| Title: | Sparse Estimation of Large Time Series Models |
|---|---|
| Description: | Estimation of large Vector AutoRegressive (VAR), Vector AutoRegressive with Exogenous Variables X (VARX) and Vector AutoRegressive Moving Average (VARMA) Models with Structured Lasso Penalties, see Nicholson, Wilms, Bien and Matteson (2020) <https://jmlr.org/papers/v21/19-777.html> and Wilms, Basu, Bien and Matteson (2021) <doi:10.1080/01621459.2021.1942013>. |
| Authors: | Ines Wilms [cre, aut], David S. Matteson [aut], Jacob Bien [aut], Sumanta Basu [aut], Will Nicholson [aut], Enrico Wegner [aut] |
| Maintainer: | Ines Wilms <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.2.3 |
| Built: | 2024-11-13 06:30:23 UTC |
| Source: | CRAN |
The bigtime package provides sparse estimators for three large time series models: Vector AutoRegressive Models, Vector AutoRegressive Models with Exogenous variables, and Vector AutoRegressive Moving Average Models. The univariate cases are also supported.
To use the facilities of this package, start with a T by k time series matrix Y (for the VAR and VARMA), and an exogenous time series matrix X (for the VARX). Run sparseVAR, sparseVARX or sparseVARMA to get the estimated model. The function lagmatrix returns the lag matrix of estimated coefficients of the estimated model. The function directforecast gives h-step ahead forecasts based on the estimated model. The function recursiveforecast can be used to recursively forecast a VAR model. The function is.stable returns whether an estimated VAR model is stable. The function diagnostics_plot returns a plot of the fitted vs. observed values as well as of the residuals. The functions fitted and residuals return the fitted, respectively the residuals of the estimated model. The function simVAR can be used to simulate a VAR model with various sparsity patterns.
Ines Wilms <[email protected]>, Jacob Bien, David S. Matteson, Sumanta Basu, Will Nicholson, Enrico Wegner
Nicholson William B., Wilms Ines, Bien Jacob and Matteson David S. (2020), “High-dimensional forecasting via interpretable vector autoregression”, Journal of Machine Learning Research, 21(166), 1-52.
Wilms Ines, Sumanta Basu, Bien Jacob and Matteson David S. (2021), “Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages”, Journal of the American Statistical Association, doi: 10.1080/01621459.2021.1942013.
# Fit a sparse VAR model data(var.example) VARfit <- sparseVAR(Y=scale(Y.var), selection = "cv") # using time series cross-validation Lhat <- lagmatrix(fit=VARfit) # get estimated lagmatrix VARforecast <- directforecast(fit=VARfit, h=1) # get one-step ahead forecasts# Fit a sparse VAR model data(var.example) VARfit <- sparseVAR(Y=scale(Y.var), selection = "cv") # using time series cross-validation Lhat <- lagmatrix(fit=VARfit) # get estimated lagmatrix VARforecast <- directforecast(fit=VARfit, h=1) # get one-step ahead forecasts
Creates a random coefficient matrix
create_rand_coef_mat( k, p, max_abs_eigval = 0.8, sparsity_pattern = c("none", "lasso", "hvar"), sparsity_options = NULL, decay = 0.5, ... )create_rand_coef_mat( k, p, max_abs_eigval = 0.8, sparsity_pattern = c("none", "lasso", "hvar"), sparsity_options = NULL, decay = 0.5, ... )
k |
Number of time series |
p |
Number of lags |
max_abs_eigval |
if < 1, then the VAR will be stable |
sparsity_pattern |
The sparsity pattern that should be simulated.
Options are: |
sparsity_options |
Named list of additional options for
when sparsity pattern is lasso or hvar. For lasso the option |
decay |
How fast should coefficients shrink when the lag increases. |
... |
Not currently used |
Returns a coefficient matrix in companion form of dimension kpxkp.
Creates a Diagnostic Plot
diagnostics_plot(mod, variable = 1, dates = NULL)diagnostics_plot(mod, variable = 1, dates = NULL)
mod |
VAR model estimated using |
variable |
Variable to show. Either numeric (which column) or character (variable name) |
dates |
Optional Date vector. |
Returns a ggplot2 plot
# VAR example dat <- simVAR(periods=200, k=2, p=5, decay = 0.1, seed = 6150533, sparsity_pattern = "hvar") mod <- sparseVAR(Y=scale(dat$Y), selection = "bic", h = 1) diagnostics_plot(mod, variable = 1) # Plotting the first variable ## Not run: # VARMA example data(varma.example) varma <- sparseVARMA(Y=scale(Y.varma), VARMAselection="cv") diagnostics_plot(varma, variable = 2) # Plotting the second variable ## End(Not run) ## Not run: # VARX example data(varx.example) varx <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx), selection="cv") diagnostics_plot(varx, variable = 1) # Plotting the first variable ## End(Not run)# VAR example dat <- simVAR(periods=200, k=2, p=5, decay = 0.1, seed = 6150533, sparsity_pattern = "hvar") mod <- sparseVAR(Y=scale(dat$Y), selection = "bic", h = 1) diagnostics_plot(mod, variable = 1) # Plotting the first variable ## Not run: # VARMA example data(varma.example) varma <- sparseVARMA(Y=scale(Y.varma), VARMAselection="cv") diagnostics_plot(varma, variable = 2) # Plotting the second variable ## End(Not run) ## Not run: # VARX example data(varx.example) varx <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx), selection="cv") diagnostics_plot(varx, variable = 1) # Plotting the first variable ## End(Not run)
Not supposed to be called directly. Rather call diagnostics_plot
## S3 method for class 'bigtime.VAR' diagnostics_plot(mod, variable = 1, dates = NULL)## S3 method for class 'bigtime.VAR' diagnostics_plot(mod, variable = 1, dates = NULL)
mod |
VAR model estimated using |
variable |
Variable to show. Either numeric (which column) or character (variable name) |
dates |
Optional Date vector. |
Not supposed to be called directly. Rather call diagnostics_plot
## S3 method for class 'bigtime.VARMA' diagnostics_plot(mod, variable = 1, dates = NULL)## S3 method for class 'bigtime.VARMA' diagnostics_plot(mod, variable = 1, dates = NULL)
mod |
VAR model estimated using |
variable |
Variable to show. Either numeric (which column) or character (variable name) |
dates |
Optional Date vector. |
Not supposed to be called directly. Rather call diagnostics_plot
## S3 method for class 'bigtime.VARX' diagnostics_plot(mod, variable = 1, dates = NULL)## S3 method for class 'bigtime.VARX' diagnostics_plot(mod, variable = 1, dates = NULL)
mod |
VARX model estimated using |
variable |
Variable to show. Either numeric (which column) or character (variable name) |
dates |
Optional Date vector. |
Function to obtain h-step ahead direct forecast based on estimated VAR, VARX or VARMA model
directforecast(fit, h = 1)directforecast(fit, h = 1)
fit |
Fitted sparse VAR, VARX or VARMA model. |
h |
Desired forecast horizon. Default is h=1. |
Vector of length k containing the h-step ahead forecasts for the k time series.
data(var.example) VARfit <- sparseVAR(Y=scale(Y.var), selection = "cv") # sparse VAR VARforecast <- directforecast(fit=VARfit, h=1)data(var.example) VARfit <- sparseVAR(Y=scale(Y.var), selection = "cv") # sparse VAR VARforecast <- directforecast(fit=VARfit, h=1)
sparseVAR
Gives the fitted values of a model estimated using
sparseVAR
## S3 method for class 'bigtime.VAR' fitted(object, ...)## S3 method for class 'bigtime.VAR' fitted(object, ...)
object |
Model estimated using |
... |
Not currently used |
Returns a matrix of fitted values
dat <- simVAR(periods=200, k=2, p=5, decay = 0.001, seed = 6150533) mod <- sparseVAR(Y=scale(dat$Y)) f <- fitted(mod)dat <- simVAR(periods=200, k=2, p=5, decay = 0.001, seed = 6150533) mod <- sparseVAR(Y=scale(dat$Y)) f <- fitted(mod)
sparseVARMA
Gives the fitted values of a model estimated using
sparseVARMA
## S3 method for class 'bigtime.VARMA' fitted(object, ...)## S3 method for class 'bigtime.VARMA' fitted(object, ...)
object |
Model estimated using |
... |
Not currently used |
Returns a matrix of fitted values data(varma.example) varma <- sparseVARMA(Y = scale(Y.varma), VARMAselection="cv") f <- fitted(varma)
sparseVARX
Gives the fitted values of a model estimated using
sparseVARX
## S3 method for class 'bigtime.VARX' fitted(object, ...)## S3 method for class 'bigtime.VARX' fitted(object, ...)
object |
Model estimated using |
... |
Not currently used |
Returns a matrix of fitted values data(varx.example) varx <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx), selection="cv") fit <- fitted(varx)
The number of non-zero coefficients are taken as the degrees of freedom. Use with care for VARMA.
get_ic_vals(mod, verbose = TRUE)get_ic_vals(mod, verbose = TRUE)
mod |
Model estimated Model estimated using |
verbose |
Should information about the optimal selection be printed? |
dat <- simVAR(periods=200, k=2, p=5, decay = 0.01) mod <- sparseVAR(Y=scale(dat$Y)) ics <- get_ic_vals(mod)dat <- simVAR(periods=200, k=2, p=5, decay = 0.01) mod <- sparseVAR(Y=scale(dat$Y)) ics <- get_ic_vals(mod)
sparseVAR
The number of non-zero coefficients are taken as the degrees of freedom.
## S3 method for class 'bigtime.VAR' get_ic_vals(mod, verbose = TRUE)## S3 method for class 'bigtime.VAR' get_ic_vals(mod, verbose = TRUE)
mod |
Model estimated using |
verbose |
Should information about the optimal selection be printed? |
Returns a list containing
ics |
Values of the ICs for all lambdas |
mins |
Which IC lead to the minimum (the row number) |
selected_lambdas |
Which lambdas were selected |
dat <- simVAR(periods = 200, k=2, p=5, decay = 0.01) mod <- sparseVAR(Y=scale(dat$Y)) ics <- get_ic_vals(mod)dat <- simVAR(periods = 200, k=2, p=5, decay = 0.01) mod <- sparseVAR(Y=scale(dat$Y)) ics <- get_ic_vals(mod)
sparseVARX
The number of non-zero coefficients in both the Phihat
and Bhat matrix are taken as the degrees of freedom.
## S3 method for class 'bigtime.VARX' get_ic_vals(mod, verbose = TRUE)## S3 method for class 'bigtime.VARX' get_ic_vals(mod, verbose = TRUE)
mod |
Model estimated using |
verbose |
Should information about the optimal selection be printed? |
Returns a list containing
ics |
Values of the ICs for all lambdas |
mins |
Which IC lead to the minimum (the row number) |
selected_lamPhi |
Which lambda Phi were selected |
selected_lamB |
Which lambda B were selected |
Selects the optimal penalty parameter using information criteria
ic_selection(mod, ic = c("bic", "aic", "hq"), verbose = FALSE)ic_selection(mod, ic = c("bic", "aic", "hq"), verbose = FALSE)
mod |
Model estimated Model estimated using |
ic |
Which information criteria should be used. Must be one of
|
verbose |
If true, some useful information will be printed during the process |
Returns a model that uses the optimal penalty
Using a model estimated by sparseVAR, this function checks whether
the resulting VAR is stable. This is the case, whenever the maximum absolute
eigenvalue of the companion matrix corresponding to the VAR is less than one.
This is sometimes also referred to as that the root lies outside the unit circle.
is.stable(mod, verbose = FALSE)is.stable(mod, verbose = FALSE)
mod |
Model estimated using |
verbose |
If |
Returns TRUE if the VAR is stable and FALSE otherwise
Creates Lagmatrix of Estimated Coefficients
lagmatrix(fit, returnplot = F)lagmatrix(fit, returnplot = F)
fit |
Fitted VAR, VARX or VARMA model. |
returnplot |
TRUE or FALSE: return plot of lag matrix or not. |
A list with estimated lag matrix of the VAR model, or lag matrices of the VARX or VARMA model. The rows contain the responses, the columns contain the predictors.
data(var.example) mod <- sparseVAR(Y=scale(Y.var), selection="cv") Lhat <- lagmatrix(fit=mod)data(var.example) mod <- sparseVAR(Y=scale(Y.var), selection="cv") Lhat <- lagmatrix(fit=mod)
Plot the Cross Validation Error Curve for a Sparse VAR or VARX
plot_cv(fit, ...)plot_cv(fit, ...)
fit |
Fitted VAR, VARMA or VARX model.
returned by |
... |
Not currently used |
Plots the recursive forecast obtained using recursiveforecast
When forecasts were made for multiple lambdas and lmbda is not a single
number, then a ribbon will be plotted that reaches from the minimum estimate
of all lambdas to the maximum.
## S3 method for class 'bigtime.recursiveforecast' plot(x, series = NULL, lmbda = NULL, last_n = floor(nrow(fcst$Y) * 0.1), ...)## S3 method for class 'bigtime.recursiveforecast' plot(x, series = NULL, lmbda = NULL, last_n = floor(nrow(fcst$Y) * 0.1), ...)
x |
Recursive Forecast obtained using |
series |
Series name. If original data has no names, then use Y1 for the first series, Y2 for the second, and so on. |
lmbda |
Lambdas to be used for plotting. If forecast was done using only one lambda, then this will be ignored. |
last_n |
Last |
... |
Not currently used |
If lmbda is of length one or forecasts were made using only one lambda,
then only a line will be plotted.
Default names for series are Y1, Y2, ... if the original data does not have any column names.
Returns a ggplot
Plots a simulated VAR
## S3 method for class 'bigtime.simVAR' plot(x, ...)## S3 method for class 'bigtime.simVAR' plot(x, ...)
x |
Simulated data of class |
... |
Not currently used |
Returns a ggplot2 plot
Recursively forecasts a VAR estimated using sparseVAR. lambda can either be NULL, in which case all lambdas that were used for model estimation are used for forecasting, or a single value, in which case only the model using this lambda will be used for forecasting.
recursiveforecast(mod, h = 1, lambda = NULL)recursiveforecast(mod, h = 1, lambda = NULL)
mod |
VAR model estimated using |
h |
Desired forecast horizon. Default is h=1. |
lambda |
Either |
Returns an object of S3 class bigtime.recursiveforecast containing
fcst |
Matrix or 3D array of forecasts |
h |
Selected forecast horizon |
lambda |
List of lambdas for which the forecasts were made |
Y |
Data used for recursive forecasting |
sim_data <- simVAR(periods=200, k=5, p=5, seed = 12345) summary(sim_data) mod <- sparseVAR(Y=scale(sim_data$Y), selection = "bic") is.stable(mod) fcst_recursive <- recursiveforecast(mod, h = 4) plot(fcst_recursive, series = "Y1") fcst_direct <- directforecast(mod) fcst_direct fcst_recursive$fcstsim_data <- simVAR(periods=200, k=5, p=5, seed = 12345) summary(sim_data) mod <- sparseVAR(Y=scale(sim_data$Y), selection = "bic") is.stable(mod) fcst_recursive <- recursiveforecast(mod, h = 4) plot(fcst_recursive, series = "Y1") fcst_direct <- directforecast(mod) fcst_direct fcst_recursive$fcst
sparseVAR
Gives the residuals for VAR models estimated using
sparseVAR
## S3 method for class 'bigtime.VAR' residuals(object, ...)## S3 method for class 'bigtime.VAR' residuals(object, ...)
object |
Model estimated using |
... |
Not currently used |
Returns a matrix of residuals.
dat <- simVAR(periods=200, k=2, p=5, decay = 0.001, seed = 6150533) mod <- sparseVAR(Y=scale(dat$Y)) res <- resid(mod)dat <- simVAR(periods=200, k=2, p=5, decay = 0.001, seed = 6150533) mod <- sparseVAR(Y=scale(dat$Y)) res <- resid(mod)
sparseVARMA
Gives the residuals for VARMA models estimated using
sparseVARMA
## S3 method for class 'bigtime.VARMA' residuals(object, ...)## S3 method for class 'bigtime.VARMA' residuals(object, ...)
object |
Model estimated using |
... |
Not currently used |
Returns a matrix of residuals.
## Not run: data(varma.example) varma <- sparseVARMA(Y = scale(Y.varma), VARMAselection="cv") res <- residuals(varma) ## End(Not run)## Not run: data(varma.example) varma <- sparseVARMA(Y = scale(Y.varma), VARMAselection="cv") res <- residuals(varma) ## End(Not run)
sparseVARX
Gives the residuals for VARX models estimated using
sparseVARX
## S3 method for class 'bigtime.VARX' residuals(object, ...)## S3 method for class 'bigtime.VARX' residuals(object, ...)
object |
Model estimated using |
... |
Not currently used |
Returns a matrix of residuals.
## Not run: data(varx.example) varx <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx), selection="cv") res <- residuals(varx) ## End(Not run)## Not run: data(varx.example) varx <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx), selection="cv") res <- residuals(varx) ## End(Not run)
Simulates a VAR(p) with various sparsity patterns
simVAR( periods, k, p, coef_mat = NULL, const = rep(0, k), e_dist = rnorm, init_y = rep(0, k * p), max_abs_eigval = 0.8, burnin = periods, sparsity_pattern = c("none", "lasso", "L1", "hvar", "HLag"), sparsity_options = NULL, decay = 1/p, seed = NULL, ... )simVAR( periods, k, p, coef_mat = NULL, const = rep(0, k), e_dist = rnorm, init_y = rep(0, k * p), max_abs_eigval = 0.8, burnin = periods, sparsity_pattern = c("none", "lasso", "L1", "hvar", "HLag"), sparsity_options = NULL, decay = 1/p, seed = NULL, ... )
periods |
Scalar indicating the desired time series length |
k |
Number of time series |
p |
Maximum lag number. In case of |
coef_mat |
Coefficient matrix in companion form. If not provided, one will be simulated |
const |
Constant term of VAR. Default is zero. Must be either a scalar, in which case it will be broadcasted to a k-vector, or a k-vector |
e_dist |
Either a function taking argument n indicating the number of variables in the system, or a matrix of dimensions k x (periods+burnin) |
init_y |
Initial values. Defaults to zero. Expects either a scalar or a vector of length (k*p) |
max_abs_eigval |
Maximum allowed eigenvalue of companion matrix. Only applicable if coefficient matrix is being simulated |
burnin |
Number of time points to be used for burnin |
sparsity_pattern |
The sparsity pattern that should be simulated.
Options are: |
sparsity_options |
Named list of additional options for
when sparsity pattern is lasso (L1) or hvar (HLag). For lasso (L1) the option |
decay |
How much smaller should parameters for later lags be. The smaller, the larger will early parameters be w.r.t. later ones. |
seed |
Seed to be used for the simulation |
... |
Additional arguments passed to |
Returns an object of S3 class bigtime.simVAR containing the following
Y |
Simulated Data |
periods |
Time series length |
k |
Number of endogenous variables |
p |
Maximum lag length; effective lag length might be shorter due to sparsity patterns |
coef_mat |
Companion form of the coefficient matrix. Will be of
dimensions ( |
is_coef_mat_simulated |
|
const |
Constant term |
e_dist |
Errors used in the construction of the data |
init_y |
Initial conditions |
max_abs_eigval |
Maximum eigenvalue to which the companion matrix was constraint |
burnin |
Burnin period used |
sparsity_pattern |
Sparsity pattern used |
sparsity_options |
Extra options for the sparsity patterns used |
seed |
Seed used for the simulation |
periods <- 200 # time series length k <- 5 # number of variables p <- 10 # maximum lag sparsity_pattern <- "HLag" # HLag sparsity structure sparsity_options <- list(zero_min = 0, # variables can be included with all lags zero_max = 10, # but some could also include no lags zeroes_in_self = TRUE) sim <- simVAR(periods=periods, k=k, p=p, sparsity_pattern=sparsity_pattern, sparsity_options=sparsity_options, seed = 12345) summary(sim)periods <- 200 # time series length k <- 5 # number of variables p <- 10 # maximum lag sparsity_pattern <- "HLag" # HLag sparsity structure sparsity_options <- list(zero_min = 0, # variables can be included with all lags zero_max = 10, # but some could also include no lags zeroes_in_self = TRUE) sim <- simVAR(periods=periods, k=k, p=p, sparsity_pattern=sparsity_pattern, sparsity_options=sparsity_options, seed = 12345) summary(sim)
Sparse Estimation of the Vector AutoRegressive (VAR) Model
sparseVAR( Y, p = NULL, VARpen = "HLag", VARlseq = NULL, VARgran = NULL, selection = c("none", "cv", "bic", "aic", "hq"), cvcut = 0.9, h = 1, eps = 0.001, check_std = TRUE, verbose = FALSE )sparseVAR( Y, p = NULL, VARpen = "HLag", VARlseq = NULL, VARgran = NULL, selection = c("none", "cv", "bic", "aic", "hq"), cvcut = 0.9, h = 1, eps = 0.001, check_std = TRUE, verbose = FALSE )
Y |
A |
p |
User-specified maximum autoregressive lag order of the VAR. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARpen |
"HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization. |
VARlseq |
User-specified grid of values for regularization parameter corresponding to sparse penalty. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARgran |
User-specified vector of granularity specifications for the penalty parameter grid: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
selection |
One of "none" (default), "cv" (Time Series Cross-Validation), "bic", "aic", "hq". Used to select the optimal penalization. |
cvcut |
Proportion of observations used for model estimation in the time series cross-validation procedure. The remainder is used for forecast evaluation. Redundant if selection is not "cv". |
h |
Desired forecast horizon in time-series cross-validation procedure. |
eps |
a small positive numeric value giving the tolerance for convergence in the proximal gradient algorithm. |
check_std |
Check whether data is standardised. Default is TRUE and is not recommended to be changed |
verbose |
Logical to print value of information criteria for each lambda together with selection. Default is FALSE |
A list with the following components
Y |
|
k |
Number of time series. |
p |
Maximum autoregressive lag order of the VAR. |
Phihat |
Matrix of estimated autoregressive coefficients of the VAR. |
phi0hat |
vector of VAR intercepts. |
series_names |
names of time series |
lambdas |
sparsity parameter grid |
MSFEcv |
MSFE cross-validation scores for each value of the sparsity parameter in the considered grid |
MSFEcv_all |
MSFE cross-validation full output |
lambda_opt |
Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure |
lambda_SEopt |
Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure and after applying the one-standard-error rule. This is the value used. |
h |
Forecast horizon h |
Nicholson William B., Wilms Ines, Bien Jacob and Matteson David S. (2020), “High-dimensional forecasting via interpretable vector autoregression”, Journal of Machine Learning Research, 21(166), 1-52.
data(var.example) VARfit <- sparseVAR(Y = scale(Y.var)) # sparse VAR ARfit <- sparseVAR(Y=scale(Y.var[,2])) # sparse ARdata(var.example) VARfit <- sparseVAR(Y = scale(Y.var)) # sparse VAR ARfit <- sparseVAR(Y=scale(Y.var[,2])) # sparse AR
Sparse Estimation of the Vector AutoRegressive Moving Average (VARMA) Model
sparseVARMA( Y, U = NULL, VARp = NULL, VARpen = "HLag", VARlseq = NULL, VARgran = NULL, VARselection = c("cv", "bic", "aic", "hq"), VARMAp = NULL, VARMAq = NULL, VARMApen = "HLag", VARMAlPhiseq = NULL, VARMAPhigran = NULL, VARMAlThetaseq = NULL, VARMAThetagran = NULL, VARMAalpha = 0, VARMAselection = c("none", "cv", "bic", "aic", "hq"), h = 1, cvcut = 0.9, eps = 10^-3, check_std = TRUE )sparseVARMA( Y, U = NULL, VARp = NULL, VARpen = "HLag", VARlseq = NULL, VARgran = NULL, VARselection = c("cv", "bic", "aic", "hq"), VARMAp = NULL, VARMAq = NULL, VARMApen = "HLag", VARMAlPhiseq = NULL, VARMAPhigran = NULL, VARMAlThetaseq = NULL, VARMAThetagran = NULL, VARMAalpha = 0, VARMAselection = c("none", "cv", "bic", "aic", "hq"), h = 1, cvcut = 0.9, eps = 10^-3, check_std = TRUE )
Y |
A |
U |
A |
VARp |
User-specified maximum autoregressive lag order of the PhaseI VAR. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARpen |
"HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization in PhaseI VAR. |
VARlseq |
User-specified grid of values for regularization parameter in the PhaseI VAR. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARgran |
User-specified vector of granularity specifications for the penalty parameter grid of the PhaseI VAR: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARselection |
Selection procedure for the first stage. Default is time series Cross-Validation. Alternatives are BIC, AIC, HQ |
VARMAp |
User-specified maximum autoregressive lag order of the VARMA. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARMAq |
User-specified maximum moving average lag order of the VARMA. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARMApen |
"HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization in the VARMA. |
VARMAlPhiseq |
User-specified grid of values for regularization parameter corresponding to the autoregressive coefficients in the VARMA. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARMAPhigran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the autoregressive coefficients in the VARMA: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARMAlThetaseq |
User-specified grid of values for regularization parameter corresponding to the moving average coefficients in the VARMA. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARMAThetagran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the moving average coefficients in the VARMA: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARMAalpha |
a small positive regularization parameter value corresponding to squared Frobenius penalty in VARMA. The default is zero. |
VARMAselection |
selection procedure in the second stage. Default is "none"; Alternatives are cv, bic, aic, hq |
h |
Desired forecast horizon in time-series cross-validation procedure. |
cvcut |
Proportion of observations used for model estimation in the time series cross-validation procedure. The remainder is used for forecast evaluation. |
eps |
a small positive numeric value giving the tolerance for convergence in the proximal gradient algorithms. |
check_std |
Check whether data is standardised. Default is TRUE and is not recommended to be changed |
A list with the following components
Y |
|
U |
Matrix of (approximated) error terms. |
k |
Number of time series. |
VARp |
Maximum autoregressive lag order of the PhaseI VAR. |
VARPhihat |
Matrix of estimated autoregressive coefficients of the Phase I VAR. |
VARphi0hat |
Vector of Phase I VAR intercepts. |
VARMAp |
Maximum autoregressive lag order of the VARMA. |
VARMAq |
Maximum moving average lag order of the VARMA. |
Phihat |
Matrix of estimated autoregressive coefficients of the VARMA. |
Thetahat |
Matrix of estimated moving average coefficients of the VARMA. |
phi0hat |
Vector of VARMA intercepts. |
series_names |
names of time series |
PhaseI_lambas |
Phase I sparsity parameter grid |
PhaseI_MSFEcv |
MSFE cross-validation scores for each value of the sparsity parameter in the considered grid |
PhaseI_lambda_opt |
Phase I Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure |
PhaseI_lambda_SEopt |
Phase I Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
PhaseII_lambdaPhi |
Phase II sparsity parameter grid corresponding to Phi parameters |
PhaseII_lambdaTheta |
Phase II sparsity parameter grid corresponding to Theta parameters |
PhaseII_lambdaPhi_opt |
Phase II Optimal value of the sparsity parameter (corresponding to Phi parameters) as selected by the time-series cross-validation procedure |
PhaseII_lambdaPhi_SEopt |
Phase II Optimal value of the sparsity parameter (corresponding to Theta parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
PhaseII_lambdaTheta_opt |
Phase II Optimal value of the sparsity parameter (corresponding to Phi parameters) as selected by the time-series cross-validation procedure |
PhaseII_lambdaTheta_SEopt |
Phase II Optimal value of the sparsity parameter (corresponding to Theta parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
PhaseII_MSFEcv |
Phase II MSFE cross-validation scores for each value in the two-dimensional sparsity grid |
h |
Forecast horizon h |
Wilms Ines, Sumanta Basu, Bien Jacob and Matteson David S. (2021), “Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages”, Journal of the American Statistical Association, doi: 10.1080/01621459.2021.1942013.
data(varma.example) VARMAfit <- sparseVARMA(Y = scale(Y.varma)) # sparse VARMA y <- matrix(Y.varma[,1], ncol=1) ARMAfit <- sparseVARMA(Y=scale(y)) # sparse ARMAdata(varma.example) VARMAfit <- sparseVARMA(Y = scale(Y.varma)) # sparse VARMA y <- matrix(Y.varma[,1], ncol=1) ARMAfit <- sparseVARMA(Y=scale(y)) # sparse ARMA
Sparse Estimation of the Vector AutoRegressive with Exogenous Variables X (VARX) Model
sparseVARX( Y, X, p = NULL, s = NULL, VARXpen = "HLag", VARXlPhiseq = NULL, VARXPhigran = NULL, VARXlBseq = NULL, VARXBgran = NULL, VARXalpha = 0, h = 1, cvcut = 0.9, eps = 10^-3, selection = c("none", "cv", "bic", "aic", "hq"), check_std = TRUE, verbose = FALSE )sparseVARX( Y, X, p = NULL, s = NULL, VARXpen = "HLag", VARXlPhiseq = NULL, VARXPhigran = NULL, VARXlBseq = NULL, VARXBgran = NULL, VARXalpha = 0, h = 1, cvcut = 0.9, eps = 10^-3, selection = c("none", "cv", "bic", "aic", "hq"), check_std = TRUE, verbose = FALSE )
Y |
A |
X |
A |
p |
User-specified maximum endogenous autoregressive lag order. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
s |
User-specified maximum exogenous autoregressive lag order. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARXpen |
"HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization in VARX. |
VARXlPhiseq |
User-specified grid of values for regularization parameter corresponding to the endogenous autoregressive coefficients in the VARX. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARXPhigran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the endogenous autoregressive coefficients in the VARX: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARXlBseq |
User-specified grid of values for regularization parameter corresponding to the exogenous autoregressive coefficients in the VARX. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARXBgran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the exogenous autoregressive coefficients in the VARX: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARXalpha |
a small positive regularization parameter value corresponding to squared Frobenius penalty. The default is zero. |
h |
Desired forecast horizon in time-series cross-validation procedure. |
cvcut |
Proportion of observations used for model estimation in the time series cross-validation procedure. The remainder is used for forecast evaluation. |
eps |
a small positive numeric value giving the tolerance for convergence in the proximal gradient algorithm. |
selection |
Model selection method to be used. Default is none, which will return all values for all penalisations. |
check_std |
Check whether data is standardised. Default is TRUE and is not recommended to be changed |
verbose |
Logical to print value of information criteria for each lambda together with selection. Default is FALSE |
A list with the following components
Y |
|
X |
|
k |
Number of endogenous time series. |
m |
Number of exogenous time series. |
p |
Maximum endogenous autoregressive lag order of the VARX. |
s |
Maximum exogenouss autoregressive lag order of the VARX. |
Phihat |
Matrix of estimated endogenous autoregressive coefficients. |
Bhat |
Matrix of estimated exogenous autoregressive coefficients. |
phi0hat |
vector of VARX intercepts. |
exogenous_series_names |
names of the exogenous time series |
endogenous_series_names |
names of the endogenous time series |
lambdaPhi |
sparsity parameter grid corresponding to endogenous autoregressive parameters |
lambdaB |
sparsity parameter grid corresponding to exogenous autoregressive parameters |
lambdaPhi_opt |
Optimal value of the sparsity parameter (corresponding to the endogenous autoregressive parameters) as selected by the time-series cross-validation procedure |
lambdaPhi_SEopt |
Optimal value of the sparsity parameter (corresponding to the endogenous autoregressive parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
lambdaB_opt |
Optimal value of the sparsity parameter (corresponding to the exogenous autoregressive parameters) as selected by the time-series cross-validation procedure |
lambdaB_SEopt |
Optimal value of the sparsity parameter (corresponding to the exogenous autoregressive parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
MSFEcv |
MSFE cross-validation scores for each value in the two-dimensional sparsity grid |
h |
Forecast horizon h |
Wilms Ines, Sumanta Basu, Bien Jacob and Matteson David S. (2017), “Interpretable vector autoregressions with exogenous time series”, NIPS 2017 Symposium on Interpretable Machine Learning, arXiv:1711.03623.
data(varx.example) VARXfit <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx)) # sparse VARX y <- matrix(Y.varx[,1], ncol=1) ARXfit <- sparseVARX(Y=y, X=X.varx) # sparse ARXdata(varx.example) VARXfit <- sparseVARX(Y=scale(Y.varx), X=scale(X.varx)) # sparse VARX y <- matrix(Y.varx[,1], ncol=1) ARXfit <- sparseVARX(Y=y, X=X.varx) # sparse ARX
Gives a small summary of a VAR simulation
## S3 method for class 'bigtime.simVAR' summary(object, plot = TRUE, ...)## S3 method for class 'bigtime.simVAR' summary(object, plot = TRUE, ...)
object |
Simulated data of class |
plot |
Should the VAR be plotted. Default is |
... |
Not currently used |
If 'plot=TRUE', then a ggplot2 plot will be returned
varx.example)The data consists of a 200x3 matrix of endogenous variables, Y.varx,
and a 200x3 matrix of exogenous variables, X.varx.
X.varxX.varx
Two matrices, X.varx and Y.varx, both of dimension 200x3
var.example)The data consists of a 200x5 data matrix, Y.var, and was simulated from a sparse
VAR model with HLag sparsity pattern.
Y.varY.var
A matrix of dimension 200x5
varma.example)The data consists of a 200x3 data matrix, Y.varma, and was simulated from a
sparse VARMA model.
Y.varmaY.varma
A matrix of dimension 200x3
varx.example)The data consists of a 200x3 matrix of endogenous variables, Y.varx,
and a 200x3 matrix of exogenous variables, X.varx.
Y.varxY.varx
Two matrices, X.varx and Y.varx, both of dimension 200x3