic = 'AIC',
      lag.max = 4,
      type =  'both',
      freq = 'month')

  # LP impulse response function
  lp.irf = sovereign::IRF(lp)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4
    )

 # impulse response function
 var.irf = sovereign::IRF(var)

  # local projection forecasts
  lp =
    sovereign::LP(
      data = Data,
      horizon = c(1:10),
      lag.ic = 'AIC',
      lag.max = 4,
      type =  'both',
      freq = 'month')

  # LP impulse response function
  lp.irf = sovereign::IRF(lp)

Estimate local projections

Description

Estimate local projections

Usage

LP(
  data,
  horizons = 1,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  NW = FALSE,
  NW_lags = NULL,
  NW_prewhite = NULL
)
LP(
  data,
  horizons = 1,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  NW = FALSE,
  NW_lags = NULL,
  NW_prewhite = NULL
)

Arguments

`data`	data.frame, matrix, ts, xts, zoo: Endogenous regressors
`horizons`	int: forecast horizons
`freq`	string: frequency of data ('day', 'week', 'month', 'quarter', or 'year')
`type`	string: type of deterministic terms to add ('none', 'const', 'trend', or 'both')
`p`	int: lags
`lag.ic`	string: information criterion to choose the optimal number of lags ('AIC' or 'BIC')
`lag.max`	int: maximum number of lags to test in lag selection
`NW`	boolean: Newey-West correction on variance-covariance matrix
`NW_lags`	int: number of lags to use in Newey-West correction
`NW_prewhite`	boolean: TRUE prewhite option for Newey-West correction (see sandwich::NeweyWest)

Value

list object with elements data, model, forecasts, residuals; if there is more than one forecast horizon estimated, then model, forecasts, residuals will each be a list where each element corresponds to a single horizon

References

Jorda, Oscar "Estimation and Inference of Impulse Responses by Local Projections" 2005.

Examples



  # simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)

  # local projection forecasts
  lp =
    sovereign::LP(
      data = Data,
      horizon = c(1:10),
      lag.ic = 'AIC',
      lag.max = 4,
      type =  'both',
      freq = 'month')

  # impulse response function
  irf = sovereign::lp_irf(lp)



# simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)

  # local projection forecasts
  lp =
    sovereign::LP(
      data = Data,
      horizon = c(1:10),
      lag.ic = 'AIC',
      lag.max = 4,
      type =  'both',
      freq = 'month')

  # impulse response function
  irf = sovereign::lp_irf(lp)

Estimate impulse response functions

Description

Estimate impulse response functions

Usage

lp_irf(lp, CI = c(0.1, 0.9), regime = NULL)
lp_irf(lp, CI = c(0.1, 0.9), regime = NULL)

Arguments

`lp`	LP output
`CI`	numeric vector: c(lower ci bound, upper ci bound)
`regime`	string: indicates regime index column of data

Value

long-form data.frame with one row per target-shock-horizon identifier

Examples



  # simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)

  # local projection forecasts
  lp =
    sovereign::LP(
      data = Data,
      horizon = c(1:10),
      lag.ic = 'AIC',
      lag.max = 4,
      type =  'both',
      freq = 'month')

  # impulse response function
  irf = sovereign::lp_irf(lp)



# simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)

  # local projection forecasts
  lp =
    sovereign::LP(
      data = Data,
      horizon = c(1:10),
      lag.ic = 'AIC',
      lag.max = 4,
      type =  'both',
      freq = 'month')

  # impulse response function
  irf = sovereign::lp_irf(lp)

Chart residuals

Description

Chart residuals

Usage

plot_error(residuals, series = NULL, verticle = FALSE)
plot_error(residuals, series = NULL, verticle = FALSE)

Arguments

`residuals`	data.frame: sovereign residuals object
`series`	string: series to plot (default to all series)
`verticle`	boolean: If true then stack all plots into one column

Value

grid of ggplot2 graphs

Chart FEVDs

Description

Chart FEVDs

Usage

plot_fevd(fevd, responses = NULL, verticle = FALSE)
plot_fevd(fevd, responses = NULL, verticle = FALSE)

Arguments

`fevd`	fevd object
`responses`	string vector: responses to plot
`verticle`	boolean: If true then stack all plots into one column

Value

grid of ggplot2 graphs

Chart forecasts

Description

Chart forecasts

Usage

plot_forecast(forecasts, series = NULL, verticle = FALSE)
plot_forecast(forecasts, series = NULL, verticle = FALSE)

Arguments

`forecasts`	data.frame: sovereign forecast object
`series`	string: series to plot (default to all series)
`verticle`	boolean: If true then stack all plots into one column

Value

grid of ggplot2 graphs

Chart HDs

Description

Chart HDs

Usage

plot_hd(hd, verticle = FALSE)
plot_hd(hd, verticle = FALSE)

Arguments

`hd`	hd object
`verticle`	boolean: If true then stack all plots into one column

Value

grid of ggplot2 graphs

Chart individual residuals

Description

Chart individual residuals

Usage

plot_individual_error(
  data,
  target,
  title = NULL,
  ylab = NULL,
  freq = NULL,
  zeroline = FALSE
)
plot_individual_error(
  data,
  target,
  title = NULL,
  ylab = NULL,
  freq = NULL,
  zeroline = FALSE
)

Arguments

`data`	data.frame: sovereign residuals object
`target`	string: series to plot
`title`	string: chart title
`ylab`	string: y-axis label
`freq`	string: frequency (acts as sub-title)
`zeroline`	boolean: if TRUE then add a horizontal line at zero

Value

ggplot2 chart

Plot an individual FEVD

Description

Plot an individual FEVD

Usage

plot_individual_fevd(fevd, response.var, title, ylab)
plot_individual_fevd(fevd, response.var, title, ylab)

Arguments

`fevd`	fevd object
`response.var`	string: name of variable to treat as the response
`title`	string: title of the chart
`ylab`	string: y-axis label

Value

ggplot2 graph

Chart individual forecast

Description

Chart individual forecast

Usage

plot_individual_forecast(
  data,
  target,
  title = NULL,
  ylab = NULL,
  freq = NULL,
  zeroline = FALSE
)
plot_individual_forecast(
  data,
  target,
  title = NULL,
  ylab = NULL,
  freq = NULL,
  zeroline = FALSE
)

Arguments

`data`	data.frame: sovereign model forecast
`target`	string: series to plot
`title`	string: chart title
`ylab`	string: y-axis label
`freq`	string: frequency (acts as sub-title)
`zeroline`	boolean: if TRUE then add a horizontal line at zero

Value

ggplot2 chart

Plot an individual HD

Description

Plot an individual HD

Usage

plot_individual_hd(hd, target.var, title)
plot_individual_hd(hd, target.var, title)

Arguments

`hd`	hd object
`target.var`	string: name of variable to decompose into shocks
`title`	string: title of the chart

Value

ggplot2 graph

Plot an individual IRF

Description

Plot an individual IRF

Usage

plot_individual_irf(irf, shock.var, response.var, title, ylab)
plot_individual_irf(irf, shock.var, response.var, title, ylab)

Arguments

`irf`	irf object
`shock.var`	string: name of variable to treat as the shock
`response.var`	string: name of variable to treat as the response
`title`	string: title of the chart
`ylab`	string: y-axis label

Value

ggplot2 graph

Chart IRFs

Description

Chart IRFs

Usage

plot_irf(irf, shocks = NULL, responses = NULL, verticle = FALSE)
plot_irf(irf, shocks = NULL, responses = NULL, verticle = FALSE)

Arguments

`irf`	irf object
`shocks`	string vector: shocks to plot
`responses`	string vector: responses to plot
`verticle`	boolean: If true then stack all plots into one column

Value

grid of ggplot2 graphs

Identify regimes via unsupervised ML algorithms

Description

Regime assignment (clustering) methods available include the unsupervised random forest, k-mean clustering, Fraley and Raftery Model-based clustering EM algorithm, and the Bai & Perron (2003) method for simultaneous estimation of multiple breakpoints.

Usage

regimes(data, method = "rf", regime.n = NULL)
regimes(data, method = "rf", regime.n = NULL)

Arguments

`data`	data.frame, matrix, ts, xts, zoo: Endogenous regressors
`method`	string: regime assignment technique ('rf', 'kmeans', 'EM', or 'BP)
`regime.n`	int: number of regimes to estimate (applies to kmeans and EM)

Value

data as a data.frame with a regime column assigning rows to mutually exclusive regimes

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate reigme
 regime =
  sovereign::regimes(
     data = Data,
     method = 'kmeans',
     regime.n = 3)


# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate reigme
 regime =
  sovereign::regimes(
     data = Data,
     method = 'kmeans',
     regime.n = 3)

Estimate regime-dependent local projections

Description

Estimate a regime-dependent local projection (i.e. a state-dependent LP), with an exogenous state indicator, of the specification:

$Y_{t+h} = X_t \beta_{s_t} + \epsilon_t$

where t is the time index, and s is a mutually exclusive state of the world observed at time t. When the regime vector is not supplied by the user, then a two-state regime series is estimated via random forest.

Usage

RLP(
  data,
  horizons = 1,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  NW = FALSE,
  NW_lags = NULL,
  NW_prewhite = NULL,
  regime = NULL,
  regime.method = "rf",
  regime.n = 2
)
RLP(
  data,
  horizons = 1,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  NW = FALSE,
  NW_lags = NULL,
  NW_prewhite = NULL,
  regime = NULL,
  regime.method = "rf",
  regime.n = 2
)

Arguments

`data`	data.frame, matrix, ts, xts, zoo: Endogenous regressors
`horizons`	int: forecast horizons
`freq`	string: frequency of data ('day', 'week', 'month', 'quarter', or 'year')
`type`	string: type of deterministic terms to add ('none', 'const', 'trend', or 'both')
`p`	int: lags
`lag.ic`	string: information criterion to choose the optimal number of lags ('AIC' or 'BIC')
`lag.max`	int: maximum number of lags to test in lag selection
`NW`	boolean: Newey-West correction on variance-covariance matrix
`NW_lags`	int: number of lags to use in Newey-West correction
`NW_prewhite`	boolean: TRUE prewhite option for Newey-West correction (see sandwich::NeweyWest)
`regime`	string: name or regime assignment vector in the design matrix (data)
`regime.method`	string: regime assignment technique ('rf', 'kmeans', 'EM', 'BP')
`regime.n`	int: number of regimes to estimate (applies to kmeans and EM)

Value

list of lists, one list per regime, each regime with objects with elements data, model, forecasts, residuals; if there is more than one forecast horizon estimated, then model, forecasts, residuals will each be a list where each element corresponds to a single horizon

References

Jorda, Oscar "Estimation and Inference of Impulse Responses by Local Projections" 2005.

Examples



  # simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)
  # add regime
  Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

  # local projection forecasts
  rlp =
    sovereign::RLP(
      data = Data,
      regime = 'reg',
      horizon = c(1:10),
      freq = 'month',
      p = 1,
      type =  'const',
      NW = TRUE,
      NW_lags = 1,
      NW_prewhite = FALSE)

 # impulse response function
 rirf = sovereign::rlp_irf(rlp)



# simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)
  # add regime
  Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

  # local projection forecasts
  rlp =
    sovereign::RLP(
      data = Data,
      regime = 'reg',
      horizon = c(1:10),
      freq = 'month',
      p = 1,
      type =  'const',
      NW = TRUE,
      NW_lags = 1,
      NW_prewhite = FALSE)

 # impulse response function
 rirf = sovereign::rlp_irf(rlp)

Estimate regime-dependent impulse response functions

Description

Estimate regime-dependent impulse response functions

Usage

rlp_irf(rlp, CI = c(0.1, 0.9))
rlp_irf(rlp, CI = c(0.1, 0.9))

Arguments

`rlp`	RLP output
`CI`	numeric vector: c(lower ci bound, upper ci bound)

Value

list of long-form data.frame with one row per target-shock-horizon identifier

Examples



  # simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)
  # add regime
  Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

  # local projection forecasts
  rlp =
    sovereign::RLP(
      data = Data,
      regime = 'reg',
      horizon = c(1:10),
      freq = 'month',
      p = 1,,
      type =  'const',
      NW = TRUE,
      NW_lags = 1,
      NW_prewhite = FALSE)

 # impulse response function
 rirf = sovereign::rlp_irf(rlp)


# simple time series
  AA = c(1:100) + rnorm(100)
  BB = c(1:100) + rnorm(100)
  CC = AA + BB + rnorm(100)
  date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
  Data = data.frame(date = date, AA, BB, CC)
  # add regime
  Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

  # local projection forecasts
  rlp =
    sovereign::RLP(
      data = Data,
      regime = 'reg',
      horizon = c(1:10),
      freq = 'month',
      p = 1,,
      type =  'const',
      NW = TRUE,
      NW_lags = 1,
      NW_prewhite = FALSE)

 # impulse response function
 rirf = sovereign::rlp_irf(rlp)

Estimate regime-dependent VAR, SVAR, or Proxy-SVAR

Description

Estimate a regime-dependent VAR (i.e. a state-dependent VAR), with an exogenous state indicator, of the specification:

$Y_{t+1} = X_t \beta_{s_t} + \epsilon_t$

where t is the time index, Y is the set of outcome vectors, X the design matrix (of p lagged values of Y), and s is a mutually exclusive state of the world observed at time t. When the regime vector is not supplied by the user, then a two-state regime series is estimated via random forest.

Usage

RVAR(
  data,
  horizon = 10,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  regime = NULL,
  regime.method = "rf",
  regime.n = 2,
  structure = "short",
  instrument = NULL,
  instrumented = NULL
)
RVAR(
  data,
  horizon = 10,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  regime = NULL,
  regime.method = "rf",
  regime.n = 2,
  structure = "short",
  instrument = NULL,
  instrumented = NULL
)

Arguments

`data`	data.frame, matrix, ts, xts, zoo: Endogenous regressors
`horizon`	int: forecast horizons
`freq`	string: frequency of data ('day', 'week', 'month', 'quarter', or 'year')
`type`	string: type of deterministic terms to add ('none', 'const', 'trend', or 'both')
`p`	int: lags
`lag.ic`	string: information criterion to choose the optimal number of lags ('AIC' or 'BIC')
`lag.max`	int: maximum number of lags to test in lag selection
`regime`	string: name or regime assignment vector in the design matrix (data)
`regime.method`	string: regime assignment technique ('rf', 'kmeans', 'EM', or 'BP')
`regime.n`	int: number of regimes to estimate (applies to kmeans and EM)
`structure`	string: type of structural identification strategy to use in model analysis (NA, 'short', 'IV', or 'IV-short')
`instrument`	string: name of instrumental variable contained in the data matrix
`instrumented`	string: name of variable to be instrumented in IV and IV-short procedure; default is the first non-date variable in data

Details

The regime-dependent VAR is a generalization of the popular threshold VAR - which trades off estimating a threshold value for an endogenous variable for accepting an exogenous regime that can be based on information from inside or outside of the system, with or without parametric assumptions, and with or without timing restrictions. Moreover, the RVAR may be extended to include structural shocks, including the use of instrumental variables.

State dependence. The RVAR augments the traditional VAR by allowing state-dependence in the coefficient matrix. The RVAR differs from the more common threshold VAR (TVAR), due to the fact that states are exegonesouly determined. As a result, the states (i.e. regimes) do not need to be based on information inside the model, moreover, regimes can be determined by any process the user determines best fits their needs. For example, regimes based on NBER dated recessions and expansions are based on a judgmental process considering hundreds of series, potentially none of which are in the VAR being modeled. Alternatively, a user may use unsupervised machine learning to assign regimes - this is the process the sovereign::regimes function facilitates.

Structural shocks. See Sims (1980) for details regarding the baseline vector-autoregression (VAR) model. The VAR may be augmented to become a structural VAR (SVAR) with one of three different structural identification strategies:

short-term impact restrictions via Cholesky decomposition, see Christiano et al (1999) for details (structure = 'short')
external instrument identification, i.e. a Proxy-SVAR strategy, see Mertens and Ravn (2013) for details (structure = 'IV')
or a combination of short-term and IV identification via Lunsford (2015) (structure = 'IV-short')

Note that including structure does not change the estimation of model coefficients or forecasts, but does change impulse response functions, forecast error variance decomposition, and historical decompositions. Historical decompositions will not be available for models using the 'IV' structure. Additionally note that only one instrument may be used in this estimation routine.

Value

List of lists, where each regime is a list with items:

data: data.frame with endogenous variables and 'date' column.
model: list with data.frame of model coefficients (in psuedo-companion form), data.frame of coefficient standard errors, integer of lags p, integer of horizons, string of frequency, string of deterministic term type, numeric of log-likelihood, regime indicator
forecasts: list of data.frames per horizon; data.frame with column for date (day the forecast was made), forecast.date (the date being forecasted), target (variable forecasted), and forecast
residuals: list of data.frames per horizon; data.frame of residuals
structure: string denoting which structural identification strategy will be used in analysis (or NA)
instrument: data.frame with 'date' column and 'instrument' column (or NULL)
instrumented: string denoting which column will be instrumted in 'IV' and 'IV-short' strategies (or NULL)

References

Christiano, Lawrence, Martin Eichenbaum, and Charles Evans "Monetary policy shocks: What have we learned and to what end?" Handbook of Macroeconomics, Vol 1, Part A, 1999.
Lunsford, Kurt "Identifying Structural VARs with a Proxy Variable and a Test for a Weak Proxy" 2015.
Mertens, Karel and Morten Ravn "The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States" 2013.
Sims, Christopher "Macroeconomics and Reality" 1980.

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate regime-dependent VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

 # impulse response functions
 rvar.irf = sovereign::rvar_irf(rvar)

 # forecast error variance decomposition
 rvar.fevd = sovereign::rvar_fevd(rvar)

 # historical shock decomposition
 rvar.hd = sovereign::rvar_hd(rvar)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate regime-dependent VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

 # impulse response functions
 rvar.irf = sovereign::rvar_irf(rvar)

 # forecast error variance decomposition
 rvar.fevd = sovereign::rvar_fevd(rvar)

 # historical shock decomposition
 rvar.hd = sovereign::rvar_hd(rvar)

Estimate regime-dependent forecast error variance decomposition

Description

Estimate forecast error variance decomposition for RVARs with either short or 'IV-short' structural errors.

Usage

rvar_fevd(rvar, horizon = 10, scale = TRUE)
rvar_fevd(rvar, horizon = 10, scale = TRUE)

Arguments

`rvar`	RVAR output
`horizon`	int: number of periods
`scale`	boolean: scale variable contribution as percent of total error

Value

list, each regime returns its own long-form data.frame

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
rvar.irf = sovereign::rvar_irf(rvar)

# forecast error variance decomposition
rvar.fevd = sovereign::rvar_fevd(rvar)

# historical shock decomposition
rvar.hd = sovereign::rvar_hd(rvar)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
rvar.irf = sovereign::rvar_irf(rvar)

# forecast error variance decomposition
rvar.fevd = sovereign::rvar_fevd(rvar)

# historical shock decomposition
rvar.hd = sovereign::rvar_hd(rvar)

Estimate regime-dependent historical decomposition

Description

Estimate historical decomposition for RVARs with either short or 'IV-short' structural errors.

Usage

rvar_hd(rvar)
rvar_hd(rvar)

Arguments

rvar

RVAR output

Value

long form data.frames

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
rvar.irf = sovereign::rvar_irf(rvar)

# forecast error variance decomposition
rvar.fevd = sovereign::rvar_fevd(rvar)

# historical shock decomposition
rvar.hd = sovereign::rvar_hd(rvar)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
rvar.irf = sovereign::rvar_irf(rvar)

# forecast error variance decomposition
rvar.fevd = sovereign::rvar_fevd(rvar)

# historical shock decomposition
rvar.hd = sovereign::rvar_hd(rvar)

Estimate regime-dependent impulse response functions

Description

Estimate regime-dependent impulse response functions

Usage

rvar_irf(
  rvar,
  horizon = 10,
  CI = c(0.1, 0.9),
  bootstrap.type = "auto",
  bootstrap.num = 100,
  bootstrap.parallel = FALSE,
  bootstrap.cores = -1
)
rvar_irf(
  rvar,
  horizon = 10,
  CI = c(0.1, 0.9),
  bootstrap.type = "auto",
  bootstrap.num = 100,
  bootstrap.parallel = FALSE,
  bootstrap.cores = -1
)

Arguments

`rvar`	RVAR output
`horizon`	int: number of periods
`CI`	numeric vector: c(lower ci bound, upper ci bound)
`bootstrap.type`	string: bootstrapping technique to use ('auto', 'standard', or 'wild'); if auto then wild is used for IV or IV-short, else standard is used
`bootstrap.num`	int: number of bootstraps
`bootstrap.parallel`	boolean: create IRF draws in parallel
`bootstrap.cores`	int: number of cores to use in parallel processing; -1 detects and uses half the available cores

Value

list of regimes, each with data.frame of columns target, shock, horizon, response.lower, response, response.upper

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

 # impulse response functions
 rvar.irf = sovereign::rvar_irf(rvar)

 # forecast error variance decomposition
 rvar.fevd = sovereign::rvar_fevd(rvar)

 # historical shock decomposition
 rvar.hd = sovereign::rvar_hd(rvar)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)
 Data = dplyr::mutate(Data, reg = dplyr::if_else(AA > median(AA), 1, 0))

 # estimate VAR
  rvar =
    sovereign::RVAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      regime.method = 'rf',
      regime.n = 2,
      lag.ic = 'BIC',
      lag.max = 4)

 # impulse response functions
 rvar.irf = sovereign::rvar_irf(rvar)

 # forecast error variance decomposition
 rvar.fevd = sovereign::rvar_fevd(rvar)

 # historical shock decomposition
 rvar.hd = sovereign::rvar_hd(rvar)

Estimate VAR, SVAR, or Proxy-SVAR

Description

Estimate VAR, SVAR, or Proxy-SVAR

Usage

VAR(
  data,
  horizon = 10,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  structure = "short",
  instrument = NULL,
  instrumented = NULL
)
VAR(
  data,
  horizon = 10,
  freq = "month",
  type = "const",
  p = 1,
  lag.ic = NULL,
  lag.max = NULL,
  structure = "short",
  instrument = NULL,
  instrumented = NULL
)

Arguments

`data`	data.frame, matrix, ts, xts, zoo: Endogenous regressors
`horizon`	int: forecast horizons
`freq`	string: frequency of data ('day', 'week', 'month', 'quarter', or 'year')
`type`	string: type of deterministic terms to add ('none', 'const', 'trend', or 'both')
`p`	int: lags
`lag.ic`	string: information criterion to choose the optimal number of lags ('AIC' or 'BIC')
`lag.max`	int: maximum number of lags to test in lag selection
`structure`	string: type of structural identification strategy to use in model analysis (NA, 'short', 'IV', or 'IV-short')
`instrument`	string: name of instrumental variable contained in the data matrix
`instrumented`	string: name of variable to be instrumented in IV and IV-short procedure; default is the first non-date variable in data

Details

See Sims (1980) for details regarding the baseline vector-autoregression (VAR) model. The VAR may be augmented to become a structural VAR (SVAR) with one of three different structural identification strategies:

short-term impact restrictions via Cholesky decomposition, see Christiano et al (1999) for details (structure = 'short')
external instrument identification, i.e. a Proxy-SVAR strategy, see Mertens and Ravn (2013) for details (structure = 'IV')
or a combination of short-term and IV identification via Lunsford (2015) (structure = 'IV-short')

Value

data: data.frame with endogenous variables and 'date' column.
model: list with data.frame of model coefficients (in psuedo-companion form), data.frame of coefficient standard errors, integer of lags p, integer of horizons, string of frequency, string of deterministic term type, numeric of log-likelihood
forecasts: list of data.frames per horizon; data.frame with column for date (day the forecast was made), forecast.date (the date being forecasted), target (variable forecasted), and forecast
residuals: list of data.frames per horizon; data.frame of residuals
structure: string denoting which structural identification strategy will be used in analysis (or NA)
instrument: data.frame with 'date' column and 'instrument' column (or NULL)
instrumented: string denoting which column will be instrumted in 'IV' and 'IV-short' strategies (or NA)

References

Christiano, Lawrence, Martin Eichenbaum, and Charles Evans "Monetary policy shocks: What have we learned and to what end?" Handbook of Macroeconomics, Vol 1, Part A, 1999.
Lunsford, Kurt "Identifying Structural VARs with a Proxy Variable and a Test for a Weak Proxy" 2015.
Mertens, Karel and Morten Ravn "The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States" 2013.
Sims, Christopher "Macroeconomics and Reality" 1980.

Examples


 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

  # impulse response functions
  var.irf = sovereign::var_irf(var)

  # forecast error variance decomposition
  var.fevd = sovereign::var_fevd(var)

  # historical shock decomposition
  var.hd = sovereign::var_hd(var)


# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

  # impulse response functions
  var.irf = sovereign::var_irf(var)

  # forecast error variance decomposition
  var.fevd = sovereign::var_fevd(var)

  # historical shock decomposition
  var.hd = sovereign::var_hd(var)

Estimate forecast error variance decomposition

Description

Estimate forecast error variance decomposition for VARs with either short or 'IV-short' structural errors.

Usage

var_fevd(var, horizon = 10, scale = TRUE)
var_fevd(var, horizon = 10, scale = TRUE)

Arguments

`var`	VAR output
`horizon`	int: number of periods
`scale`	boolean: scale variable contribution as percent of total error

Value

long-form data.frame

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::var_irf(var)

# forecast error variance decomposition
var.fevd = sovereign::var_fevd(var)

# historical shock decomposition
var.hd = sovereign::var_hd(var)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::var_irf(var)

# forecast error variance decomposition
var.fevd = sovereign::var_fevd(var)

# historical shock decomposition
var.hd = sovereign::var_hd(var)

Estimate historical decomposition

Description

Estimate historical decomposition for VARs with either short or 'IV-short' structural errors.

Usage

var_hd(var)
var_hd(var)

Arguments

var

VAR output

Value

long-from data.frame

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::var_irf(var)

# forecast error variance decomposition
var.fevd = sovereign::var_fevd(var)

# historical shock decomposition
var.hd = sovereign::var_hd(var)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

# impulse response functions
var.irf = sovereign::var_irf(var)

# forecast error variance decomposition
var.fevd = sovereign::var_fevd(var)

# historical shock decomposition
var.hd = sovereign::var_hd(var)

Estimate impulse response functions

Description

Estimate impulse response functions

Usage

var_irf(
  var,
  horizon = 10,
  CI = c(0.1, 0.9),
  bootstrap.type = "auto",
  bootstrap.num = 100,
  bootstrap.parallel = FALSE,
  bootstrap.cores = -1
)
var_irf(
  var,
  horizon = 10,
  CI = c(0.1, 0.9),
  bootstrap.type = "auto",
  bootstrap.num = 100,
  bootstrap.parallel = FALSE,
  bootstrap.cores = -1
)

Arguments

`var`	VAR output
`horizon`	int: number of periods
`CI`	numeric vector: c(lower ci bound, upper ci bound)
`bootstrap.type`	string: bootstrapping technique to use ('auto', 'standard', or 'wild'); if auto then wild is used for IV or IV-short, else standard is used
`bootstrap.num`	int: number of bootstraps
`bootstrap.parallel`	boolean: create IRF draws in parallel
`bootstrap.cores`	int: number of cores to use in parallel processing; -1 detects and uses half the available cores

Value

data.frame with columns target, shock, horizon, response.lower, response, response.upper

Examples



 # simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

 # impulse response functions
 var.irf = sovereign::var_irf(var)

 # forecast error variance decomposition
 var.fevd = sovereign::var_fevd(var)

 # historical shock decomposition
 var.hd = sovereign::var_hd(var)



# simple time series
 AA = c(1:100) + rnorm(100)
 BB = c(1:100) + rnorm(100)
 CC = AA + BB + rnorm(100)
 date = seq.Date(from = as.Date('2000-01-01'), by = 'month', length.out = 100)
 Data = data.frame(date = date, AA, BB, CC)

 # estimate VAR
  var =
    sovereign::VAR(
      data = Data,
      horizon = 10,
      freq = 'month',
      lag.ic = 'BIC',
      lag.max = 4)

 # impulse response functions
 var.irf = sovereign::var_irf(var)

 # forecast error variance decomposition
 var.fevd = sovereign::var_fevd(var)

 # historical shock decomposition
 var.hd = sovereign::var_hd(var)

Package 'sovereign'

Help Index

Lenza-Primiceri Covid Shock Correction

Description

Usage

Arguments

Value

See Also

Examples

Estimate forecast error variance decomposition

Description

Usage

Arguments

Value

See Also

Examples

Estimate historical decomposition

Description

Usage

Arguments

Value

See Also

Examples

Estimate impulse response functions

Description

Usage

Arguments

Value

See Also

Examples

Estimate local projections

Description

Usage

Arguments

Value

References

See Also

Examples

Estimate impulse response functions

Description

Usage

Arguments

Value

See Also

Examples

Chart residuals

Description

Usage

Arguments

Value

Chart FEVDs

Description

Usage

Arguments

Value

Chart forecasts

Description

Usage

Arguments

Value

Chart HDs

Description

Usage

Arguments

Value

Chart individual residuals

Description

Usage

Arguments

Value

Plot an individual FEVD

Description

Usage

Arguments

Value

Chart individual forecast

Description

Usage

Arguments

Value